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Chapter 1

Sustainability Assessment of Solar Technologies Based on Linguistic Information Fausto Cavallaro and Luigi Ciraolo

Abstract The leading role in the decision-making process is generally assigned to the decision maker who evaluates the various alternatives and ranks them. In some circumstances the decision is based on the use of different types of information often affected by uncertainty; thus the decision maker is not able to produce all the information necessary to make a strictly rational choice. In many cases the information can be expressed only by using linguistic labels, e.g. ‘‘very low’’, ‘‘medium’’, ‘‘high’’, ‘‘fair’’, ‘‘very high’’, etc. It is not easy to precisely quantify the rating of each alternative and precision-based methods are often inadequate. Vagueness results when language is used, whether professional or not, to describe the observation or to measure the result of an experiment. This happens particularly when it is necessary to work with experts’ opinions which are translated into linguistic expressions. The use of fuzzy set theory has yielded very good results for modelling qualitative information because of their ability to handle the impreciseness that is common in rating alternatives. In this chapter a modified multicriteria method (F-PROMETHEE) that uses fuzzy sets is proposed to handle linguistic information in comparing a set of solar energy technologies using only linguistic variables.

F. Cavallaro (&) Department of Economics, Management, Society and Institutions, University of Molise, Via De Sanctis, 86100 Campobasso, Italy e-mail: [email protected] L. Ciraolo Department RIAM, University of Messina, P.zza Pugliatti 1, 98121 Messina, Italy e-mail: [email protected]

F. Cavallaro (ed.), Assessment and Simulation Tools for Sustainable Energy Systems, Green Energy and Technology 129, DOI: 10.1007/978-1-4471-5143-2_1, Springer-Verlag London 2013

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F. Cavallaro and L. Ciraolo

1.1 Introduction Targeting renewable sources entails making profound changes to the current organisation of the energy industry; to move towards a system that is increasingly more geographically scattered, technologically advanced and able to handle power generation and demand spread over a wide geographical area. The desired system would be one that: reduces the energy production chain, creates electricity and power directly from the sun and wind, and would gradually allow small users to become increasingly self-sufficient and thus become less dependent on large installations generating and distributing energy. The challenge lies in getting environmental and energy objectives to converge and the overall success of future energy policy will depend on demonstrating that economic growth, an assured energy supply, and environmental protection are compatible goals. Although some technologies exploiting renewable energy sources (RES) have reached a certain maturity, there are numerous hurdles impeding their market penetration. It is fundamental to kick-start the launch of RES in order to accelerate and increase their market share. This strategy would favour the creation of economies of scale and consequently reduce costs. Currently, the intense attention directed towards the environment has prioritised those RES that would have a minimal impact not only on the environment, but also on health and the quality of life. Therefore, this growing awareness of environmental issues has partially modified the traditional decision-making structure in the energy field. Indeed, the need to incorporate strictly qualitative considerations into energy planning has resulted in the adoption of multicriteria decision models. Decision support systems based on multicriteria algorithms do not replace decision makers, rather they assist them in all the phases of the decision-making process by supplying useful information to reach decisions that are transparent with a clearly documented trail. Broadly speaking, the decision is generated by a dynamic and interactive process involving the various players. Nevertheless, the leading role in the decision-making process is generally assigned to the decision maker who evaluates the various alternatives and ranks them. In the decision-making process, decision makers often make great efforts to find the optimal solution. The activity linked to the search for a ‘best compromise’ solution requires a suitable assessment method and the various multicriteria methods available seem best suited to such a purpose. Buchanan et al. (1998), Henig and Buchanan (1996) have argued that good decisions will typically come from a good decision process and suggest that, where possible, the subjective and objective parts of the decision process should be separated. A decision problem can be conceived as comprising two components: a set of objectively defined alternatives and a set of subjectively defined criteria. The relationship between the alternatives and the criteria is described using attributes which describe, as objectively as possible, the features of the alternatives that are relevant to the decision problem. Each criterion attempts to reflect a decision maker’s preference

