Dynamic Quality Index for agricultural soils based on ...

Ecological Indicators 60 (2016) 678–692

Contents lists available at ScienceDirect

Ecological Indicators journal homepage: www.elsevier.com/locate/ecolind

Dynamic Quality Index for agricultural soils based on fuzzy logic ˜ Esther Rodríguez a,∗ , Roberto Peche a , Carlos Garbisu b , Inaki Gorostiza c , Lur Epelde b , d e e a Unai Artetxe , Amaia Irizar , Manuel Soto , José M Becerril d , Javier Etxebarria c a Department of Chemical and Environmental Engineering, University College of Engineering of Vitoria-Gasteiz, University of the Basque Country UPV/EHU, Nieves Cano 12, 01006 Vitoria-Gasteiz, Spain b NEIKER-Tecnalia, Dept. Ecology and Natural Resources, Soil Microbial Ecology Group, Parcel 812, Berreaga 1, E-48160 Derio, Bizkaia, Spain c GAIKER-IK4 Technology Centre, Ed. 202, 48.170 Zamudio, Bizkaia, Spain d Department of Plant Biology and Ecology, Faculty of Science and Technology, University of the Basque Country UPV/EHU, Barrio Sarriena s/n, 489400 Leioa, Bizkaia, Spain e Department of Zoology and Animal Cell Biology, CBET Research Group, Faculty of Science and Technology, University of the Basque Country UPV/EHU, Barrio Sarriena s/n, 489400 Leioa, Bizkaia, Spain

a r t i c l e

i n f o

Article history: Received 29 March 2015 Received in revised form 3 August 2015 Accepted 7 August 2015 Available online 27 August 2015 Keywords: Soil quality Fuzzy Index Agriculture Fuzzy logic

a b s t r a c t The increasing number of successful applications of fuzzy logic and fuzzy sets theory to dealing with the uncertainty, imprecision and subjectivity inherent to environmental quality assessments, and the recent development of new procedures based on fuzzy logic for the design of environmental quality indexes open new ways to carry out more rigorous and realistic estimations of soil quality. With these considerations in mind, the aim of this work is to design an index based on fuzzy logic, which is especially addressed to assess the dynamic quality of agricultural soils – Soil Dynamic Quality Index (S-DQI). This index is described by a group of three indexes (S-DQIPHYS , S-DQICHEM , S-DQIBIOL ), each one designed to evaluate the dynamic quality of agricultural soils with regard to their physical, chemical and biological characteristics, respectively. Each index is determined from the joint opinion of a panel of experts, which decides: (i) the attributes or properties of soil which determine its dynamic quality for farming; (ii) the most suitable indicator for quantifying each of them; (iii) the influence of the values taken by these indicators on the quality of agricultural soils, which is expressed by means of membership functions, and (iv) the relative importance of the attributes in the respective index, which is expressed by means of normalized priority vectors. The value of each of these indexes is finally obtained as a result of a fuzzy inference procedure, which is a crisp value ranging from 0 to 1. This procedure allows us to express the values taken by the indicators in a particular agroecosystem by means of both crisp values and fuzzy numbers, the latter being frequently a more rigorous and realistic way of representing the estimations of the soil properties in any emplacement. Verification tests show the satisfactory response capability of the index to changes in the soil properties. The use of the designed S-DQI for routine monitoring of the quality of farming soil allows the estimation of the changes induced in the soil due to use, which is helpful to assess systematically the sustainability of the agricultural practices. © 2015 Elsevier Ltd. All rights reserved.

1. Introduction Fuzzy logic and fuzzy sets theory are being increasingly used in the environmental field, since they are the appropriate

∗ Corresponding author. Tel.: +34 945013236; fax: +34 945013270. E-mail addresses: [email protected] (E. Rodríguez), [email protected] (R. Peche), [email protected] (C. Garbisu), [email protected] (I. Gorostiza), [email protected] (L. Epelde), [email protected] (U. Artetxe), [email protected] (A. Irizar), [email protected] (M. Soto), [email protected] (J.M. Becerril), [email protected] (J. Etxebarria). http://dx.doi.org/10.1016/j.ecolind.2015.08.016 1470-160X/© 2015 Elsevier Ltd. All rights reserved.

mathematical tools to deal with the uncertainty and imprecision (Klir and Yuan, 1995) which are frequently inherent to the nature of many data handled in environmental studies (Chowdhury, 2012; Darbra et al., 2008; Dong et al., 2014). Thus, fuzzy approaches – procedures based on fuzzy logic – have been successfully used in the assessment of health and environmental risks associated with the management of both water (Cabanillas et al., 2012; Deng et al., 2012) and solid waste (Srivastava and Nema, 2011), as well as in the management of air quality (Ping et al., 2010; Zhang and Huang, 2011). Several fuzzy models have also been applied to the assessment of sustainability (Liu et al., 2012; Pislaru et al., 2008) and to environmental impact assessments (Biswas et al., 2011;

E. Rodríguez et al. / Ecological Indicators 60 (2016) 678–692

Duarte et al., 2007), for which new methodologies based on fuzzy logic have been developed in recent years (Peche and Rodríguez, 2009, 2011). Fuzzy logic is also especially useful in the assessment of air quality (Assimakopoulos et al., 2013; Carbajal-Hernandez et al., 2012) and water quality (Gharibi et al., 2012; Rahimi and Mokarram, 2012), although its application to soil quality assessment is still rather scarce (Torbert et al., 2008; Xue et al., 2010, 2011). Fuzzy logic has also been successfully used in combination with genetic algorithms (GA) and Geographical Information Systems (GIS) to carry out environmental assessments, such as aquatic habitat suitability (Fukuda et al., 2011) and diverse soil characteristics (Giordano and Liersch, 2012; Liu et al., 2013). The most common assessment of environmental quality is carried out by means of quality indexes (QI). The use of quality indexes is a widespread practice, in particular, in the assessment of soil quality (Andrews et al., 2002; Rahmanipour et al., 2014). This is conditioned, among other factors, by the functionality of the soil under assessment and by its geophysical and morphological characteristics. However, soil heterogeneity, seasonal variation of some of its physicochemical and biological characteristics and, ultimately, the inherent complexity of soil make it difficult to rigorously assess its quality or suitability for a particular function by means of a universal conventional index, which can be systematically used for that purpose (Qui et al., 2009). For these reasons, it is necessary to design specific indexes to assess soil quality in terms of the soil functionality, which can also be adapted – if necessary – to the characteristics of the region in which it is located (Andrews et al., 2004; Imaz et al., 2010). In general, the design procedures of soil quality indexes (SQI) are based on: (i) identifying the minimum set of indicators of the physicochemical and biological properties which determine the soil quality for a given function, (ii) estimating subsequently the relative importance of these properties as a measure of its contribution to the soil quality under consideration, and (iii) grouping all the indicators into a single index of soil quality, for which their relative importance is taken into consideration (Askari and Holden, 2014; Rodrigues de Lima et al., 2008). The most recently applied methodologies for the assessment of soil quality by means of an index consist of the selection of a Minimum Data Set (MDS) of sensitive physical, chemical and biological indicators by Principal Component Analysis (PCA), the subsequent application of diverse weighting methods to measure the importance of these indicators, and the ultimate development of a quality index by means of linear or non-linear score functions (Chen et al., 2013; Rahmanipour et al., 2014; Swanepoel et al., 2014; Tesfahunegn, 2014). However, the imprecision and inaccuracy inherent to many parameters and variables included in the quality indexes, and the subjectivity of the estimation of the contribution of these parameters to the SQI suggest that the use of fuzzy approaches should enable more rigorous and realistic estimations of soil quality to be carried out (Arunraj and Maiti, 2009; Gentile et al., 2003; Khan et al., 2002, 2004; Li et al., 2008). Moreover, the recent development of new procedures based on fuzzy logic for the design of environmental quality indexes opens new ways for assessing the soil quality (Peche and Rodríguez, 2012). In line with these considerations, the aim of this work is to design an index based on fuzzy logic, which is addressed to assess the dynamic quality of agricultural soils – Soil Dynamic Quality Index (S-DQI). The use of this S-DQI for routine monitoring of the dynamic quality of soil in agricultural farms allows the changes induced in the soil due to its use to be estimated, which is helpful to assess the sustainability of the agricultural practices, and therefore to prevent soil degradation. The dynamic quality of agricultural soils is determined by the values which are taken by certain physical, chemical and biological properties, which efficiently and effectively monitor critical soil functions for farming (Karlen et al., 2003). For

679

this reason, this S-DQI is described by a group of three indexes (S-DQIPHYS , S-DQICHEM , S-DQIBIOL ), each one designed to evaluate the dynamic quality of the agricultural soil with respect to their physical, chemical and biological characteristics, respectively. In order to check the response capability of the S-DQI as a diagnostic tool for the measurement of the dynamic quality of agricultural soils, it is used to verify the dynamic quality of some soils which had been previously categorized by the panel according to their physicochemical and biological characteristics. 2. Design of the Dynamic Quality Index for agricultural soils Each index of the group (S-DQIPHYS , S-DQICHEM , S-DQIBIOL ) is designed from the opinion of a panel of experts by means of a previously developed versatile and rigorous methodology based on fuzzy logic, which enables the design of specific indexes for the assessment of the quality in any environmental compartment (Peche and Rodríguez, 2012). The design procedure requires: (a) the selection of the physical (ai-PHYS ), chemical (ai-CHEM ) and biological (ai-BIOL ) attributes or properties of the soil which determine its dynamic quality for farming, and the indicator for quantifying each of them – (Ii-PHYS ), (Ii-CHEM ) and (Ii-BIOL ), respectively; (b) the estimation of the beneficial contributions of the attributes to the corresponding index by means of fuzzy sets, which are described by its membership functions  ¯ B¯ (Si-PHYS ),  ¯ B¯ (Si-CHEM ) and  ¯ B¯ (Si-BIOL ); and (c) i i i the estimation of the relative importance of the attributes in their respective index by means of the Analytical Hierarchical method (AHM) (Saaty, 2008), which is expressed by the normalized priority vectors W PHYS , W CHEM and W BIOL . Finally, the value of each of these indexes is obtained as a result of a fuzzy inference procedure (Takagi and Sugeno, 1985), which is a crisp value ranging from 0 to 1. The different stages of the design procedure of the indexes S-DQIPHYS , S-DQICHEM , S-DQIBIOL are described in detail below. A diagram is included at the end of this section in order to provide a comprehensive overview of the index design procedure. 2.1. The panel The design of the index was carried out by a panel, which was coordinated by two experts in the management of environmental information, as well as in the use of fuzzy logic, fuzzy sets theory and the mathematical treatments required for the design of the index. The research groups of different university departments and technology centers of the Basque Country were contacted in order to organize the panel, whose area of expertise was in the study and management of soil. They were informed about the characteristics of the S-DQI, the design methodology and the tasks and estimations they would be asked to do in the procedure. In order to consider the different aspects related to the quality of agricultural soils, it was agreed to include eight panelists, among them, eco-microbiologists, eco-biologists, vegetal biologists, chemists, environmentalists and environmental technologists. Each group decided which of their members would take part as panelists, in accordance to their expertise and to the required composition of the panel. The general working method of the panel at the different stages of the procedure was as follows: (a) A meeting was held during which the panel was informed by the coordinators about the work to be done at each stage. The coordinators provided them with the necessary material – questionnaires, matrixes, graphs, . . . –, which was specifically designed to get the required information, estimations and/or assessments, and gave them the instructions to use it. (b) Each panelist did his or her work according to his or her criteria, in collaboration with their respective research groups – if necessary –, and sent it to the coordinators. (c) The coordinators organized and analyzed the information and/or the estimations sent by the

