using of the fuzzy topsis and fuzzy ahp methods for ...

INTERNATIONAL JOURNAL Of ACADEMIC RESEARCH

Vol. 3. No. 1. January, 2011, Part III

USING OF THE FUZZY TOPSIS AND FUZZY AHP METHODS FOR WASTEWATER TREATMENT PROCESS SELECTION 1

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A.R. Karimi , N. Mehrdadi , S.J. Hashemian , Gh.R. Nabi-Bidhendi , R. Tavakkoli-Moghaddam

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1

Ph.D. Student of Environmental Engineering, Faculty of Environment, University of Tehran, 2 Associate Professor, Faculty of Environment, University of Tehran, 3 Associate Professor, Institute of Water & Energy, Sharif University of Technology, 4 Professor, Faculty of Environment, University of Tehran, 5 Professor, Department of Industrail Engineering, University of Tehran, Tehran (IRI) E-mails: [email protected], [email protected], [email protected], [email protected], [email protected] ABSTRACT Selection of the wastewater treatment process is a multi-criteria decision making (MCDM) problem. The conventional methods for process selection are inadequate for dealing with the imprecise or vague nature of linguistic assessment. To overcome this difficulty, fuzzy MCDM methods are proposed. The aim of this study is to use the fuzzy order preference by similarity to ideal solution (TOPSIS) and fuzzy analytic hierarchy process (AHP) methods, as wellknown tools in MCDM, for selection of the treatment process. This paper investigates five different anaerobic wastewater treatment processes operated in Iranian industrial estates. These processes are Up-flow Anaerobic Sludge Blanket (UASB), Up-flow Anaerobic Fix-Bed Reactor (UAFB), Anaerobic Baffled Reactor (ABR), Contact process, and Anaerobic Lagoon. Then, the most appropriate treatment process is selected by using of the proposed methods. Based on general condition in industrial estate's wastewater treatment plants, technical, economic, environmental, and administrative criteria are weighted and then criteria evaluation and priorities of alternatives have been done by fuzzy TOPSIS and fuzzy AHP methods by the use of triangular fuzzy numbers. Finally, selection of these five processes is ranked by these foregoing methods, in which their differences are discussed. Key words: Fuzzy TOPSIS; Fuzzy AHP; MCDM; Anaerobic wastewater treatment process; Industrial estates. 1. INTRODUCTION Appropriate treatment process selection is an important issue before designing and implementing each wastewater treatment plant (WWTP). According to quantity diversity of industrial wastewater and local condition of effluent sources, it is impossible to use general criteria in treatment process selection. However, some points are available in process selection which is applied for almost all kinds of industrial wastewater to achieve the prior treatment process. The general procedure for making process selection usually consists of the following steps:  Decide on the criteria that will be used to evaluate alternatives.  Identify criteria that are important.  Develop treatment alternatives.  Evaluate alternatives and select the best one. Designers should consider both quantitative and qualitative criteria very well [1-3]. There are many criteria that influence the treatment process selection. In this study, following four criteria and their sub-criteria take into consideration. 1) Technical criteria, such as performance, reliability, process applicability, resistance to hydraulic shocks, consistency to organic loading shocks, adaptability, compatibility, less electromechanical facilities. 2) Economic criteria, such as capital cost, operation & maintenance cost, sludge disposal cost, land requirement and energy requirement. 3) Environmental criteria, such as treatment degree requirement, odor generation, visual and safety. 4) Administrative criteria, such as technical skills requirements, simple operation, simple maintenance, local availability to facilities and stability of wastewater treatment plant operation and use of online monitoring. In real-world situation, the evaluation data of the treatment process suitability for various subjective criteria and the weights of the criteria are usually expressed in linguistic terms. So, to efficiently resolve the ambiguity frequently arising in available information and do more justice to the essential fuzziness in human judgment and preference, the fuzzy set theory has been used to establish multiple criteria decision-making (MCDM) problems [4]. In this paper, Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) and Analytical Hierarchy Process (AHP) methods in a fuzzy environment are proposed for treatment process selection, in which the ratings of various alternatives under various subjective criteria and the weights of all criteria are represented by fuzzy numbers. Although, there are many studies in the literature that use fuzzy TOPSIS and fuzzy AHP methods for different MCDM problems; however, we propose these methods for the anaerobic treatment process selection. Then, the related results are compared with each other. There are many applications of fuzzy TOPSIS in the literature. Chu (2002) presented a fuzzy TOPSIS method under group decisions for solving the facility location selection problem [5]. Chen et al. (2006) presented a fuzzy TOPSIS approach to deal with the supplier selection problem in a supply chain system [6]. Yang and Hung (2007) used TOPSIS and fuzzy TOPSIS methods for a plant layout design problem [7].