1 Sustainability Assessment of Solar Technologies

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with respect to a certain feature of the decision problem. These preferences, being specific to a decision maker, are subjective. In many circumstances the decision is affected by uncertainty; thus the decision maker is not able to produce all the information necessary to make a strictly rational choice. In such circumstances it is said that the decision maker works under conditions of bounded rationality and the outcome of the decision will therefore depend on circumstances of which knowledge is imperfect (Simon 1957). In the majority of cases the problem of uncertainty in the evaluation process emerges when the assessor does not have a reasonably clear idea of what the consequences and effects of the decision taken will be. The comparison of the preferability of the various options is based on the probability of random or unknown circumstances occurring. A first source of uncertainty comes from the variability of the data, due to the non-deterministic nature of social and natural phenomena. Another type of uncertainty is the imprecision that appears when observing or measuring the values of a variable, due to both the measuring instrument and the observer undertaking this task. Finally, vagueness results when language is used, whether professional or not, to describe the observation or to measure the result of an experiment. This happens particularly when it is necessary to work with experts’ opinions which are translated into linguistic expressions. The main objective of this study is to propose and to test the validity and effectiveness of a fuzzy multicriteria method called F-PROMETHEE to help the decision-making process to compare a set of solar energy technologies using only linguistic variables (e.g., ‘‘very low’’, ‘‘low’’, ‘‘rather low’’, ‘‘medium’’, ‘‘rather high’’, ‘‘high’’, ‘‘very high’’). This chapter is organised as follows: Sect. 1.2 reviews the literature, Sect. 1.3 describes the main principles of fuzzy linguistic variables and the fuzzy PROMETHEE method, finally Sect. 1.4 is dedicated to the assessment of sustainable solar energy technologies using the proposed approach.

1.2 Linguistic Terms in Decision Making: Literature Review The use of fuzzy set theory has yielded very good results for modelling qualitative information. Fuzziness measures to what extent something is found or to what degree a condition holds. The introduction of fuzzy logic therefore modifies considerably all the underlying principles of traditional logic. A non-dichotomic and approximate approach and the use of linguistic variables and rules in place of traditional mathematical models are the features of fuzzy systems that bring them closer to the way the human mind works. They are propounded mainly as a means by which to attempt a quantitative description of natural language. Fuzzy logic resembles an approach that represents human thinking using empirical rules (sometimes approximate) derived from common sense or from

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experience, but hard to pin down in analytical terms. Fuzzy set theory was introduced by Lofti Zadeh 33 years ago with the publication of a paper that still now constitutes a milestone (Zadeh 1965). It is unlikely that Zadeh could ever have imagined what an impact this theory was to make on so many and so disparate fields, from control to modelling to the programming of calculators and decision support systems. Today, many control systems work using this logic and the number of applications in the field of decision-making systems is greatly increasing. Traditional mathematics is well-suited to modelling and finding solutions to crisp problems or problems in which vague parameters are stochastic. Vagueness includes phenomena that are inherently imprecise (Zadeh 1965; Bellman and Zadeh 1970). In many real situations it is more useful to model linguistic information using fuzzy set theory (Zadeh 1975a, b, c). As suggested by Martinez et al. (2010) different approaches and computational techniques have been proposed to deal with linguistic information. As regards linguistic computational models based on membership functions we can cite: Anagnostopoulos et al. (2008), Chang and Yeh (2002), Chen and Chen (2003), Degani and Bortolan (1988), Chen and Klein (1997), Chen and Tzeng (2004), Chiou et al. (2005), Martin and Klir (2006). Some very interesting papers on the computational model that uses type-2 fuzzy sets to model linguistic terms are the following: Mendel (2002), Turksen (2002), Dongrui and Mendel (2007). Linguistic symbolic computational models can be found in: Yager (1981a), Delgado et al. (1993), Xu (2004), Yager (1993). Finally, about the 2-tuple linguistic computational model the most interesting papers are: Herrera and Martìnez (2000, 2001), Wang and Hao (2006), Xu (2004), Martìnez (2007), Martìnez et al. (2006), Martìnez and Herrera (2012). In recent years, many papers have been developed using linguistic terms for expressing ratings and weight importance within the energy assessment procedure. One important study that has contributed substantially to the advancement of knowledge on this topic is Doukas et al. (2009), which presents an approach to assess the sustainability of renewable energy options. The proposed method extends the numerical method TOPSIS in order to process linguistic terms in the form of 2-tuples thereby reducing the loss of information. Other studies are: García-Cascales and Lamata (2007) who proposed a multicriteria decision method where only linguistic information was available; García-Cascales et al. (2012) used the TOPSIS method to aggregate all the information combined with the use of fuzzy sets in order to model the use of linguistic labels in the process and Kahraman et al. (2012) who analysed the interactions between the criteria using Chouquet integral methodology to determine the best energy alternative in Turkey. The authors claim that the Chouquet integral is a suitable method to capture the vagueness and uncertainty of linguistic variables. Chen et al. (2012) presented a two-phase fuzzy decision-making method based on multigranular linguistic assessment seeking to overcome the drawbacks of ELECTRE and TOPSIS in dealing with decision problem. Yan et al. (2011) proposed a linguistic energy planning model with computation based exclusively on words considering the decision maker’s preference information. Wu and Xu (2012) investigated multiple attribute decision-making (MADM) problems for evaluating investment in