LSRD LSF LS LSWHC LSpH LSEC LSCEC LSESP LSOM LSTKN LSP-OLSEN LSKex LSSMB-C LSN-NH4+ LSBSR-CO2 LSAWCD-BIOLOG LSH  -BIOLOG SRD SF S SWHC SpH SEC SCEC SESP SOM STKN SP-OLSEN SKex SSMB-C SN-NH4+ SBSR-CO2 SAWCD-BIOLOG SH  -BIOLOG S1-PHYS S2-PHYS S3-PHYS S4-PHYS S1-CHEM S2-CHEM S3-CHEM S4-CHEM S5-CHEM S6-CHEM S7-CHEM S8-CHEM S1-BIOL S2-BIOL S3-BIOL S4-BIOL S5-BIOL [0, 150] [0.1, 2.0] [1.3, 1.7] [70, 250] [3.5, 8.5] [0.1, 4.0] [3.0, 200.0] [2.0, 15.0] [0.5, 15.0] [200.0, 2400.0] [2.0, 600.0] [60.0, 3000.0] [50.0, 3000.0] [20.0, 170.0] [0.0, 30.0] [0.0, 1.5] [2.0, 4.0] cm cm h−1 g cm−3 mm m−1 pH units dS m−1 meq H/100g % % ppm ppm ppm mg C kg−1 h−1 mg NH4+ kg−1 h−1 mg CO2 kg−1 h−1 Ab. (595 nm) H -BIOLOG units I1-PHYS I2-PHYS I3-PHYS I4-PHYS I1-CHEM I2-CHEM I3-CHEM I4-CHEM I5-CHEM I6-CHEM I7-CHEM I8-CHEM I1-BIOL I2-BIOL I3-BIOL I4-BIOL I5-BIOL Root growth capacity Water infiltration capacity Soil porosity Water availability Acidity/basicity Salinity Exchange cation retention Sodicity Organic matter Nitrogen content Phosphorous content Potassium content Microbial biomass-C Microbial activity-N Microbial activity-CO2 Microbial activity Microbial biodiversity a1-PHYS a2-PHYS a3-PHYS a4-PHYS a1-CHEM a2-CHEM a3-CHEM a4-CHEM a5-CHEM a6-CHEM a7-CHEM a8-CHEM a1-BIOL a2-BIOL a3-BIOL a4-BIOL a5-BIOL

Rooting depth (RD) Infiltration rate (F) Bulk density () Water holding capacity (WHC) pH Electrical conductivity (EC) Cation exchange capacity (CEC) Exchangeable sodium percentage (ESP) Organic matter (OM) Total Kjeldahl nitrogen (TKN) Phosphorous OLSEN (POLSEN ) Exchangeable K extraction NH4 Ac (KEX ) Soil microbial biomass C (SMB-C) Potentially mineralizable N (N-NH4 + ) Basal soil respiration (BSR-CO2 ) Average well-color develop. (AWCD-BIOLOG) Shannon Biodiversity Index (H -BIOLOG)

Denom.

Normalized indicator

Si Range [minIi , maxIi ] Unit Ii

Denomination

Conventional indicator

Denomination

The panel agreed upon the set of attributes which provides the necessary and sufficient information about the biological and physicochemical properties of soil, which efficiently and effectively monitor critical soil functions for farming. Then, they selected the most suitable conventional indicator to quantify each of them. Table 1 shows the attributes selected by the panel and their corresponding indicators, together with their respective denominations, symbols and units. The selected physical attributes were those which affect plant growth, soil aeration and hydratation, and the movement of water and nutrients through the soil. Among them was the thickness of the soil layer accessible by plants (RD), the capacity of soil to allow water movement into and through the soil profile (F), the ability of soil to ease the aeration and the movement of water and nutrients () and the capacity of soil to hold water (WHC). The selected chemical attributes were those which affect the properties and processes of soil, the availability of nutrients, the activity of microorganisms and soil fertility. Among them were the acidity/basicity (pH), the amount of soluble salts in soil (EC), the capacity of soil to store exchangeable cations (CEC) and the sodicity (ESP), together with the content of organic matter (OM), the available N (TKN) and P (POLSEN ) and the readily available forms of potassium (HH4 Ac (KEX) ). The biological attributes selected by the panel were those which affect the soil microbial activity and biodiversity and so, the soil fertility. Among them, the microbial biomass carbon (SMB-C) and the potentially mineralizable nitrogen (N-NH4 ), which influence – respectively – the decomposition and transformation of the organic matter and the fraction of nitrogen easily decomposable by soil microorganisms. The basal soil respiration (BSR-CO2 ), which reflects the soil microbial activity, and two complementary parameters to assess the functional diversity of soil microorganisms – the average well color development (AWCD-BIOLOG) as a measure of the catabolic potential, and the Shannon biodiversity index (H BIOLOG) in order to inform about the abundance and diversity of microorganisms. Subsequently, the panel agreed upon the range of values [minIi-PHYS , maxIi-PHYS ], [minIi-CHEM , maxIi-CHEM ] and [minIi-BIOL , maxIi-BIOL ] for each Ii by setting minIi and maxIi as the limit values of the indicator which can be most commonly expected on a site of potential agricultural use. It must be pointed out that these ranges may differ depending on the features of the agricultural soils in different regions – and/or, if necessary, the characteristics expected for a specific kind of crop. Table 1 shows the corresponding ranges for each indicator, which can be generally expected in agricultural soil in the Basque Country (Spain). Finally, all the indicators were normalized in order to quantify the corresponding attributes by means of non dimensional indicators, the universe of discourse of which is Ui = [0, 100]. The normalized indicators Si-PHYS , Si-CHEM and

ai

2.2. Selection of the attributes ai-PHYS , ai-CHEM and ai-BIOL and their corresponding indicators Ii-PHYS , Ii-CHEM and Ii-BIOL

Attribute

panelists and, when necessary, they carried out the corresponding mathematical treatments in order to obtain a joint estimation of the panel about the information and/or assessment required during the stage. Next, they elaborated a report of the results and sent it to the panelists for them to analyze and reconsider their estimations, if necessary. This process was repeated until a satisfactory convergence and/or consistency in the estimations sent by all the panelists was reached. (d) Finally, the individual and joint results were discussed in a panel working session in order to analyze the results from different points of view and/or to agree a joint opinion, which could be accepted for all of them. The contributions of the panel at each stage of the procedure will be specified in the corresponding sections, all of them having been obtained by using this working method.

Linguistic variable LSi

E. Rodríguez et al. / Ecological Indicators 60 (2016) 678–692 Table 1 Physical (ai-PHYS ), chemical (ai-CHEM ) and biological (ai-BIOL ) attributes selected by the panel to be included in the indexes S-DQIPHYS , S-DQICHEM and S-DQIBIOL , respectively, and their corresponding indicators Ii-PHYS , Ii-CHEM and Ii-BIOL and ranges [Imin , Imax ] Symbols of the respective normalized indicators Si-PHYS , Si-CHEM and Si-BIOL and their corresponding linguistic variables LSi-PHYS , LSi-CHEM and LSi-BIOL .

680

E. Rodríguez et al. / Ecological Indicators 60 (2016) 678–692

Si-BIOL are calculated from their respective indicators Ii-PHYS , Ii-CHEM and Ii-BIOL by means of the following general expression: Si =

Ii − min Ii 100 max Ii − min Ii

681

μ B ( S RD ) 1 0.8

(1)

Table 1 shows the symbols of all the Si and the symbols of the linguistic variables LSi assigned to each of them, the values of which are fuzzy sets defined on the same universe of discourse than Si .

0.6 0.4 0.2 0 0

2.3. Estimation of the beneficial contribution of the attributes ai-PHYS , ai-CHEM and ai-BIOL to their respective indexes S-DQIPHYS , S-DQICHEM , S-DQIBIOL by means of fuzzy sets B¯ i Once the attributes and indicators were selected, their corresponding normalized indicators were defined and the linguistic variables were assigned to each of them, the panel estimated the beneficial contribution to the dynamic quality of agricultural soil of each of the attributes. For this, a fuzzy set B¯i was assigned to each LSi , which is described by means of its membership function B¯ (Si ), on condition that there is always at least one value of the indicator Si for which its membership function equals 1. The members of the panel drew the profile of the functions B¯ (Si ) vs Si ∀i, which represents – in their opinion – the extent to which each value of Si contributes favorably to the dynamic quality of a farming soil. Subsequently, these profiles were modeled and an average membership function  ¯ B¯ (Si ) was calculated ∀i. Then, all the panelists were asked to reconsider – if necessary – their initial estimations in view of all the  ¯ B¯ (Si ) and the graphs proposed by the remaining members of the panel. Finally, after discussion, they agreed upon the definitive profile of all these graphs, which were mathematically modeled in order to obtain the final  ¯ B¯ (Si ) ∀i. Figs. 1, 2 and 3 show the graphical representations of the final membership functions  ¯ B¯ (Si−PHYS ),  ¯ B¯ (Si−CHEM ) and  ¯ B¯ (Si−BIOL ) agreed by the panel. As can be observed, all the membership functions could be modeled by means of straight line segments. The beneficial contribution  ¯ B¯ (Si ) of some physical, chemical and biological attributes increases from 0 to 1 as the values of their respective normalized indicators Si cover their universe of discourse from 0 to 100. This is the case of the water availability, the nitrogen content, the microbial biomass-C, the microbial activity, the microbial activity-N and the microbial biodiversity. The  ¯ B¯ of the root growth capacity and the phosphorous content only exhibit similar behavior for a particular interval of values of the universe of discourse of their respective normalized indicators. Other attributes have the opposite behavior. Thus, the beneficial contribution of the soil porosity decreases from 1 to 0 as its normalized indicator increases from 0 to 100. Similar behavior shows the  ¯ B¯ of the sodicity for a particular interval of values of the universe of discourse of its corresponding normalized ¯ B¯ of the remaining physical, chemical and biologiindicator. The  cal attributes increases up to 1, then it generally remains constant through a particular interval of values, and finally, it decreases, as the values of their respective Si cover their universe of discourse from 0 to 100. This is the case of the water infiltration capacity, the acidity/basicity, the salinity, the exchange cation retention, the organic matter, the potassium content, and the microbial activity-CO2 . Once  ¯ B¯ (Si-PHYS ),  ¯ B¯ (Si-CHEM ) and  ¯ B¯ (Si-BIOL ) were obtained, the membership functions  ¯ D¯ (Si-PHYS ),  ¯ D¯ (Si-CHEM ) and  ¯ D¯ (Si-BIOL ) were calculated, in order to represent the detrimental contribution of the attributes to their respective Dynamic Quality Index. For this, a fuzzy set D¯ i was assigned to each LSi , which is the fuzzy complement ¯ B¯ (Si ) of B¯i . Consequently, once the final membership functions 