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The AHP method, which was first introduced by Saaty (1980), is an effective method for solving MCDM problems [8]. It has been widely used for multi-criteria decision making and applied to many practical problems successfully. Traditional AHP requires exact or crisp judgments. However, due to the complexity and uncertainty involved in real-world decision problems, decision makers may be more reluctant to provide crisp judgments than fuzzy ones. Furthermore, even when they use the same words, individual judgments of events are invariably subjective, and the interpretations attached to the same words may differ. This is why fuzzy numbers and fuzzy sets have been introduced to characterize linguistic variables used to represent the imprecise nature of human cognition when we try to translate people’s opinions into spatial data. The preferences in AHP are essentially human judgments based on human perceptions, so fuzzy approaches allow for a more accurate description of the decision-making process [9]. A number of methods have been developed to handle fuzzy AHP. The first study of fuzzy AHP was proposed by Van Laarhoven and Pedrycz (1983) who compared fuzzy ratios described by triangular fuzzy numbers [10]. Anagnostopoulos et al., (2007) performed the fuzzy extension of AHP in order to evaluate alternative wastewater treatment process with the use of economic, environmental and social criteria [11]. 2. MATERIALS AND METHODS To consider anaerobic treatment processes and related efficiency in industrial estates, a field study is carried out. The data analysis and related questionnaires are used for determining the processes efficiency. Process selection criteria have been issued on the basis of objectivity in industrial estates and the fuzzy TOPSIS and fuzzy AHP methods specified for the processes assessment and selection. 2.1. Anaerobic Treatment Alternatives This paper considers five anaerobic treatment processes, which are operating in Iran industrial estates. These are as follows: 1) Up-flow Anaerobic Sludge Blanket (UASB) operating in 9 industrial estates in Iran; 2) Upflow Anaerobic Fixed Bed (UAFB),operating with 7 reactors currently; 3) Anaerobic Baffled Reactors (ABR) used as an anaerobic system of many treatment plants in Iran's industrial estates; 4) Contact anaerobic process operating as an anaerobic system of Abbarik Industrial estate's treatment plant successfully, and designing in some other estates; and 5) Anaerobic lagoons operating in some wastewater treatment plants of industrial estates in Iran. 2.2. Fuzzy TOPSIS Method The TOPSIS method was firstly proposed by Hwang and Yoon (1981). The basic concept of this method is that the chosen alternative should have the shortest distance from the positive ideal solution and the farthest distance from a negative ideal solution [12]. A positive ideal solution is a solution that maximizes the benefit criteria and minimizes cost criteria; whereas, a negative ideal solution maximizes the cost criteria and minimizes the benefit criteria [13]. In the classical TOPSIS method, the weights of the criteria and the ratings of alternatives are known precisely and crisp values are used in the evaluation process. However, under many conditions crisp data are inadequate to model real-life decision problems. Therefore, the fuzzy TOPSIS method is proposed, in which the weights of criteria and ratings of alternatives are evaluated by linguistic variables represented by fuzzy numbers to deal with the deficiency in the traditional TOPSIS [14]. This paper presents an extension of the TOPSIS method proposed by Chen (2000) and Chen et al. (2006). The related algorithm can be described as follows [6, 15]: Step 1: A committee of the decision-makers is formed. Fuzzy rating of each decision maker, Dk= (k=1, 2,...,K), can be represented as triangular fuzzy number

~ Rk  (k  1, 2 ,..., K ) with membership function  R~k ( x)

Step 2: Criteria evaluation is determined. Step 3: After that, appropriate linguistic variables are chosen for evaluating criteria and alternatives. Step 4: Then the weight of criteria are aggregated. The aggregated fuzzy rating can be determined by:

~ R  (a, b, c ), k  1,2,..., K . where, a  min ak , b  k

1 K

K

 b , c  max c  k

k 1

k

k

(1)

1 K cijk  (2)  bijk , cij  max k k K k 1 ~ Then, the aggregated fuzzy weights wij  of each criterion are calculated by: w~   w , w , w  (3) aij  minaijk , bij 

j

where,

j1

j2

j3

w j1  min w jk 1, w j 2  k

1 K w jk 3   w jk 2 , w j 3  max k k k 1

(4)

Step 5: Then the fuzzy decision matrix is constructed. Step 6: The above matrix is normalized. Step 7: Considering the different weight of each criterion, the weighted normalized decision matrix is computed by multiplying the importance weights of evaluation criteria and the values in the normalized fuzzy decision matrix.