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renewable distributed energy generation using triangular fuzzy linguistic information. Al-Yahyai et al. (2012) proposed an approach in which a linguistic quantifier’s version of AHP-OWA aggregation function was used to classify lands based on their suitability for wind farm installation. Doukas et al. (2012) conducted a thorough investigation of the most appropriate RES technology which can be gradually introduced in the energy sector of Tajikistan. Adopted linguistic variables have been used in multi-dimensional methodology. Kabak and Ruan (2011) suggested a cumulative belief degree approach based on the belief structure. This is used to aggregate the incomplete expert evaluations that are represented with fuzzy linguistic terms. Kaya and Kahraman (2011) proposed a modified fuzzy TOPSIS methodology for the selection of the best energy technology alternative using linguistic terms. Ruan et al. (2010) developed a fuzzy multicriteria group decision software tool to analyse long-term scenarios for belgian energy policy in terms of linguistic variables. Van Der Heide and Triviño 2009, presented a method which is applied to automatically generate linguistic summaries of real-world time series data provided by a utility company. Abouelnaga et al. (2009) use the multiattribute utility theory (MAUT) to optimise the selection process of energy sources. Linguistic appraisal of all attributes was applied to MAUT. Finally, Doukas and Psarras (2009) presented a multiple criteria decision support model for appraising RES options using linguistic variables.

1.3 Use of Linguistic Variables Within Fuzzy PROMETHEE 1.3.1 Fuzzy Sets and Uncertainty: Basic Elements Traditional mathematics is well-suited to modelling and finding solutions to crisp problems or problems in which vague parameters are stochastic. Vagueness includes phenomena that are inherently imprecise (Zimmermann 1983; Munda et al. 1994). The result of any decision-making model depends basically on the availability of information and, since the set of input data can take different forms, the assessment process should give due consideration to this potential lack of uniformity. Generally the information used in decision-making models should be precise, certain, exhaustive and unequivocal. This is not possible in real life and often one is obliged to use data that do not possess these characteristics (Munda et al. 1994), particularly when dealing with problems concerning energy and the environment. In many real-life situations the judgements formulated by a decision maker are often characterised by vagueness. In such cases the level of preference cannot be adequately defined by numerical figures. It is difficult for conventional quantification to express realistically situations that are complex or hard to define. The linguistic variable is extremely useful in such cases, namely to deal with

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situations that are not well-defined but need to be expressed quantitatively. Vagueness includes phenomena which are intrinsically vague such as ‘‘good labour relations’’, ‘‘acceptable profits’’ and ‘‘high visual amenity’’. For example ‘‘environmental impact’’ is a linguistic variable which can be evaluated as: very low, low, medium, high, very high, etc. Clearly, traditional mathematics is not adequate as a tool for modelling these kinds of phenomena, whereas the linguistic variable is useful in dealing with such situations (Zimmermann 1983). The phenomena are represented in words or sentences where each linguistic variable can be modelled by a fuzzy set (fuzzy-numbers). Linguistic terms are intuitively easier to use when decision makers wish to express the subjectivity and imprecision of their assessment. It is for this reason that fuzzy sets are becoming a popular approach to use in assessment procedures. The linguistic approach considers the variables which impinge on the problem being assessed by means of linguistic terms instead of numerical figures. Therefore, a term set is needed that defines the granularity of the uncertainty, which represents the level of distinction among different quantifications of uncertainty (Herrera et al. 2000). Fuzzy sets, as devised by Zadeh, are based therefore on the simple notion of introducing the degree to which an item belongs to a set. Let us assume that symbol X means the universe of discourse, in classical set theory, given a subset A of X each element x 2 X satisfies the condition: either x belongs to A or does not belong to A. A function for belonging can be defined lA ð xÞ which establishes the relationship between the elements x and the set A, and can have only two values, zero or one. The subset A is represented by a function lA : X ! f0; 1g: ( ) 1 if x 2 A ð1:1Þ lA ð xÞ ¼ 0 if x 62 A Fuzzy set theory extends classical theory by introducing the concept of the degree of membership. The theory acknowledges that an element can partially belong to a set, on the basis of a membership function as a real value in the interval [0,1]. For example, the statement ‘‘the air is fresh’’ creates partial conditions: the air can be 20 % fresh and at the same time 80 % not fresh (Kosko and Isaka 1993). A fuzzy set is a set of items in which there are no clear-cut boundaries between the items that belong or do not belong to it. A fuzzy set can be defined as a set of ordered pairs: A ¼ fx; lA ð xÞg;