20

40

60

80

20

40

60

80

SF

100

20

40

60

80

Sρ

100

20

40

60

80

S RD

100

μ B ( SF ) 1 0.8 0.6 0.4 0.2 0 0

μ B ( Sρ ) 1 0.8 0.6 0.4 0.2 0 0

μ B ( SWHC ) 1 0.8 0.6 0.4 0.2 0 0

SWHC 100

Fig. 1. Graphical representation of the membership functions  ¯ B¯ (Si-PHYS ) which depict the joint estimation of the panel concerning the beneficial contribution of the different values of Si-PHYS to the index S-DQIPHYS .

were determined,  ¯ D¯ (Si ) could be easily calculated by means of the following general expression:  ¯ D¯ (Si ) = 1 −  ¯ B¯ (Si )

(2)

All these membership functions  ¯ B¯ (Si ) and  ¯ D¯ (Si ) will be later used for calculating the values of the indexes in the fuzzy inference procedures.

682

E. Rodríguez et al. / Ecological Indicators 60 (2016) 678–692

Fig. 2. Graphical representation of the membership functions  ¯ B¯ (Si-CHEM ) which depict the joint estimation of the panel concerning the beneficial contribution of the different values of Si-CHEM to the index S-DQICHEM .

2.4. Estimation of the relative importance of the attributes ai-PHYS , ai-CHEM and ai-BIOL in their corresponding indexes S-DQIPHYS , S-DQICHEM and S-DQIBIOL The estimation of the relative importance of the attributes in their corresponding indexes is expressed by means of the priority vectors WPHYS , WCHEM and WBIOL , which are calculated from

the corresponding pair-wise comparison matrixes X¯ PHYS , X¯ CHEM and X¯ BIOL . These matrixes are obtained from the estimations of the relative importance of the attributes made by the panel, which are expressed by the superior triangular matrices TPHYS = [tij-PHYS ], TCHEM = [tij-CHEM ] and TBIOL = [tij-BIOL ], respectively. Next, the procedure to achieve the matrixes T¯ from the panel is shown, and the subsequent calculation of matrixes X¯ and vectors W.

E. Rodríguez et al. / Ecological Indicators 60 (2016) 678–692

683

TCHEM and TBIOL of all the panelists. Table 2 shows the joint superior triangular matrixes, together with the dispersion matrix corre¯ PHYS , D ¯ CHEM and D ¯ BIOL show sponding to each of them. The matrixes D that the dispersion of the elements of the matrixes TPHYS , TCHEM and TBIOL is inferior to 10%, which evidences that the convergence of the final triangular matrixes TPHYS , TCHEM and TBIOL proposed by the panelists can be considered satisfactory. Next, the reciprocal matrixes or pair-wise comparison matrixes XPHYS = [xij-PHYS ], XCHEM = [xij-CHEM ] and XBIOL = [xij-BIOL ] were calculated, respectively, from the final matrixes TPHYS = [tij-PHYS ], TCHEM = [tij-CHEM ] and TBIOL = [tij-BIOL ], so that the following general conditions were fulfilled: xij = tij

∀j > i = 1, 2, . . ., n

xij = (tji )−1

(3)

∀j < i = 1, 2, . . ., n

(4)

xij = 1 ∀i = j = 1, 2, . . ., n

(5)





Finally, the joint pair-wise comparison matrixes X¯ PHYS = x¯ij -PHYS ,     X¯ CHEM = x¯ij -CHEM and X¯ BIOL = x¯ij -BIOL were determined, the elements x¯ij of which were calculated by the geometric mean of the corresponding elements xij of matrixes X. Table 3 shows the obtained X¯ PHYS , X¯ CHEM and X¯ BIOL , which would subsequently be used to determine the corresponding priority vectors.

Fig. 3. Graphical representation of the membership functions  ¯ B¯ (Si-BIOL ) which depict the joint estimation of the panel concerning the beneficial contribution of the different values of Si-BIOL to the index S-DQIBIOL .

2.4.1. Estimation of the pair-wise comparison matrixes X¯ PHYS , X¯ CHEM and X¯ BIOL The panelists were asked to define a superior triangular matrix T = [tij ] for each set of physical, chemical and biological attributes, so that each element tij represents the relative importance of the attribute ai with respect to aj in the corresponding index. The criteria used to assign the relative importance between two attributes in a particular index were the following ones (Saaty and Hu, 1998): (i) 0.1 if ai is “much less important” than aj , (ii) 1 if ai is “equally important” than aj , and (iii) 10 if ai is “much more important” than aj . According to these criteria, the panelists assigned intermediate values of the range [0.1, 1] to graduate the relative importance from “much less important” to “equally important”, and intermediate values of the range [1, 10] to graduate the relative importance from “equally important” to “much more important”. According to this, each panelist built three superior triangular matrixes TPHYS = [tij-PHYS ], TCHEM = [tij-CHEM ] and TBIOL = [tij-BIOL ]. Subsequently, from these matrixes, the corresponding joint superior triangular matrixes were calculated, these being T¯ PHYS = t¯ij −PHYS , T¯ CHEM =     t¯ij and T¯ BIOL = t¯ij . The elements t¯ij , t¯ij and -CHEM

-BIOL

-PHYS

−CHEM

t¯ij −BIOL of these matrixes were respectively obtained by the arithmetic mean of the corresponding elements tij-PHYS , tij-CHEM and tij-BIOL of the matrixes TPHYS , TCHEM , and TBIOL provided by the pan  ¯ PHYS = d¯ij ¯ CHEM = , D elists. Next, the dispersion matrixes D









-PHYS

¯ BIOL = d¯ij d¯ij -CHEM and D were calculated of which, the ele-BIOL ¯ ¯ ¯ ments dij -PHYS , dij -CHEM and dij -BIOL are the coefficients of variation (%CV) of the corresponding elements tij-PHYS , tij-CHEM and tij-BIOL ∀tij = / 0 and tij = / 1 of the matrixes TPHYS , TCHEM and TBIOL , respec¯ PHYS , tively. Subsequently, the three pairs of matrixes T¯ PHYS − D ¯ CHEM and T¯ BIOL − D ¯ BIOL were sent to the panelists, for them T¯ CHEM − D to reconsider – if necessary – their initial estimations. It was necessary to carry out this process twice for TPHYS and TBIOL and three times for TCHEM , in order to achieve the definite estimations of TPHYS ,

2.4.2. Determination of the priority vectors WPHYS , WCHEM and WBIOL The priority vectors were subsequently calculated from matrixes X¯ PHYS , X¯ CHEM and X¯ BIOL , which are represented by the following expressions: WPHYS = (w1-PHYS , w2-PHYS , w3-PHYS , w4-PHYS ) WCHEM = (w1-CHEM , w2-CHEM , w3-CHEM , w4-CHEM , w5-CHEM , w6-CHEM , w7-CHEM , w8-CHEM ) WBIOL = (w1-BIOL , w2-BIOL , w3-BIOL , w4-BIOL , w5-BIOL ) Each component wi of a vector W quantifies the relative importance of the corresponding attribute ai in the quality index, and it is calculated by the geometric mean of the elements of i-row of the ¯ as follows: matrix X,

⎡ ⎤1/n n  x¯ij ⎦ wi = ⎣ ∀i = 1, 2, . . ., n

(6)

j=1

Table 3 shows the obtained priority vectors WPHYS , WCHEM and WBIOL , which represent the relative importance of the physical, chemical and biological attributes in their respective indexes. These vectors were subsequently normalized in order to express the relative importance of the attributes in parts per unit. Consequently, the components wi  of a normalized vector W fulfill the condition n  that w = 1, and they are calculated by means of the following i=1 general expression: w i =

wi

n

i=1

wi

∀i = 1, 2, . . ., n

(7)

Table 3 shows the obtained normalized priority vectors W PHYS ,  CHEM and W BIOL , which represent the joint opinion of the panel. Finally, the coherence of the joint pair-wise comparison matrixes X¯ PHYS , X¯ CHEM and X¯ BIOL was determined, which is the absence of internal contradictions in the pair-wise comparisons. To this end, the deviation of each matrix was calculated with respect to the W

684

E. Rodríguez et al. / Ecological Indicators 60 (2016) 678–692 Table 2 Joint estimation of the panel of the relative importance of the attributes ai-PHYS , ai-CHEM and ai-BIOL in their corresponding indexes S-DQIPHYS , S-DQICHEM and ¯ PHYS , D ¯ CHEM and D ¯ BIOL . S-DQIBIOL : Joint superior triangular matrixes T¯ PHYS , T¯ CHEM and T¯ BIOL and their respective dispersion matrixes D

consistency condition by means of the following Index of Consistency Deviation (ICD): n n



  ıij 

ICD =

i=1(i = / j) j=1

n(n − 1)

/ıij =

wi − 1 ıij = 0 ∀i = j wj x¯ ij

(8)

where ıij is the relative deviation of the element x¯ij with regard to the consistency condition (wi /wj = x¯ij ∀i, j = 1, 2, . . ., n). Table 3

shows the obtained values of the ICD (%) corresponding to the matrixes X¯ PHYS , X¯ CHEM and X¯ BIOL . As can be observed, these values were less than 10% for matrixes X¯ PHYS and X¯ BIOL , and less than 20% for X¯ CHEM . These values of the ICD show that the joint assessments of the panel concerning the relative importance of the attributes by means of the final pair-wise comparison matrixes X¯ can be considered to be sufficiently coherent, as they can when they are expressed by the priority vectors W and W . Consequently, it was not necessary to repeat the process of convergence in this case. It

Table 3 Joint estimation of the panel of the relative importance of the attributes ai-PHYS , ai-CHEM and ai-BIOL in their corresponding indexes S-DQIPHYS , S-DQICHEM and S-DQIBIOL : Joint pair-wise comparison matrixes X¯ PHYS , X¯ CHEM and X¯ BIOL , priority vectors WPHYS , WCHEM and WBIOL , normalized priority vectors W PHYS , W CHEM and ¯ W BIOL and index of consistency deviation (ICD) of the matrixes X.