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Vol. 3. No. 1. January, 2011, Part III *



Step 8: Then, the fuzzy positive ideal solution (FPIS, A ) and fuzzy negative ideal solution (FNIS, A ) are determined by:

A*  (v~1* , ~ v2* , ..., v~n* ) , A  (v~  , v~  , ..., ~ v ) 1

Where,

(5) (6)

n

2

~ v j*  maxvij 3

and

i

v~j  min vij1 i

i=1,2,…,m ; j=1,2,…,n Step 9: Then, the distance of each alternative from FPIS and FNIS are calculated by: n

di*   dv (~ vij , ~ v j* )

i=1, 2, …, m

(7)

j 1 n

d i   d v (~ vij , ~ v j )

i=1, 2, …, m

(8)

j 1

where, dv(.,.) is the distance measurement between two fuzzy numbers. Step 10: A closeness coefficient (CCi) is defined to rank all possible alternatives. The closeness coefficient represents the distances to the fuzzy positive ideal solution

( A )

( A* )

and fuzzy negative ideal solution

simultaneously. The closeness coefficient of each alternative is calculated by:

CCi 

d i d i*  d i

,

i=1, 2, …, m

(9)

Step 11: According to the closeness coefficient, the ranking of the alternatives can be determined. Obviously, according to Eq. (9), alternative Ai will be closer to FPIS and farther from FNIS as CCi approaches to1. 2.3. Fuzzy analytic hierarchy process In the fuzzy extension of AHP, the weights of the nine level fundamental scales of judgments are expressed via the triangular fuzzy numbers (TFN) in order to represent the relative importance among the hierarchy's criteria [16]. A TFN is fully characterized by a triple of real numbers (l, m, u), where parameter m gives the maximal grade of the membership function µ(x), and parameters l and u are the lower and upper bounds that limit the field of the possible evaluation [16-17].

 ( x  l ) /( m  l ) x  [l , m]   ( x )  (u  x ) /( u  m ) x  [ m, u ]  0 otherwise 

(10)

The Fuzzy AHP method is a popular approach for MCDM that has been widely used in the literature. In this paper, the extent fuzzy AHP is utilized, which was originally introduced by Chang (1996) [18]. The steps of the Chang’s (1996) extent analysis can be given as follows: Step 1: The value of the fuzzy synthetic extent with respect to the i-th object is defined by: m

Si   M j 1

j gi

n m    M gji   i 1 j 1 

1

(11)

j

where, all the M g (j=1,2,…,m) are triangular fuzzy numbers. i

Step 2: As M1= (l1, m1, u1) and M2= (l2, m2, u2) are two triangular fuzzy numbers, the degree of possibility of M1≥ M2 is defined by:

  1, if m 2  m1  V (M 2  M 1 )  0, if l1  u 2  l1  u 2 ,   (m2  u 2 )  (m1  l1 )

(12)

otherwise

Step 3: To compare M1and M2, we need both the values of V(M1≥ M2) and V(M2≥ M1). The degree possibility for a convex fuzzy number to be greater than k convex fuzzy numbers

M i (i  1,2,..., k ) can be defined by: V (M  M1 , M 2 ,..., M k )

(13)

 V [( M  M 1 ) and ( M  M 2 ) and...and ( M  M k )  min V ( M  M i ) ,

i  1,2,..., k

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Vol. 3. No.1. January, 2011, Part III

d ( Ai )  min V ( Si  S k ) For k =1,2,...,n ; k≠i.

Then the weight vector is given by:

W   (d ( A1 ), d ( A2 ),..., d ( An )) T where,

(14)

Ai (i  1,2,..., n) are n elements.