8x 2 U

ð1:2Þ

The map lA : X ! A defines the space M called the membership space, which is imagined as a closed interval [0, 1], where 0 and 1 represent, respectively, the lowest and greatest degree of membership. Thus, for 0\lA ð xÞ\1, x belongs to A only up to a certain degree. The underlying assumption is that a fuzzy set, despite the vagueness of its boundaries, can be precisely defined by associating a number of between 0 and 1 to each element x [ A.


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1.3.2 Fuzzy Numbers Fuzzy numbers are useful tools when working with imprecise numerical figures, such as ‘‘about 8’’, ‘‘nearly 10’’ and ‘‘between 5 and 10’’. The use of fuzzy set theory allows them to be represented correctly, as fuzzy subsets of the set of real numbers. A fuzzy number is a convex and normalised fuzzy set defined on the set < of real numbers. A triangular fuzzy number (TFN) is generally written as A ¼ ða; m; bÞ. The concept of a triangular number can be demonstrated by an example; if asked to hypothesise what the CO2 per kWh will be, we can reply ‘‘approximately 150 g/kWh’’. When an uncertain value has to be defined, a can be considered the smallest possible value, b as the largest possible value and m as the most plausible value. A TFN is defined via a triplet of the type A ¼ ða; m; bÞ where a and b are the lower and higher extremes of the figure while m is the element to which the highest degree of membership attaches (Fig. 1.1). 8 xa < ma ; a x m bx lAð xÞ ¼ bm ; mxb ð1:3Þ : 0; otherwise

1.3.3 The PROMETHEE Method and Fuzzy Approach The preference ranking organization method of enrichment evaluation (PROMETHEE) method was devised by Brans and Vincke (1985), Brans and Mareschal (1994, 1998), Brans et al. (1986). This technique is based on ranking and is wellsuited to problems in which there are a finite number of actions to be assessed on the basis of a range of conflicting criteria. Once the set of criteria and the alternatives have been selected then the payoff matrix is built. This matrix tabulates, for each criterion–alternative pair, the Fig. 1.1 A triangular fuzzy number

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quantitative and qualitative measures of the effect produced by that alternative with respect to that criterion. The matrix may on a cardinal contain data measured or an ordinal scale. Each alternative Ai ¼ ai;1 ; . . .ai;j ; . . .; ai;m is composed of a group of evaluations aij representing the evaluation given to the alternative i with respect to the criteria j. For each criterion the decision maker can choose from a set of six different types of preference functions to model the decision maker’s preferences. A preference function Pk(d) is associated with each criterion and represents the difference between the value of the two alternatives, thus it can be expressed as follows (Brans and Mareschal 1998): Pk ð a i ; a m Þ ¼ P k ½ d ð a i ; a m Þ

ð1:4Þ

Pk ðck ðai Þ ck ðam ÞÞ ¼ Pk ðdÞ 2 ½0; 1

ð1:5Þ

The degree of preference of an alternative ai in comparison to am is expressed by a number between 0 and 1 (from 0 indicating no preference or indifference up to 1 for an outright preference). Once the decision maker has described the preference function Pk (k = 1, 2, 3,…n represent the criteria) then a vector containing the weights of each criterion must be defined as W T ¼ ½w1 ; . . .; wk . The weights p represent the relative importance of the criteria used for the assessment. In addition to weighting, the method involves setting thresholds that delineate the decision maker’s preferences for each criterion and the critical thresholds are thus: the indifference threshold qi and the preference threshold pi (a more exhaustive description of the procedure can be found in the literature). The degrees of preference are used to estimate the index of preference P calculated for each pair of actions ai and am as the weighted average of preferences calculated for each criterion. The index P is therefore defined as follows (Brans et al 1986): Y