E. Rodríguez et al. / Ecological Indicators 60 (2016) 678–692

should be pointed out that the ICD usually increases as does the number of attributes to be compared, due to the inherent difficulty of being entirely coherent in such pair-wise comparisons. Consequently, it is difficult – but not impossible – to get reasonably acceptable values of the ICD when the number of attributes is higher than 10. 2.5. Comprehensive overview of the index design procedure Fig. 4 shows a diagram which schematizes the three stages of the proposed procedure for the design of each of the three indexes (S-DQIPHYS , S-DQICHEM , S-DQIBIOL ) included in the S-DQI. Each stage summarizes the tasks which have to be carried out by both the panelists and the coordinators. The diagram indicates, by means of dashed lines, the tasks which require convergence processes. The panel and the coordinators work in collaboration throughout the whole procedure. The panel contributes its knowledge about soils and their agricultural functionality. The coordinators organize and analyze the panellists’ estimations and perform the required mathematical treatments in order to obtain a joint estimation of the panel for each stage of the procedure, after having achieved satisfactory convergence and/or consistency in the panel’s estimations. Once all this information is available, the index is ready to be used for the calculation of the dynamic quality of agricultural soils. The designed S-DQI is of general application for routine monitoring of the quality of farming soils, in order to estimate the changes induced in soil due to agricultural practices. Nevertheless, if the index S-DQI were used in a region or area where the limit values [minIi , maxIi ] of the indicators Ii were not suitable for the characteristics of that regional farming soil and/or for a specific kind of crop, the index design procedure presented here would be equally applicable by merely considering the suitable intervals [minIi  , maxIi  ] for such a case and by estimating the beneficial contribution  ¯ B¯ (Si ) of the attributes in those new intervals. 3. Results and discussion In order to verify the response capability of the designed S-DQI, it was used to calculate the dynamic quality of diverse agricultural soils selected by the panel. Each of the three values (S-DQIPHYS , S-DQICHEM , S-DQIBIOL ) which describe the dynamic quality of the soil was obtained as a result of a fuzzy inference procedure. The application of this procedure to the selected soils and the results obtained in each case are described below. 3.1. Calculation of the index S-DQI (S-DQIPHYS , S-DQICHEM , S-DQIBIOL ): Fuzzy inference procedure The procedure proposed here is based on the zero-order fuzzy inference method of Takagi–Sugeno (Takagi and Sugeno, 1985), in which the consequent of every fuzzy rule and the final result of the inference procedure are represented by crisp variables – which simplifies and speeds up the calculations inherent in the procedure. This method can be considered as an advantageous alternative to the fuzzy inference methods usually used in environmental quality assessments, in which both the consequents of the rules and the result of the inference procedure are fuzzy sets (Arunraj and Maiti, 2009; Caniani et al., 2011; Genske and Heinrich, 2009) and consequently, subsequent defuzzifications are required in order to achieve a crisp value of the quality index – which complicates and lengthens the calculations. The procedure proposed here requires: (i) the description of the physical, chemical and biological

charac teristics of the soil by means of fuzzy sets S est¯ , S est¯



and

est¯ Si-BIOL

i-PHYS

i-CHEM

, respectively, (ii) the definition of the set of fuzzy

685

rules which constitutes each of the knowledge bases KBPHYS , KBCHEM and KBBIOL , and (iii) assessing to what extent the fuzzy estimations est¯ est ¯ est¯ Si−PHYS , Si−CHEM and Si−BIOL comply with the antecedents of the fuzzy rules of their respective knowledge base, which is expressed by means of the level of activation of each of their rules. The result of each fuzzy inference procedure is eventually obtained from the level of activation and the consequent of each fuzzy rule of the KBPHYS , KBCHEM and KBBIOL , which is S-DQIPHYS , S-DQICHEM and S-DQIBIOL , respectively. These procedures were applied to calculate the dynamic quality of diverse agricultural soils selected by the panel. Next, the fuzzy inference procedures are illustrated in detail for just two of the studied soils, in order to avoid repetition which is unnecessary to explain the calculation procedure.

3.1.1. Selected agricultural soils The panel agreed to define three soils of different levels of quality for farming, according to the criteria which had been previously used for the design of the index: a high quality soil (AQ), an intermediate quality soil (BQ) and a medium-low quality soil (CQ). For this, the physical, chemical and biological properties of each soil were defined by assigning a value range to each indicator Ii-PHYS , Ii-CHEM and Ii-BIOL on condition that its beneficial contribution to the soil quality was high for the soil QA, intermediate for the soil QB and medium-low for the soil QC, in accordance with the correspond¯ B¯ (Si-PHYS ),  ¯ B¯ (Si-CHEM ) and  ¯ B¯ (Si-BIOL ) ing membership functions  which had been previously estimated by the panel. The extent of the value range of each indicator on each soil was determined by the value interval which met the required beneficial contribution in each case. Additionally, the panel also agreed to utilize the index to assess the dynamic quality of three kinds of soils of the Basque Country (Spain), which could be considered representative of: (i) an agricultural soil of standard quality (SQ), (ii) a soil similar to the previous one, but compacted by agricultural practices (COMP), and (iii) a soil which was potentially affected by residual metal pollution (MP). The physicochemical and biological properties of these three soils were also described by the range of values taken by the indicators Ii-PHYS , Ii-CHEM and Ii-BIOL in each case, which is frequently a more realistic way of representing the estimations of the soil properties at any emplacement. The required data were obtained from previous studies which had been carried out by the panellists’ working groups with these kinds of regional soils. The value of an indicator Ii on a soil was described by the range of values [Ii (l) , Ii (r) ]. This range includes the values which are usually taken by Ii in that soil according to the available data and so, they fulfill the condition that Ii (l) < Ii < Ii (r) . Table 4 shows the physicochemical and biological properties of the two groups of soils selected by the panel. The “Soil Group I” (SI) includes the soils of three different levels of quality defined by the panel, and the “Soil Group II” (SII) includes the regional farming soils.

3.1.2. Fuzzy estimations of the status of the selected soils The physical, chemical and biological attributes

of the soils were est ¯ described by means of the fuzzy sets S , S est¯ and



est¯ Si-BIOL

i-PHYS

i-CHEM

¯ were represented by triangu. The fuzzy estimations Siest



(l)

(c)

(r)

lar fuzzy numbers Si , Si , Si



(l)

, where Si is the value of Si from

¯ stops being zero, S (c) the which the degree of membership to Siest i value of Si corresponding to the maximum degree of membership ¯ , and S (r) the value of S from which the degree of memberto Siest i i ¯ starts to be zero again. The values S (l) , S (c) and S (r) of ship to S est i

i

i

i

¯ were calculated by means of Eq. (1) from the correspondeach Siest ¯ = ing values of the respective fuzzy estimations Iiest



(l)

(c)

(r)

Ii , I i , I i



.

686

E. Rodríguez et al. / Ecological Indicators 60 (2016) 678–692

Fig. 4. Diagram of the design procedure of the S-DQI.

¯ (est) The triangular fuzzy numbers Ii were obtained from the range of values corresponding to the respective conventional indicators (l) (c) Ii , Ii being the left end of the interval, Ii being the central value (r)

of the interval, and Ii being the right end of the interval. If the indicators Ii had been described by crisp numbers, the fuzzy esti¯ (est) mations Ii would have been represented by singleton fuzzy sets. Table 5 shows the fuzzy estimations of the conventional indicators and their corresponding normalized indicators obtained for two of the soils referred to in Table 4. Similar calculations provided the fuzzy estimations of the remaining soils referred to in this table.

3.1.3. Definition of the knowledge bases KBPHYS , KBCHEM and KBBIOL The knowledge bases are constituted by a set of IF-THEN fuzzy rules, the antecedents of which are related with the connector AND, and the consequents of which are always crisp values. Each j-rule of the knowledge bases KBPHYS , KBCHEM and KBBIOL expresses j ¯ the relation between the corresponding set of fuzzy values Si-PHYS , j ¯ j ¯ Si-CHEM and Si-BIOL (the antecedents), which are taken by their corresponding linguistic variables, and the crisp value of the index (the consequent), which is (S-DQIPHYS )j , (S-DQICHEM )j and (S-DQIBIOL )j ,

Table 4 Range of values which describe the physical, chemical and biological attributes of the agricultural soils selected for the assessment of the dynamic quality by means of the index S-DQI. Conventional indicator (Ii ) RD F  WHC pH EC CEC ESP OM TKN POLSEN KEX SMB-C N-NH4 + BSR-CO2 AWCD-BIOLOG H -BIOLOG

Soil Group I

Soil Group II

A quality (SI-AQ)

B quality (SI-BQ)

C quality (SI-CQ)

Standard quality (SII-SQ)

Compacted (SII-COMP)

Metal polluted (SII-MP)

[90, 110] [0.7, 1.1] [1.3, 1.4] [230, 250] [5.3, 6.5] [0.6, 0.9] [40.0, 55.0] [9.0, 10.5] [3.5, 5.0] [2200.0, 2400.0] [35.0, 60.0] [275.0, 500.0] [2900.0, 3000.0] [165.0, 170.0] [18.0, 20.0] [1.3, 1.5] [3.8, 4.0]

[45, 60] [0.3, 0.5] [1.4, 1.6] [140, 180] [4.5, 5.0] [2.0, 2.7] [15.0, 25.0] [11.0, 12.0] [1.5, 2.0] [1100.0, 1500.0] [20.0, 30.0] [100.0, 200.0] [1200.0, 1800.0] [80.0, 110.0] [6.0, 10.0] [0.6, 0.9] [2.8, 3.2]