Stop 4: Via normalization, the normalized weight vectors are:

W  (d ( A1 , d ( A2 ),..., d ( An ))T

(15)

where, W is a non-fuzzy number. 3. RESULTS AND DISCUSSION Combined anaerobic–aerobic processes have more attended due to industrial unit and related wastewater diversity, and quantitative and qualitative variation of effluents. According to object of this paper, a different method of operating anaerobic processes in wastewater treatment plants of industrial estates in Iran have been surveyed. This process including UASB, UAFB, ABR, contact process and anaerobic lagoons has investigated. Fuzzy TOPSIS and fuzzy AHP methods as assessment tools have been used to select an effective treatment process. Tables 1 and 2 illustrate linguistic variables and related triangular fuzzy numbers to assess the criteria weight importance and alternatives grading, respectively. Table 1. Linguistic variables for the importance weight of each criterion Linguistic variables Very low (VL) Low (L) Medium low (ML) Medium (M) Medium high (MH) High (H) Very high (VH)

Triangular fuzzy numbers (0, 0, 0.2) (0.1, 0.2, 0.3) (0.2, 0.35, 0.5) (0.4, 0.5,0.6) (0.5, 0.65, 0.8) (0.7, 0.8, 0.9) (0.8, 1,1)

Table 2. Linguistic variables for ratings Linguistic variables Very poor (VP) Poor (P) Medium poor (MP) Fair (F) Medium good (MG) Good (G) Very good (VG)

Triangular fuzzy numbers (0, 0, 2) (1, 2, 3) (2, 3.5, 5) (4, 5, 6) (5, 6.5, 8) (7, 8, 9) (8, 10, 10)

3.1. Application with a Fuzzy TOPSIS method In this section, fuzzy TOPSIS method is used for the anaerobic treatment process selection. Decisionmakers evaluated the importance of criteria by using the linguistic variables which are illustrated in Table 1. The importance weights of the criteria are shown in Table 3. Linguistic variables presented in Table 2 are used for rating of alternatives assessment regarding to each criterion. Regarding to the mentioned baselines, grades of 5 alternatives have been issued according to four criteria as shown in Table 4. Then, the fuzzy decision matrix is formed on the basis of triangular fuzzy numbers related to criteria and alternatives. Finally, the fuzzy weights of alternatives are determined. Table 5 shows the result of the mentioned functions. The normalized fuzzy decision matrix is formed as shown in Table 6. Finally, the weighted normalized fuzzy decision matrix is formed on the basis of Table 6 and the related results are presented in Table 7. Table 3. Importance weight of the criteria from three decision-makers Criteria Technical Economical Environmental Administrative

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Linguistic variables DM1 DM2 DM3 VH H VH H MH MH H VH VH MH H H

Triangular fuzzy numbers (0.7, 0.93,1) (0.5, 0.7, 0.9) (0.7, 0.93,1) (0.5, 0.75, 0.9)

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Vol. 3. No. 1. January, 2011, Part III

Table 4. Ratings of alternatives by the decision-makers under four criteria Criteria

Linguistic variables DM1 DM2 DM3 MG MG MG G G G MG G G G MG MG G G G G G G G G G VG VG VG MG MG MG F F F G MG MG G G G MG MG G MG MG MG F F F F F F MG MG MG MG G G G G G G MG G

Alternatives UASB UAFB ABR Contact Process Anaerobic Lagoon UASB UAFB ABR Contact Process Anaerobic Lagoon UASB UAFB ABR Contact Process Anaerobic Lagoon UASB UAFB ABR Contact Process Anaerobic Lagoon

Technical

Economical

Environmental

Administrative

Triangular fuzzy numbers (5, 6.5, 8) (7, 8, 9) (5, 7.5, 9) (5, 7, 9) (7, 8, 9) (7, 8, 9) (7, 8, 9) (8, 10, 10) (5, 6.5, 8) (4, 5, 6) (5, 7, 9) (7, 8, 9) (5, 7, 9) (5, 6.5, 8) (4, 5, 6) (4, 5, 6) (5, 6.5, 8) (5, 7.5, 9) (7, 8, 9) (5, 7.5, 9)

Table 5. Fuzzy decision matrix and fuzzy weights of alternatives Alternatives Criteria Technical Economical Environmental Administrative

UASB

UAFB

ABR

(5, 6.5, 8) (7, 8, 9) (5, 7, 9) (4, 5, 6)