K P

ð ai ; am Þ ¼

wk Pk ðck ðai Þ ck ðam ÞÞ

k¼1 K P

ð1:6Þ Wk

k¼1

The preference index P (ai, am) represents the strength of the decision maker’s preference for action ai over action am considering all criteria simultaneously and P (am, ai) how much am is preferred above ai. Its value falls between 0 and 1. Finally, we can consider how each alternative ai 2 A is evaluated against (n-1) another in A and thereby define the two following outranking flows (Brans et al. 1986; Brans and Mareschal 1994): Uþ ðai Þ ¼

X 1 P ð ai ; am Þ n 1 x2A

ð1:7Þ

This indicates a preference for action ai above all others and shows how ‘good’ action ai is (positive outranking flow).


U ðai Þ ¼

X 1 P ð am ; ai Þ n 1 x2A

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ð1:8Þ

This indicates a preference for all the other actions compared with ai and shows how weak action ai is (negative outranking flow). According to PROMETHEE I ai is superior to am if the leaving flow of ai is greater than the leaving flow of am and the entering flow of ai is smaller than the entering flow of am. (for further explanation see the method). PROMETHEE I method can provide a partial preorder of the alternatives, whereas the PROMETHEE II method can give the complete preorder by using a net flow, although it loses much of the information of preference relations. Under the PROMETHEE I method some actions remain incomparable, in this case a complete preorder is required that eliminates any incomparable items, then PROMETHEE II can give a complete ranking as follows (Brans and Mareschal 1994): Unet ðai Þ ¼ Uþ ðai Þ U ðai Þ

ð1:9Þ

The net flow is the difference between the outflow and the inflow. The fuzzy PROMETHEE method is preferable because crisp numbers are not adequate to express accurately the qualitative data used for the application analysed. The first studies in the literature to develop an integration between PROMETHEE and fuzzy numbers were proposed by Le Teno and Mareschal (1998), Geldermann et al. (2000), Goumas and Lygerou (2000). Other interesting applications have been developed in recent years by Bilsel et al. (2006), Tuzkaya et al. (2010), Chou et al. (2007), Li and Li (2009), Giannopoulos and Founti (2010), Oberschmidt et al. (2010), Yuen and Ting (2012), Liu and Guan (2009), Halouani et al. (2009), Lee and To (2010), Yang et al. (2012), Shirinfar and Haleh (2011), Zhang et al. (2009), Moreira et al. (2009), Chen et al. (2011a, b). In this chapter the performances of qualitative criteria are considered as linguistic variables and translated into fuzzy numbers. The semantics of the elements of the set of linguistic terms is provided by fuzzy numbers defined in the interval (0,1) and by the membership functions. We have used linear triangular membership functions as being fit to capture the vagueness of the linguistic assessments. The linguistic variables can be represented as positive TFNs as shown in Fig. 1.1. According to Dubois and Prade (1978), the representation of a TFN can be presented in the form x = (m,a,b)LR. If the variable x is equivalent to the value m, its membership function is f(x) = 1. Where its value is smaller than (m-a) and larger than (m ? b), it does not belong to the set and f(x) = 0. If its value falls within the interval between m-a \ x\m ? b, its degree of membership is a number between 0 and 1. The letters L and R are used to refer to the left and right spreads of m. The following F-PROMETHEE equations are based on the representation of a TFN (m, a, b). When a linear preference function, with preference p and indifference q threshold, is selected (type V), on introducing the fuzzy numbers the evaluation function becomes as follows (Goumas and Lygerou 2000):

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(a)

(b)

(e)

(c)

(f)

(d)

(g)

Fig. 1.2 Solar technologies. a Solar tower (SPT). Source OECD/IEA; b Parabolic solar trough (PST). Source OECD/IEA; c Compact linear Fresnel (CLFR) Source OECD/IEA; d Dish stirling (DS). Source OECD/IEA; e Photovoltaic in buildings (PVbuild). Source NREL; f Photovoltaic centralised (PVcentr). Source First solar; g Solar chimney (SC). Source Schlaich et al. 2005

Pk ð a i ; am Þ ¼

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