[18, 28] [0.1, 0.2] [1.6, 1.7] [70, 90] [3.5, 3.7] [3.8, 4.0] [3.0, 6.0] [14.4, 15.0] [0.5, 0.8] [200.0, 220.0] [2.0, 6.0] [50.0, 55.0] [50.0, 200.0] [20.0, 40.0] [0.2, 3.0] [0.1, 0.3] [2.0, 2.3]

[85, 100] [1.4, 1.6] [1.3, 1.4] [200, 240] [6.0, 6.6] [0.5, 1.2] [85.0, 140.0] [3.5, 4.2] [2.8, 5.0] [2100.0, 2300.0] [40.0, 100.0] [250.0, 500.0] [2800.0, 2950.0] [130.0, 160.0] [15.0, 20.0] [1.3, 1.5] [3.8, 4.0]

[70, 80] [0.6, 0.8] [1.5, 1.6] [180, 215] [5.8, 6.5] [1.1, 1.4] [90.0, 130.0] [3.4, 4.5] [2.8, 3.2] [2085.0, 2275.0] [40.0, 85.0] [245.0, 450.0] [2450.0, 2700.0] [125.0, 150.0] [15.0, 17.0] [1.2, 1.4] [3.8, 3.9]

[85, 95] [1.3, 1.6] [1.3, 1.4] [210, 240] [5.4, 5.8] [0.7, 1.2] [30.0, 60.0] [3.8, 5.2] [1.7, 2.3] [1460.0, 1850.0] [45.0, 80.0] [235.0, 420.0] [1000.0, 1300.0] [85.0, 120.0] [10.0, 12.0] [0.6, 0.8] [2.8, 3.0]

E. Rodríguez et al. / Ecological Indicators 60 (2016) 678–692

687

Table 5  (est)   (est)  ¯ ¯ and normalized Si indicators which describe the characteristics of the soils SI-BQ and SII-SQ referred to in Table 4. Fuzzy estimations of the conventional Ii Linguistic variable LSi

Soil I-B quality (SI-BQ)

Soil II-standard quality (SII-SQ)

¯ (est)

¯ (est)

Ii

LSRD LSF LS LSWHC LSpH LSEC LSCEC LSESP LSOM LSTKN LSP-OLSEN LSKex LSSMB-C LSN-NH4+ LSBSR-CO2 LSAWCD-BIOLOG LSH  -BIOLOG

¯ (est)

¯ (est)

(Ii (l) , Ii (c) , Ii (r) )

(Si (l) , Si (c) , Si (r) )

Si

Ii

(Ii (l) , Ii (c) , Ii (r) )

(Si (l) , Si (c) , Si (r) )

(45, 53, 60) (0.3, 0.4, 0.5) (1.4, 1.5, 1.6) (140, 160, 180) (4.5, 4.8, 5.0) (2.0, 2.4, 2.7) (15.0, 20.0, 25.0) (11.0, 11.5, 12.0) (1.5, 1.8, 2.0) (1100.0, 1300.0, 1500.0) (20.0, 25.0, 30.0) (100.0, 150.0, 200.0) (1200.0, 1500.0, 1800.0) (80.0, 95.0, 110.0) (6.0, 8.0, 10.0) (0.60, 0.8, 0.90) (2.8, 3.0, 3.2)

(37.5, 43.8, 50.0) (10.5, 15.8, 21.1) (25.0, 50.0, 75.0) (38.9, 50.0, 61.1) (20.0, 25.0, 30.0) (48.7, 57.7, 66.7) (6.1, 8.6, 11.2) (69.2, 73.1, 76.9) (6.9, 8.6, 10.3) (40.9, 52.3, 59.1) (3.0, 3.8, 4.7) (1.4, 3.1, 4.8) (39.0, 49.2, 59.3) (40.0, 50.0, 60.0) (20.0, 26.7, 33.3) (40.0, 50.0, 60.0) (40.0, 50.0, 60.0)

(85, 93, 100) (1.4, 1.5, 1.6) (1.3, 1.35, 1.4) (200, 220, 240) (6.0, 6.3, 6.6) (0.5, 0.9, 1.2) (85.0, 112.5, 140.0) (3.5, 3.9, 4.2) (2.8, 3.9, 5.0) (2100.0, 2200.0, 2300.0) (40.0, 70.0, 100.0) (250.0, 375.0, 500.0) (2800.0, 2875.0, 2950.0) (130.0, 145.0, 160.0) (15.0, 17.5, 20.0) (1.3, 1.4, 1.5) (3.8, 3.9, 4.0)

(70.8, 77.1, 83.3) (68.4, 73.7, 79.0) (0.0, 12.5, 25.0) (72.2, 83.3, 94.4) (50.0, 56.0, 62.0) (10.3, 19.2, 28.2) (41.6, 55.6, 69.5) (11.5, 14.2, 16.9) (15.9, 23.5, 31.0) (86.4, 90.9, 95.5) (6.4, 11.4, 16.4) (6.8, 11.0, 15.3) (93.2, 95.8, 98.3) (73.3, 83.3, 93.3) (50.0, 58.3, 66.7) (86.7, 93.3, 100.0) (90.0, 95.0, 100.0)

respectively. According to this, the j-rule of these knowledge bases is formulated as follows:

Si

0 to 1. It is higher, the greater the number of the LSi is which takes the value B¯i and the greater the relative importance of their corre-

¯j ¯j j¯ j¯ IF LSRD = SRD AND LSF = SF AND LS = S AND LSWHC = SWHC

(9)

THEN S-DQIPHYS = (S-DQIPHYS )j j¯ j¯ j¯ j¯ IF LSpH = SpH AND LSEC = SEC AND LSCEC = SCEC AND LSESP = SESP AND j¯ j¯ j ¯ j¯ LSOM = SOM AND LSTKN = STKN AND LSP-OLSEN = SP-OLSEN AND LSKex = SKex

(10)

THEN S-DQICHEM = (S-DQIECHEM )j j ¯ j ¯ j ¯ IF LSSMB-C = SSMB-C AND LSN-NH4+ = SN-NH4+ AND LSBSR-CO2 = SBSR-CO

AND

2

¯

j

j

¯

(11)

LSAWCD-BIOLOG = SAWCD-BIOLOG AND LSH  -BIOLOG = SH  -BIOLOG THEN S-DQIBIOL = (S-DQIBIOL )j The condition for writing the set of fuzzy rules of each KB is that ¯j the fuzzy values Si which can be taken by the linguistic variables LSi in a rule is either B¯i or D¯ i ∀i = 1, 2, . . ., n. Consequently, the set of antecedents of each fuzzy rule is obtained by assigning to the n linguistic variables one of the variations of the fuzzy values B¯i or D¯ i taken n at a time with repetitions, in order to take into account all the possible interrelationships between the beneficial and detrimental contributions of all the indicators. Therefore, the number of fuzzy rules is m = 2n , where n is the number of attributes included in the corresponding index. Accordingly, the number of fuzzy rules included in the knowledge bases KBPHYS , KBCHEM and KBBIOL is 24 , 28 and 25 , this is 16, 256 and 32 fuzzy rules, respectively. The consequent of a fuzzy j-rule is the crisp value (S-DQI)j . It is determined as a function of the relative importance of the attributes ai corresponding to the LSi included in the rule and the fuzzy value taken by the LSi in the rule, which is B¯i or D¯ i . It is calculated by means of the following general expression: j (S-DQI) =

n

w  i i

(j)

∀j = 1, 2, . . ., m

(12)

i=1

sponding attributes ai is in the index. Tables 6 and 7 show the fuzzy rules of the knowledge bases KBPHYS and KBBIOL , respectively. Supplementary Appendix A shows the knowledge base KBCHEM , which includes 256 rules. 3.1.4. Calculation of the level of activation ˛ of the rules of the KBPHYS , KBCHEM and KBBIOL The level of activation (˛) of each fuzzy rule of the knowledge bases KBPHYS , KBCHEM and KBBIOL quantifies to what extent the fuzzy est¯ est¯ est¯ estimations Si-PHYS , Si-CHEM and Si-BIOL comply with their respective rules. The ˛ is the minimum value of the degrees of consistency (i ) of all its antecedents, which can be expressed as follows: ˛ = min{1 , 2 , . . ., i , . . ., n }

(13)

The i of the i-th antecedent of a rule is determined by means of the following general expression: i = max

min[

S

¯ (est) i

(Si ), S¯ (Si )] i

(14)

¯ is the fuzzy value taken by the linguistic variable LS on where Siest i the soil under assessment, and S¯i is the fuzzy value taken by this LSi

where wi  is the component of the normalized priority vector W ¯j and i j is a parameter the value of which in a j-rule is 1 when Si takes the fuzzy value B¯i and is 0 when it takes the value D¯ i . Accord-

in the rule. Consequently, according to Eq. (14), i is the maximum of the minima obtained by comparing the membership functions  (est) ¯ (Si ) and S¯ (Si ) for each value of Si . Tables 6 and 7 show the i

ing to this, the value of the consequent of a fuzzy j-rule varies from

and ˛ of the fuzzy rules of the knowledge bases KBPHYS and KBBIOL ,

S

i

i

688

E. Rodríguez et al. / Ecological Indicators 60 (2016) 678–692

Table 6 Set of fuzzy rules of the knowledge base KBPHYS * . Degrees of consistency () of the antecedents and activations levels (˛ and ) of the fuzzy rules of KBPHYS for soils SI-BQ and SII-SQ referred to in Table 4. Rule no.