(7, 8, 9) (7, 8, 9) (7, 8, 9) (5, 6.5, 8)

(5, 7.5, 9) (8, 10, 10) (5, 7, 9) (5, 7.5, 9)

Contact Process (5, 7, 9) (5, 6.5, 8) (5, 6.5, 8) (7, 8, 9)

Weight

Anaerobic Lagoon (7, 8, 9) (4, 5, 6) (4, 5, 6) (5, 7.5, 9)

(0.7, 0.93,1) (0.5, 0.7, 0.9) (0.7, 0.93,1) (0.5, 0.75, 0.9)

Table 6. Normalized fuzzy decision matrix Criteria

UASB

UAFB

ABR

Technical Economical Environmental Administrative

(0.5, 0.65, 0.8) (0.7, 0.8, 0.9) (0.5, 0.7, 0.9) (0.4, 0.5, 0.6)

(0.7, 0.8, 0.9) (0.7, 0.8, 0.9) (0.7, 0.8, 0.9) (0.5, 0.65, 0.8)

(0.5, 0.75, 0.9) (0.8, 1, 1) (0.5, 0.7, 0.9) (0.5, 0.75, 0.9)

Contact Process (0.5, 0.7, 0.9) (0.5, 0.65, 0.8) (0.5, 0.65, 0.8) (0.7, 0.8, 0.9)

Anaerobic Lagoon (0.7, 0.8, 0.9) (0.4, 0.5, 0.6) (0.4, 0.5, 0.6) (0.5, 0.75, 0.9)

Table 7. Weighted normalized fuzzy decision matrix Criteria Technical Economical Environmental Administrative

UASB

UAFB

ABR

(0.35,0.6,0.8) (0.35,0.56,0.81) (0.35,0.65,0.9) (0.2,0.38,0.54)

(0.49,0.74,0.9) (0.35,0.56,0.81) (0.49,0.74,0.9) (0.25,0.49,0.72)

(0.35,0.7,0.9) (0.4,0.7,0.9) (0.35,0.65,0.9) (0.25,0.56,0.81)

Contact Process (0.35,0.65,0.9) (0.25,0.45,0.72) (0.35,0.6,0.8) (0.35,0.6,0.81)

Anaerobic Lagoon (0.49,0.74,0.9) (0.2,0.35,0.54) (0.28,0.46,0.6) (0.25,0.56,0.81)

After the weighted normalized fuzzy decision matrix is formed, the fuzzy positive ideal solution (FPIS) and fuzzy negative ideal solution (FNIS) are determined by: A* = [(0.9,0.9,0.9),(0.9,0.9,0.9),(0.9,0.9,0.9),(0.81,0.81,0.81)] A = [(0.35,0.35,0.35),(0.2,0.2,0.2),(0.28,0.28,0.28),(0.2,0.2,0.2)] Then, the distance of each alternative from the FPIS and FNIS with respect to each criterion is calculated by using the vertex method by:

1 (0.9  0.35) 2  (0.9  0.6) 2  (0.9  0.8) 2  0.37 3



d ( A1 , A* )  d ( A1 , A ) 



1 (0.35  0.35) 2  (0.35  0.6) 2  (0.35  0.8) 2  0.30 3





Here only the calculation of the distance of the first alternative to the FPIS and FNIS for the first criterion is shown, as the calculations are similar in all steps. The results of all alternatives’ distances from the FPIS and FNIS are shown in Tables 8 and 9.

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Table 8. Distances between alternatives and A with respect to each criterion Technical *

d(A1,A ) * d(A2,A ) * d(A3,A ) * d(A4,A ) * d(A5,A )

Economical

0.37 0.25 0.34 0.35 0.25

Environmental

Administrative

0.35 0.25 0.35 0.37 0.47

0.46 0.38 0.35 0.29 0.35

0.38 0.38 0.31 0.47 0.55 −

Table 9. Distances between alternatives and A with respect to each criterion Technical

Economical

Environmental

Administrative

0.30 0.40 0.38 0.36 0.40

0.42 0.42 0.51 0.34 0.21

0.42 0.46 0.42 0.36 0.21

0.22 0.34 0.41 0.43 0.41

-

d(A1,A ) d(A2,A ) d(A3,A ) d(A4,A ) d(A5,A )