Knowledge base KBPHYS Antecedents (IF)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Soil I-B quality (SI-BQ) Conseq. (THEN)

Degree of consistency ()

Soil II-standard quality (SII-SQ) Activation level

Degree of consistency ()

Activation level

LSRD

LSF

LS

LSWHC

S-DQIPHYS

RD

F



WHC

˛



RD

F



WHC

˛



1 1 1 1 0 1 1 1 0 0 0 1 0 0 0 0

1 1 1 0 1 1 0 0 1 1 0 0 1 0 0 0

1 1 0 1 1 0 1 0 0 1 1 0 0 1 0 0

1 0 1 1 1 0 0 1 1 0 1 0 0 0 1 0

1.000 0.760 0.730 0.860 0.650 0.490 0.620 0.590 0.380 0.410 0.510 0.350 0.140 0.270 0.240 0.000

0.516 0.516 0.516 0.516 0.581 0.516 0.516 0.516 0.581 0.581 0.581 0.516 0.581 0.581 0.581 0.581

0.500 0.500 0.500 0.625 0.500 0.500 0.625 0.625 0.500 0.500 0.625 0.625 0.500 0.625 0.625 0.625

0.600 0.600 0.600 0.600 0.600 0.600 0.600 0.600 0.600 0.600 0.600 0.600 0.600 0.600 0.600 0.600

0.550 0.550 0.550 0.550 0.550 0.550 0.550 0.550 0.550 0.550 0.550 0.550 0.550 0.550 0.550 0.550

0.500 0.500 0.500 0.516 0.500 0.500 0.516 0.516 0.500 0.500 0.550 0.516 0.500 0.550 0.550 0.550

0.060 0.060 0.060 0.062 0.060 0.060 0.062 0.062 0.060 0.060 0.067 0.062 0.060 0.067 0.067 0.067

1.000 1.000 1.000 1.000 0.065 1.000 1.000 1.000 0.065 0.065 0.065 1.000 0.065 0.065 0.065 0.065

1.000 1.000 1.000 0.074 1.000 1.000 0.074 0.074 1.000 1.000 0.074 0.074 1.000 0.074 0.074 0.074

0.889 0.889 0.222 0.889 0.889 0.222 0.889 0.222 0.222 0.889 0.889 0.222 0.222 0.889 0.222 0.222

0.850 0.250 0.850 0.850 0.850 0.250 0.250 0.850 0.850 0.250 0.850 0.250 0.250 0.250 0.850 0.250

0.850 0.250 0.222 0.074 0.065 0.222 0.074 0.074 0.065 0.065 0.065 0.074 0.065 0.065 0.065 0.065

0.361 0.106 0.094 0.031 0.027 0.094 0.031 0.031 0.027 0.027 0.027 0.031 0.027 0.027 0.027 0.027

*1: The fuzzy number corresponding to the linguistic variable LSi-PHYS is B¯i −PHYS . *0: The fuzzy number corresponding to the linguistic variable LSi-PHYS is D¯ i −PHYS .

respectively, for the soils referred to in Table 4. As can be observed, the ˛ of each fuzzy rule is the minimum value of the degrees of consistency of all the antecedents of each rule, according to the criterion expressed by Eq. (13). Appendix A shows the i and ˛ of the fuzzy rules of the knowledge base KBCHEM corresponding to both soils. Similar calculations provided the i and ˛ corresponding to the fuzzy rules of the KBPHYS , KBCHEM and KBBIOL for the remaining soils referred to in Table 4. 3.1.5. Result of the fuzzy inference procedures: the value of the S-DQI (S-DQIPHYS , S-DQICHEM , S-DQIBIOL ) of the selected soils Once the level of activation of all the fuzzy rules of the knowledge bases was determined, the final values of the S-DQIPHYS , S-DQICHEM and S-DQIBIOL were calculated by means of the following general expression: S-DQI =

m

(j) (S-DQI)j

(15)

j=1

where (S-DQI)j is the consequent of the j-rule and (j) is the normalized level of activation of the rule, m being the number of rules of the KB. The normalized level of activation of a rule () was obtained from the value ˛ of the rule as follows: (j) =

˛(j)

m

j=1

˛(j)

(16)

Consequently,  represents the level of activation of the rule in parts per unit and so, it satisfies the condition that: m

(j) = 1

(17)

j=1

Tables 6 and 7 show the  corresponding to the fuzzy rules of the knowledge bases KBPHYS and KBBIOL , respectively, for the soils referred to in Table 4. Supplementary Appendix A shows the  of the fuzzy rules of the knowledge base KBCHEM corresponding to both soils. Similar calculations provided the  of the rules of the KBPHYS , KBCHEM and KBBIOL for the remaining soils referred to in Table 4. After the calculation of the normalized levels of activation of the fuzzy rules, the values of the S-DQIPHYS , S-DQICHEM and S-DQIBIOL were finally calculated for each soil under study by means of Eq.

(15). Table 8 shows the triad of values included in the S-DQI, which describes the dynamic quality of the soils selected by the panel. 3.1.6. Comprehensive overview of the index calculation procedure Fig. 5 shows a diagram which schematizes the two stages of the proposed fuzzy inference procedure for the calculation of each of the three indexes (S-DQIPHYS , S-DQICHEM , S-DQIBIOL ) included in the S-DQI. Each stage summarizes the calculations which have to be carried out in order to obtain the value of each index. All these calculations are carried out by the coordinators by using conventional IT applications. The data required for calculating the value of each index are the values taken by the corresponding indicators I = {I1 , I2 , . . ., Ii , . . ., In } on the soil under assessment. Each Ii can be described by a range of values [Ii (l) , Ii (r) ] or by a crisp value, the fuzzy estimations of which are triangular fuzzy numbers and singletons, respectively. The value of any index whose design was based on the design procedure proposed in Section 2, could be achieved as a result of an entirely similar fuzzy inference procedure. 3.2. Index response capability to changes in soil quality As stated above, the index is a triad of crisp values (S-DQIPHYS , S-DQICHEM , S-DQIBIOL ) each one ranging from 0 to 1. Fig. 6 shows the linguistic terms used to graduate the quality on this scale, in accordance to the criteria used by the panel for the design of the index. The assessment of the quality of soils of different characteristics showed the index response capability to changes in soil properties, the results of which are shown in Table 8. The results obtained for the Soil Group I show the index response to the three different quality levels of the soils included in the group. The three values of the soil SI-AQ are higher than 0.80, which correspond to a high quality level in the index scale. The three values of the soil SI-BQ are equal to 0.50, which is the intermediate quality level on the index scale – medium quality. Finally, the three values which describe the quality of the soil SI-CQ are lower than 0.35, which correspond to a medium-low quality level on the index scale. These results are consistent with the value intervals taken by the attributes in these soils, which were estimated to have – respectively – a high, an intermediate and a medium-low beneficial contribution to the quality of farming soil, in accordance to the criteria used by the panel for the design of the index.

Table 7 Set of fuzzy rules of the knowledge base KBBIOL * . Degrees of consistency () of the antecedents and activations levels (˛ and ) of the fuzzy rules of KBBIOLS for soils SI-BQ and SII-SQ referred to in Table 4. Rule no.

Knowledge base KBBIOL

Soil I-B quality (SI-BQ)

Antecedents (IF)

* *

Degree of consistency ()

Activation level

Degree of consistency ()

Activation level

LSSMB-C

LSN-NH4 +

LSBSR-CO2

LSAWCD-BIOLOG

LSH  -BIOLOG

S-DQIBIOL

SMB−C

N−NH4 +

BSR−CO2

AWCD−BIOLOG

H’−BIOLOG

˛



SMB−C

N−NH4 +

BSR−CO2

AWCD−BIOLOG

H’−BIOLOG

˛



1 1 1 1 0 1 1 1 0 0 0 1 0 0 0 0 1 1 1 1 0 1 1 1 0 0 0 1 0 0 0 0

1 1 1 0 1 1 0 0 1 1 0 0 1 0 0 0 1 1 1 0 1 1 0 0 1 1 0 0 1 0 0 0

1 1 0 1 1 0 1 0 0 1 1 0 0 1 0 0 1 1 0 1 1 0 1 0 0 1 1 0 0 1 0 0

1 0 1 1 1 0 0 1 1 0 1 0 0 0 1 0 1 0 1 1 1 0 0 1 1 0 1 0 0 0 1 0

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1.000 0.830 0.920 0.850 0.790 0.750 0.680 0.770 0.710 0.620 0.640 0.600 0.540 0.470 0.560 0.390 0.610 0.440 0.530 0.460 0.400 0.360 0.290 0.380 0.320 0.230 0.250 0.210 0.150 0.080 0.170 0.000

0.538 0.538 0.538 0.538 0.554 0.538 0.538 0.538 0.554 0.554 0.554 0.538 0.554 0.554 0.554 0.554 0.538 0.538 0.538 0.538 0.554 0.538 0.538 0.538 0.554 0.554 0.554 0.538 0.554 0.554 0.554 0.554

0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545

0.476 0.476 0.619 0.476 0.476 0.619 0.476 0.619 0.619 0.476 0.476 0.619 0.619 0.476 0.619 0.619 0.476 0.476 0.619 0.476 0.476 0.619 0.476 0.619 0.619 0.476 0.476 0.619 0.619 0.476 0.619 0.619

0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545

0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.545

0.476 0.476 0.538 0.476 0.476 0.538 0.476 0.538 0.545 0.476 0.476 0.538 0.545 0.476 0.545 0.545 0.476 0.476 0.538 0.476 0.476 0.538 0.476 0.538 0.545 0.476 0.476 0.538 0.545 0.476 0.545 0.545

0.029 0.029 0.033 0.029 0.029 0.033 0.029 0.033 0.033 0.029 0.029 0.033 0.033 0.029 0.033 0.033 0.029 0.029 0.033 0.029 0.029 0.033 0.029 0.033 0.033 0.029 0.029 0.033 0.033 0.029 0.033 0.033

0.959 0.959 0.959 0.959 0.066 0.959 0.959 0.959 0.066 0.066 0.066 0.959 0.066 0.066 0.066 0.066 0.959 0.959 0.959 0.959 0.066 0.959 0.959 0.959 0.066 0.066 0.066 0.959 0.066 0.066 0.066 0.066

0.848 0.848 0.848 0.242 0.848 0.848 0.242 0.242 0.848 0.848 0.242 0.242 0.848 0.242 0.242 0.242 0.848 0.848 0.848 0.242 0.848 0.848 0.242 0.242 0.848 0.848 0.242 0.242 0.848 0.242 0.242 0.242

0.930 0.930 0.186 0.930 0.930 0.186 0.930 0.186 0.186 0.930 0.930 0.186 0.186 0.930 0.186 0.186 0.930 0.930 0.186 0.930 0.930 0.186 0.930 0.186 0.186 0.930 0.930 0.186 0.186 0.930 0.186 0.186

0.937 0.125 0.937 0.937 0.937 0.125 0.125 0.937 0.937 0.125 0.937 0.125 0.125 0.125 0.937 0.125 0.937 0.125 0.937 0.937 0.937 0.125 0.125 0.937 0.937 0.125 0.937 0.125 0.125 0.125 0.937 0.125

0.952 0.952 0.952 0.952 0.952 0.952 0.952 0.952 0.952 0.952 0.952 0.952 0.952 0.952 0.952 0.952 0.095 0.095 0.095 0.095 0.095 0.095 0.095 0.095 0.095 0.095 0.095 0.095 0.095 0.095 0.095 0.095

0.848 0.125 0.186 0.242 0.066 0.125 0.125 0.186 0.066 0.066 0.066 0.125 0.066 0.066 0.066 0.066 0.095 0.095 0.095 0.095 0.066 0.095 0.095 0.095 0.066 0.066 0.066 0.095 0.066 0.066 0.066 0.066

0.225 0.033 0.049 0.064 0.018 0.033 0.033 0.049 0.018 0.018 0.018 0.033 0.018 0.018 0.018 0.018 0.025 0.025 0.025 0.025 0.018 0.025 0.025 0.025 0.018 0.018 0.018 0.025 0.018 0.018 0.018 0.018

E. Rodríguez et al. / Ecological Indicators 60 (2016) 678–692

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

Conseq. (THEN)

Soil II-standard quality (SII-SQ)

1: The fuzzy number corresponding to the linguistic variable LSi-BIOL is B¯i −PHYS . 0: The fuzzy number corresponding to the linguistic variable LSi-BIOL is D¯ i −BIOL .

689

690

E. Rodríguez et al. / Ecological Indicators 60 (2016) 678–692

Table 8 Values of the Dynamic Quality Index S-DQI (S-DQIPHYS , S-DQICHEM , S-DQIBIOL ) of the farming soils referred to in Table 4 obtained as a result of the fuzzy inference procedures. Group

Soil

S-DQI (S-DQIPHYS , S-DQICHEM , S-DQIBIOL )

Characteristics

Symbol

I

A Quality B Quality C Quality

SI-AQ SI-BQ SI-CQ

(0.824, 0.860, 0. 815) (0.495, 0.504, 0.497) (0.334, 0.335, 0.338)

II

Standard quality Compacted Metal polluted

SII-SQ SII-COMP SII-MP

(0.704, 0.778, 0.651) (0.542, 0.752, 0.620) (0.702, 0.699, 0.490)

Fig. 5. Diagram of the calculation procedure of the S-DQI.

LOW

0.0

MEDIUM MEDIUM MEDIUM HIGH LOW

0.2

0.4

0.6

0.8

HIGH

1.0

Fig. 6. Index scale: Linguistic terms used to graduate the dynamic quality of soils by means of the index S-DQI (S-DQIPHYS , S-DQICHEM , S-DQIBIOL ).

Table 8 also shows the results obtained in the quality assessment of Soil Group II, which can be explained in light of the considerations taken into account for Soil Group I. The soil SII-SQ is a representative soil of the standard quality of regional farming soils. The three values (S-DQIPHYS , S-DQICHEM , S-DQIBIOL ) are higher than 0.65 and lower than 0.78, which indicates that, according to the index scale, it is a medium-high quality farming soil, the physicochemical quality of which is higher than the biological quality. The soil SII-COMP represents a soil similar to the previous one, which had been compacted by agricultural practices. As can be observed in Table 8, the values of the S-DQIPHYS , S-DQICHEM and S-DQIBIOL are lower than the corresponding values for the standard quality soil SII-SQ, as a result of the influence of the compaction on the soil properties. The value of the S-DQIPHYS is 0.54, which corresponds to a medium quality in the index scale, and shows evidence of the significant influence of compaction on the physical properties of the soil. The influence of the soil compaction on their chemical and biological characteristics is logically much less significant and so, despite the compaction, the values of the indexes S-DQICHEM and

S-DQIBIOL enable the soil to be qualified as being of medium-high quality from a chemical and biological point of view. Finally, the values of the S-DQIPHYS , S-DQICHEM and S-DQIBIOL for the soil SII-MP, which represents a soil potentially affected by residual metal pollution, present no evidence of its physical properties having been affected. However, its chemical properties were slightly affected and the biological properties were significantly affected, if they are compared to the values taken by the corresponding indexes in the soil of standard quality (SII-SQ) – which can be considered as a reference since its properties are unaltered. Nevertheless, despite the biological quality of this soil being medium-low, the soil maintains a medium-high physicochemical quality. These results obtained in the quality assessment of the two soil groups show that the designed S-DQI responds adequately to the changes in the soil properties and so can be considered suitable to be used for routine monitoring of the quality of farming soils, in order to estimate the changes induced in the soil due to agricultural practices.

4. Conclusions Although the use of quality indexes is a widespread practice in the assessment of soil quality, the intrinsic complexity of soil, the imprecision and inaccuracy inherent to many of the variables included in the indexes and the subjectivity of some quality estimations make it difficult to rigorously assess the quality of soil for a particular function, such as agriculture. The use of fuzzy logic and fuzzy set theory to deal with the uncertainty, imprecision

E. Rodríguez et al. / Ecological Indicators 60 (2016) 678–692

and subjectivity inherent to the data involved in soil quality assessments opens new ways to carry out more rigorous and realistic estimations of soil quality. With these considerations in mind, this work proposes an index based on fuzzy logic, which is especially addressed to assess the dynamic quality of agricultural soils – Soil Dynamic Quality Index (S-DQI). The index is described by a group of three indexes (S-DQIPHYS , S-DQICHEM , S-DQIBIOL ), each one designed to evaluate the dynamic quality of the agricultural soil with respect to their physical, chemical and biological characteristics, respectively. The designed index was based on the joint opinion of a panel of experts, which took into consideration the different aspects influencing the quality of agricultural soils from different perspectives and with diverse points of view, all of which were included in the index. The panel agreed upon: (i) the physical ai-PHYS , chemical ai-CHEM and biological ai-BIOL attributes or properties of soil which determine its dynamic quality for farming; (ii) the most suitable conventional indicators Ii-PHYS , Ii-CHEM and Ii-BIOL for quantifying each of them, respectively; (iii) the range of values [minIi , maxIi ] for each indicator Ii by setting minIi and maxIi as the limit values of Ii which can be most commonly expected on a site of potential agricultural use; (iv) the estimation of the beneficial contributions of the attributes in the corresponding index by means of fuzzy sets, which are described by its membership functions  ¯ B¯ (Si-PHYS ),  ¯ B¯ (Si-CHEM ) and,  ¯ B¯ (Si-BIOL ), Si being the normalized indicator corresponding to Ii ; and (iv) the relative importance of the attributes in their respective index, which is expressed by means of the normalized priority vectors W PHYS , W CHEM and W BIOL . Each of the three values S-DQIPHYS , S-DQICHEM and S-DQIBIOL , which describe the dynamic quality of an agricultural soil was obtained as a result of a fuzzy inference procedure. This procedure is based on the zero-order fuzzy inference method of Takagi–Sugeno (Takagi and Sugeno, 1985), in which both the consequent of every fuzzy rule and the final result of the inference procedure are represented by crisp variables, which simplifies and speeds up the calculations inherent in the procedure. This method can be considered as an advantageous alternative to the fuzzy inference methods usually used in environmental quality assessments, in which both the consequents of the rules and the result of the inference procedure are fuzzy sets, and consequently, subsequent defuzzifications are required in order to achieve a crisp value of the quality index. The calculation procedure proposed here requires: (i) the description of the physical, chemical characteristics the soil by and biological



of est est est ¯ ¯ ¯ means of fuzzy sets S , S and S , respeci-PHYS

i-CHEM

i-BIOL

tively, (ii) the definition of the set of IF-THEN fuzzy rules which constitutes each of the knowledge bases KBPHYS , KBCHEM and KBBIOL , est¯ , and (iii) assessing to what extent the fuzzy estimations Si-PHYS est est ¯ ¯ and S comply with the antecedents of the fuzzy rules of S i-CHEM

i-BIOL

their corresponding knowledge base, which is expressed by means of the level of activation (˛) of each of their rules. The result of each fuzzy inference procedure is obtained from the normalized level of activation () and the consequent of each fuzzy rule of the KBPHYS , KBCHEM and KBBIOL , which is S-DQIPHYS , S-DQICHEM and S-DQIBIOL , respectively, all of them being crisp values ranging from 0 to 1. All the calculations inherent to the procedure were carried out by using est¯ est¯ conventional IT applications. The fuzzy estimations Si-PHYS , Si-CHEM est ¯ and S of the soil properties were determined from the correi-BIOL

est¯ est ¯ est¯ , each I est ¯ being sponding fuzzy estimations Ii-PHYS , Ii-CHEM and Ii-BIOL i



(l)

(c)

(r)

the triangular fuzzy number Ii , Ii , Ii

691

of the soil properties on any agricultural plot. Nevertheless, the calculation procedure proposed here also allows us to express the indicator values by means of crisp values, singletons being the ¯ and their corresponding S est ¯ in this fuzzy expressions of the Iiest i case. The assessment of the quality of two groups of soils of different characteristics showed the response capability of the index to changes in the soil quality. The triad of values (S-DQIPHYS , S-DQICHEM , S-DQIBIOL ) obtained for the three soils of different quality levels included in Group I were, respectively, higher than 0.80, equal to 0.50 and lower than 0.35, which correspond to a high, medium and medium-low quality level in the index scale. These results are consistent with the value intervals taken by the attributes in these soils, which were estimated to have – respectively – a high, an intermediate and a medium-low beneficial contribution to the quality of farming soil, in accordance to the criteria used by the panel for the design of the index. The use of the index to assess the quality of the three regional farming soils included in Group II enable these soils to be qualified according to the index scale, in light of the considerations taken into account for Soil Group I. Thus, the three values (0.70, 0.78, 0.65) obtained for the regional soil of standard quality indicate that it is a medium-high quality farming soil. The three values (0.54, 0.75, 0.62) obtained for the compacted soil show that the influence of compaction is significant on its physical properties, if it is compared to the soil of standard quality. Finally, the three values (0.70, 0.70, 0.50) obtained for the soil potentially affected by residual metal pollution show that chemical and biological properties are, respectively, slightly and more significantly affected, whereas there is no evidence of the physical properties having been affected, if this soil is also compared to the soil of standard quality – which can be considered as a reference since its properties are unaltered. These results show the satisfactory response capability of the SDQI and so, the index is ready to be used for the assessment of the dynamic quality of agricultural soils. The index S-DQI is of general application for the assessment of the dynamic quality of any agricultural soil. Nevertheless, if it were used in a region or area where the limit values [minIi , maxIi ] of the indicators Ii were not suitable for the characteristics of that regional farming soil and/or for a specific kind of crop, the index design procedure would be equally applicable by merely considering the suitable intervals [minIi  , maxIi  ] and by estimating the beneficial contribution  ¯ B¯ (Si ) of the attributes in those new intervals. The values (S-DQIPHYS , S-DQICHEM , S-DQIBIOL ) in such a case would be achieved as a result of entirely similar fuzzy inference procedures to those proposed here. The use of this index for routine monitoring of the quality of farming soil enables the estimation of the changes induced in the soil due to use, which will be helpful to soil managers wishing to systematically assess the sustainability of the agricultural practices.