Then closeness coefficients of alternatives are calculated by Eq. (6). According to the closeness coefficient of alternatives, the ranking order of alternatives is determined. The first alternative is determined as the most appropriate anaerobic process for industrial estates. Value of this parameters and final ranking order of alternatives are presented in Table 10. *

-

Table 10. Computation of di , di and CCi and the rating order of alternatives

*

di di CCi

UASB

UAFB

ABR

1.55 1.36 0.467

1.26 1.62 0.563

1.36 1.72 0.559

Contact process 1.47 1.48 0.502

Anaerobic lagoon 1.63 1.24 0.431

Ranking order UAFB > ABR > Contact process > UASB > Anaerobic lagoon

3.2. Application with fuzzy AHP method In this section, the fuzzy AHP method is proposed for the same problem of the anaerobic treatment process. A group decision is used based on fuzzy AHP. Firstly, each decision-maker (Dp), individually carry out pair-wise comparison as shown in Eq. (16):

 b11 p b 21 p Dp      bm1 p

b12 p b221 p  bm 2 p

 b1mp   b2 mp       bmmp 

p=1, 2, …, t

(16)

The pair-wise comparison of three decision-makers for the four criteria is as follows:

C1 D1  C2 C3 C4

C1 D2  C 2 C3 C4 C1 D3  C2 C3 C4

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C1  1 1 / 3  1 / 3  1 / 5 C1  1 1 / 3   3   1 C1  1 1/ 5   1  1 / 3

C2 C3 C4 3 3 5 1 1 3 1 1 3  1 / 3 1 / 3 1 C 2 C3 C4 3 1/ 3 1  1 1 / 5 1 / 3 5 1 3   3 1/ 3 1  C2 C3 C4 5 1 3  1 1 / 5 1 / 3 1/ 5 1 3   3 1/ 3 1 

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Then, a comprehensive pair-wise comparison matrix is built as shown in Table 11 by integrating the grades of three decision-makers via Eq. (17). By this way, the pair-wise comparison values of the decision-makers are transformed into triangular fuzzy numbers. t

b l je  min(b jep ) , m je 

jep

p 1

,

p

p=1,2,…,t

u je  max(b jep )

j=1,2,…,m

~ b je  (l je , m je , u je ) ,

(17)

e=1,2,…,m

j=1,2,…,m

e=1,2,…,m

Table 11. Fuzzy evaluation matrix with respect to goal Tech. Criteria (C1) (1, 1, 1) (0.2,0.29, 0.33) (0.33, 1.44, 3) (0.2, 0.51, 1)

Tech. Criteria (C1) Eco. Criteria (C2) Env. Criteria (C3) Admin. Criteria (C4)

Eco. Criteria (C2) (3, 3.67, 5) (1, 1, 1) (0.2, 2.07, 5) (0.33, 2.11, 3)

Env. Criteria (C3) (0.33, 1.44, 3) (0.2, 0.47, 1) (1, 1, 1) (0.33, 0.33, 0.33)

Admin. Criteria (C4) (1, 3, 5) (0.33, 1.22, 3) (3, 3, 3) (1, 1, 1)

From Table 11, according to the extent analysis synthesis, the value respect to the main goal is calculated as the same as Eq. (11): Sc1  (5.33, 9.11, 14)  (1 / 36.66, 1/ 23.55, 1/ 13.45) = (0.145, 0.387, 1.041)

Sc 2  (1.73, 2.98, 5.33)  (1 / 36.66, 1 / 23.55, 1 / 13.45) = (0.047, 0.127, 0.396) Sc3  (4.53, 7.51, 12)  (1/ 36.66, 1/ 23.55, 1/ 13.45) = (0.124, 0.387, 0.892) Sc 4  (1.86, 3.95, 5.33)  (1 / 36.66, 1 / 23.55, 1 / 13.45) = (0.051, 0.168, 0.396) These fuzzy values are compared by using Eq. (12), and these values are obtained by:

V (Sc1  Sc3 )  1,

V ( S c1  S c 2 )  1 , V (Sc2  Sc1 )  0.491,

V ( S c 2  S c 3 )  0.511 ,

V (S c3  S c1 )  1 , V ( Sc 4  Sc1 )  0.534 ,

V (Sc1  Sc 4 )  1 V (Sc 2  Sc 4 )  0.894

V (Sc3  Sc 4 )  1

V (Sc 3  Sc 2 )  1 ,

V ( Sc 4  Sc 2 )  1 ,

V ( S c 4  S c 3 )  0.554

Then, priority weights are calculated by using Eq. (13):

d (C1 )  min(1, 1, 1)  1 d (C 2 )  min(0.491, 0.511, 0.894)  0.491 d (C 3 )  min(1, 1, 1)  1 d (C 4 )  min( 0.534,1, 0.554)  0.534 Priority weights form W   (1, 0.491, 1, 0.534 ) vector. After the normalization of these values priority weight respect to main goal is calculated as (0.331, 0.162, 0.331, 0.176). After the priority weights of the criteria are determined, the priority of the alternatives is determined for each criterion. From the pair-wise comparison of the decision makers for five alternatives, evaluation matrixes are formed as illustrated in Tables 12 to 15. Then, priority weights of alternatives for each criterion are determined by making the same calculation as shown Table 16. Table 12. Fuzzy evaluation matrix with respect to technical criteria (C1) Tech. Criteria (C1) UASB UAFB ABR Contact process Anaerobic Lagoon

UASB

UAFB

ABR

Contact process

(1, 1, 1) (0.88, 1.23, 1.8) (0.63, 1.15, 1.8) (0.63, 1.08, 1.8) (0.88, 1.23, 1.8)

(0.56, 0.81, 1.14) (1, 1, 1) (0.56, 0.94, 1.29) (0.56, 0.88, 1.29) (0.78, 1, 1.29)

(0.56, 0.87, 1.6) (0.78, 1.07, 1.8) (1, 1, 1) (0.56, 0.93, 1.8) (0.78, 1.07, 1.8)

(0.56, 0.93, 1.6) (0.78, 1.14, 1.8) (0.56, 1.07, 1.8) (1, 1, 1) (0.78, 1.14, 1.8)

Anaerobic Lagoon (0.56, 0.81, 1.14) (0.78, 1, 1.29) (0.56, 0.94, 1.29) (0.56, 0.88, 1.29) (1, 1, 1)

Table 13. Fuzzy evaluation matrix with respect to economic criteria (C2) Eco. Criteria (C2) UASB UAFB ABR Contact process Anaerobic Lagoon

UASB

UAFB

ABR

(1, 1, 1) (0.78, 1, 1.29) (0.89, 1.25, 1.43) (0.56, 0.83, 1.14) (0.44, 0.63, 0.86)

(0.78, 1, 1.29) (1, 1, 1) (0.89, 1.25, 1.43) (0.56, 0.83, 1.14) (0.44, 0.63, 0.86)

(0.7, 0.8, 1.13) (0.7, 0.8, 1.13) (1, 1, 1) (0.5, 0.66, 1) (0.4, 0.5, 0.75)

Contact process (0.88, 1.28, 1.8) (0.88, 1.23, 1.8) (1, 1.54, 2) (1, 1, 1) (0.5, 0.77, 1.2)

Anaerobic Lagoon (1.17, 1.6, 2.25) (1.17, 1.6, 2.25) (1.33, 2, 2.5) (0.83, 1.32, 2) (1, 1, 1)

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Table 14. Fuzzy evaluation matrix with respect to environmental criteria (C3) Env. Criteria (C3)

UASB

UASB UAFB ABR Contact process Anaerobic Lagoon

(1, 1, 1) (0.78, 1.14, 1.8) (0.56, 1, 1.8) (0.56, 0.93, 1.6) (0.44, 0.71, 1.2)

UAFB

ABR

(0.56, 0.88, 1.29) (1, 1, 1) (0.56, 0.88, 1.29) (0.56, 0.81, 1.14) (0.44, 0.63, 0.86)

(0.56, 1, 1.8) (0.78, 1.14, 1.8) (1, 1, 1) (0.56, 0.93, 1.6) (0.44, 0.71, 1.2)

Contact process (0.63, 1.08, 1.8) (0.88, 1.23, 1.8) (0.63, 1.08, 1.8) (1, 1, 1) ((0.5, 0.77, 1.2)

Anaerobic Lagoon (0.83, 1.4, 2.25) (1.17, 1.6, 2.25) (0.83, 1.4, 2.25) (0.83, 1.3, 2) (1, 1, 1)