Acknowledgements This research was supported by the University of the Basque Country UPV/EHU through contract EHU 10/20 and by the Department of Industry, Innovation, Trade and Tourism of the Basque Government through contract IE09-242.



obtained from the range

of values corresponding to the indicator Ii on the soil. The representation of the values of the indicators Ii by means of triangular fuzzy numbers enables the modeling of variable degrees of verisimilitude – by means of their corresponding membership functions –, which is a rigorous and realistic way of representing the estimations

Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.ecolind.2015. 08.016.

692

E. Rodríguez et al. / Ecological Indicators 60 (2016) 678–692

References Andrews, S.S., Karlen, D.L., Mitchell, J.P., 2002. A comparison of soil quality indexing methods for vegetable production systems in Northern California. Agr. Ecosyst. Environ. 90, 25–45. Andrews, S.S., Karlen, D.L., Cambardella, C.A., 2004. The soil management assessment framework. Soil Sci. Soc. Am. J. 68 (6), 1945–1962. Arunraj, N.S., Maiti, J., 2009. Development of environmental consequence index (ECI) using fuzzy composite programming. J. Hazard. Mater. 162, 29–43. Askari, M.S., Holden, N.M., 2014. Indices for cuantitative evaluation of soil quality under grassland management. Geoderma 230–231, 131–142. Assimakopoulos, M.N., Dounis, A., Spanou, A., Santamouris, M., 2013. Indoor air quality in a metropolitan area metro using fuzzy logic assessment system. Sci. Total Environ. 449, 461–469. Biswas, S., Roy, P.K.R., Datta, S., 2011. IWRM: application of fuzzy EIA in defining river water quality. J. Indian Assoc. Environ. Manag. 38 (2), 75–78. Cabanillas, J., Ginebreda, A., Guillen, D., Martinez, E., Barcelo, D., Moragas, L., Robuste, J., Darbra, R.M., 2012. Fuzzy logic based risk assessment of effluents from wastewater treatment plants. Sci. Total Environ. 439, 202–210. Caniani, D., Lioi, D.S., Mancini, I.M., Masi, S., 2011. Application of fuzzy logic and sensitivity analysis for soil contamination hazard classification. Waste Manage. 31, 583–594. Carbajal-Hernandez, J.J., Sanchez-Fernandez, L.P., Carrasco-Ochoa, J.A., MartinezTrinidad, J.F., 2012. Assessment and prediction of air quality using fuzzy logic and autoregressive models. Atmos. Environ. 60, 37–50. Chen, Y.D., Wang, H.Y., Zhou, J.M., Xing, L., Zhu, B.S., Zhao, Y.C., Chen, X.Q., 2013. Minimum data set for assessing soil quality in farmaland of Northeast China. Pedosphere 23 (5), 564–576. Chowdhury, S., 2012. Decision making with uncertainty. An example of water treatment approach selection. Water Qual. Res. J. Canada 47 (2), 153–165. Darbra, R.M., Eljarrat, E., Barcelo, D., 2008. How to measure uncertainties in environmental risk assessment. Trends Anal. Chem. 27 (4), 377–385. Deng, Y., Ni, F., Yao, Z., 2012. The Monte Carlo-based uncertainty health risk assessment associated with rural drinking water quality. J. Water Resour. Protect. 4 (9), 772–778. Dong, C., Tan, Q., Huang, G.H., Cai, Y.P., 2014. A dual-inexact fuzzy stochastic model for water resources management and non-point source pollution mitigation under multiple uncertainties. Hydrol. Earth Syst. Sci. 18 (5), 1793–1803. Duarte, O.G., Requena, I., Rosario, Y., 2007. Fuzzy techniques for EnvironmentalImpact Assessment in the mineral deposit of Punta Gorda (Moa, Cuba). Environ. Technol. 28 (6), 659–669. Fukuda, S., De Baets, B., Mouton, A.M., Waegeman, W., Nakajima, J., Mukai, T., Hiramatsu, K., Onikura, N., 2011. Effect of model formulation on the optimization of a genetic Takagi–Sugeno fuzzy system for fish habitat suitability evaluation. Ecol. Model. 222, 1401–1413. Genske, D.D., Heinrich, K., 2009. A knowledge-based fuzzy expert system to analyse degraded terrain. Expert Syst. Appl. 36, 2459–2472. Gentile, M., Rogers, W.J., Mannan, M.S., 2003. Development of a fuzzy logic-based inherent safety index. Trans. IChemE Process Saf. Environ. Prot. 81 (B), 444–456. Gharibi, H., Mahvi, A.H., Nabizadeh, R., Arabalibeik, H., Yunesian, M., Sowlat, M.H., 2012. A novel approach in water quality assessment based on fuzzy logic. J. Environ. Manage. 112, 87–95. Giordano, R., Liersch, S., 2012. A fuzzy GIS-based system to integrate local and technical knowledge in soil salinity monitoring. Environ. Modell. Softw. 36, 49–63. Imaz, M.J., Virto, I., Bescansa, P., Enrique, A., Fernandez-Ugalde, O., Karlen, D.L., 2010. Soil quality indicator response to tillage and residue management on semi-arid Mediterranean cropland. Soil. Tillage Res. 107 (1), 17–25. Karlen, D.L., Ditzler, C.A., Andrews, S.S., 2003. Soil quality: why and how? Geoderma 114, 145–156. Khan, F.I., Sadiq, R., Husain, T., 2002. GreenPro-I: A methodology for risk-based process plant design considering life cycle assessment. Environ. Modell. Softw. 17, 669–692.

Khan, F.I., Sadiq, R., Veitch, B., 2004. Life cycle iNdeX (LInX): a new indexing procedure for process and product design and decision-making. J. Clean. Prod. 12, 59–76. Klir, G.J., Yuan, B., 1995. Fuzzy sets and fuzzy logic: theory and applications, 1st ed. Prentice Hall, Upper Saddle River, NJ. Li, W.X., Zhang, X.X., Wu, B., Sun, S.L., Chen, Y.S., Pan, W.Y., Zhao, D.Y., Cheng, S.P., 2008. A comparative analysis of environmental quality assessment methods for heavy metal-contaminated soils. Pedosphere 18 (3), 344–352. Liu, G., Baniyounes, A., Rasul, M.G., Amanullah, M.T.O., Khan, M.M.K., 2012. Fuzzy logic based environmental indicator for sustainability assessment of renewable energy system using life cycle assessment. Procedia Eng. 49, 35–41. Liu, Y., Jiao, L., Liu, Y., He, J., 2013. A self-adapting fuzzy inference system for the evaluation of agricultural land. Environ. Modell. Softw. 40, 226–234. Peche, R., Rodríguez, E., 2009. Environmental impact assessment procedure: a new approach based on fuzzy logic. Environ. Impact Assess. Rev. 29, 275–283. Peche, R., Rodríguez, E., 2011. Environmental impact assessment by means of a procedure based on fuzzy logic: a practical application. Environ. Impact Assess. Rev. 31, 87–96. Peche, R., Rodríguez, E., 2012. Development of environmental quality indexes based on fuzzy logic. A case study. Ecol. Ind. 23, 555–565. Ping, J., Chen, B., Husain, T., 2010. Risk assessment of ambient air quality by stochastic-based fuzzy approaches. Environ. Eng. Sci. 27 (3), 233–246. Pislaru, M., Avasilcai, S., Trandabat, A., 2008. Environmental sustainability based on fuzzy models. Environ. Eng. Manage. J. 7 (1), 25–29. Qui, Y., Darilek, J.L., Huang, B., Zhao, Y., Sun, W., Gu, Z., 2009. Evaluating soil quality indices in an agricultural region of Jiangsu Province, China. Geoderma 149 (3–4), 325–334. Rahimi, D., Mokarram, M., 2012. Assessing the groundwater quality by applying fuzzy logic in GIS environment – a case study in Southwest Iran. Int. J. Environ. Sci. 2 (3), 1798–1806. Rahmanipour, F., Marzaioli, R., Bahrami, H.A., Fereidouni, Z., 2014. Assessment of soil quality indices in agricultural lands of Qazvin Province. Iran. Ecol. Ind. 40, 19–26. Rodrigues de Lima, A.C., Hoogmoed, W., Brussaard, L., 2008. Soil quality assessment in rice production systems: establishing a minimum data set. J. Environ. Qual. 37 (2), 623–630. Saaty, T.L., 2008. Relative measurement and its generalization in decision making, why pairwise comparisons are central in mathematics for the measurement of intangible factors. The Analytic Hierarchy/Network Process. Rev. R. Acad. Cien. Serie A Mat. 102, 251–318. Saaty, T.L., Hu, G., 1998. Ranking by eigenvector versus other methods in the Analytic Hierarchy Process. Appl. Math. Comput. Lett. 11, 121–125. Srivastava, A.K., Nema, A.K., 2011. Fuzzy parametric programming model for integrated solid waste management under uncertainty. J. Environ. Eng. 137 (1), 69–83. Swanepoel, P.A., Du Preez, C.C., Botha, P.R., Snyman, H.A., Habig, J., 2014. Soil quality characteristics of kikuyu-ryegrass pastures in South Africa. Geoderma 232–234, 589–599. Takagi, T., Sugeno, M., 1985. Fuzzy identification of systems and its application to modelling and Control. IEEE Trans. Syst. Man Cybern. 15, 116–132. Tesfahunegn, G.B., 2014. Soil quality assessment for evaluating soil degradation in Northern Ethiopia. App. Environ. Soil Sci., 15, 646502-1-646502/15. Torbert, H.A., Krueger, E., Kurtener, D., 2008. Soil quality assessment using fuzzy modeling. Int. Agrophys. 22 (4), 365–370. Xue, Y.J., Liu, S.G., Hu, Y.M., Yang, J.F., 2010. Soil quality assessment using weighted fuzzy association rules. Pedosphere 20 (3), 334–341. Xue, L., Luo, W., Lu, Y., Wang, T., Chen, C., Giesy, J.P., Zhang, Y., Li, J., Gosens, J., 2011. Status and fuzzy comprehensive assessment of metals and arsenic contamination in farmland soils along the Yanghe River, China. Chem. Ecol. 27 (5), 415–426. Zhang, X., Huang, G.H., 2011. Assessment of BTEX-induced health risk under multiple uncertainties at a petroleum-contaminated site: an integrated fuzzy stochastic approach. Water Resour. Res. 47 (12), W12533/1-W12533/2533.