Table 15. Fuzzy evaluation matrix with respect to administrative criteria (C4) Admin. Criteria (C4) UASB UAFB ABR Contact process Anaerobic Lagoon

UASB

UAFB

ABR

Contact process

(1, 1, 1) (0.83, 1.3, 2) (0.83, 1.5, 2.25) (1.17, 1.6, 2.25) (0.83, 1.5, 2.25)

(0.5, 0.77, 1.2) (1, 1, 1) (0.63, 1.15, 1.8) (0.88, 1.23, 1.8) (0.63, 1.15, 1.8)

(0.44, 0.67, 1.2) (0.56, 0.87, 1.6) (1, 1, 1) (0.78, 1.07, 1.8) (0.56, 1, 1.8)

(0.44, 0.63, 0.86) (0.56, 0.81, 1.14) (0.56, 0.94, 1.29) (1, 1, 1) (0.56, 0.94, 1.29)

Anaerobic Lagoon (0.44, 0.67, 1.2) (0.56, 0.87, 1.6) (0.56, 1, 1.8) (0.78, 1.07, 1.8) (1, 1, 1)

Table 16. Summary of priority weights of the main criteria

Weight Alternatives UASB UAFB ABR Contact process Anaerobic Lagoon

Tech. Criteria (C1) 0.331

Eco. Criteria (C2) 0.162

0.183 0.215 0.206 0.2 0.196

0.221 0.221 0.279 0.179 0.101

Env. Criteria Admin. Criteria (C3) (C4) 0.331 0.176 0.211 0.229 0.211 0.195 0.154

0.153 0.195 0.215 0.222 0.215

Alternative priority weight

0.202 0.215 0.219 0.197 0.168

According to Table 16, the weight vectors of the technical, economic, environmental, administrative, criteria are calculated as follows, respectively. (0.183, 0.215, 0.206, 0.2, 0.196), (0.221, 0.221, 0.279, 0.179, 0.101), (0.211, 0.229, 0.211, 0.195, 0.154), and (0.153, 0.195, 0.215, 0.222, 0.215). The ranking order of the alternatives with the fuzzy AHP method is ABR > UAFB > UASB > Contact process > Anaerobic Lagoon. These results are near to the results obtained by the fuzzy TOPSIS method. 4. CONCLUSIONS By using fuzzy TOPSIS and fuzzy AHP methods, uncertainty and vagueness from subjective perception and the experiences of the decision-maker can be effectively represented and reached to a more effective decision. In this paper, the anaerobic process selection with fuzzy TOPSIS and fuzzy AHP methods has been proposed. The decision criteria were technical, economical, environmental, and administrative criteria and their sub-criteria. These criteria were evaluated to determine the order of anaerobic alternatives for selecting the most appropriate one. In fuzzy TOPSIS, the decision makers have used the linguistic variables to assess the importance of the criteria and evaluate the each alternative with respect to each criterion. These linguistic variables were converted into triangular fuzzy numbers, and the fuzzy decision matrix was formed. Then, the normalized fuzzy decision matrix and weighted normalized fuzzy decision matrix were formed. After FPIS and FNIS were defined, the distance of each alternative to FPIS and FNIS was calculated. Then, the closeness coefficient of each alternative was calculated separately. According to the closeness coefficient of alternatives, the ranking order of alternatives has been determined as UAFB> ABR> Contact process> UASB>Anaerobic lagoon. In fuzzy AHP, the decisionmakers made pair-wise comparisons for the criteria and alternatives under each criterion. Then, these comparisons have been integrated, and the pair-wise comparison values of the decision-makers were transformed into triangular fuzzy numbers. The priority weights of criteria and alternatives were determined by the Chang’s extent analysis. According to the combination of the priority weights of criteria and alternatives, the best alternative was determined. According to fuzzy AHP, the best alternative was ABR and the ranking order of the alternatives is ABR > UAFB > UASB > Contact process > Anaerobic Lagoon. The results of these two methods were near to each other, and UAFB and ABR were the appropriate anaerobic treatment process for industrial estates in Iran. 5. ACKNOWLEDGEMENTS Herein after, there are special thanks for Iran Small Industries and Industrial Estates Organization along with financial supports as well as the following grant: "Comprehensive investigation of wastewater treatment plant which are operating in Iran industrial estates and appropriate treatment process selection"

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