Fuzzy Multi-criteria Group Decision Support in Long-term Options of Belgian Energy Policy

Fuzzy Multi-criteria Group Decision Support in Long-term Options of Belgian Energy Policy Da Ruan1, Jie Lu2, Erik Laes1, Guangquan Zhang2, Fengjie Wu2, and Frank Hardeman1 1

2

Expertise Group of Society and Policy Support Belgian Nuclear Research Centre (SCK•CEN) Boeretang 200, 2400 Mol, Belgium {druan, elaes, fhardema}@sckcen.be

Faculty of Information Technology University of Technology, Sydney(UTS) PO Box 123, Broadway, NSW 2007, Australia {jielu, zhangg, fengjiew}@it.uts.edu.au

Abstract - Decision making requires multiple perspectives of different people as one single decision maker may have not enough knowledge to well solve a problem alone. This is particularly true when the decision environment becomes more complex. More organizational decisions are made now in groups than ever before. Group decision making is thus a process of arriving at a judgment or a solution for a decision problem based on the input and feedback of multiple individuals. At the same time in practice, multi-criteria problems at tactical and strategic levels often involve fuzziness in their criteria and decision makers’ judgments. Relevant alternatives are evaluated according to a number of criteria. Fuzzy logic based multi-criteria group decision support is justified to analysis long-term options for Belgian energy policy in this paper.

Air pollution

Occupatio nal health

©2007 IEEE

Impacts of air pollution on human health: long-term Impacts on occupational health (gas+coal) Radiological health impacts (nuclear) Need for long-term management of HLW

Radiologic al health impacts

Visual impact on landscape Noise amenity

(I): Environmen tal & human health and safety

I. INTRODUCTION The Belgian parliament has recently voted a law to progressively phase out existing nuclear power plants. This decision has roused quite some contestation between a number of historically active social groups in the energy policy debate. Referring to this relatively controversial climate, the research reported in [3] stretches the scope of the debate outside the boundaries of political (parliamentary) decision making. Among many interesting issues related to nuclear energy and sustainable development, Laes (2006) attempted to shed some light on the question whether nuclear electricity generation can contribute to the transition towards a sustainable energy future for Belgium, and, if so, under which conditions. For the details of the substantial answers to these questions and some methodological aspects of the project, readers are referred to [3]. The study includes four important issues (high-level criteria): (I) Environmental and human health & safety, (II) Economic welfare, (III) Social, political, cultural and ethical needs, and (IV) Diversification. Just for the item (I), it has seven aspects (intermediatelevel criteria): (1) Air pollution, (2) Occupational health, (3) Radiological health impacts, (4) Aesthetic, (5) Other environmental impacts, (6) Resource use, and (7) Other energy related pressures. Each aspect would have one or more low-level criteria. For instance, the aspect of air pollution has both mid and long term impacts. Figure 1 shows the combined value tree for environmental and human health & safety.

Impacts of air pollution on human health: mid -term

Aesthetic Impact on natural ecosystems (air pollution): mid-term Other environmenta l impacts

Resource use

Impact on natural ecosystems (air pollution): long-term Environmental impact from solid waste (coal) Land use

Water use

Other energy related pressures

Catastrophic risk: nuclear

Geographical distribution risks / benefits

Fig. 1 Hierarchy of criteria

There are many ways to evaluate this policy option study. Standard multi-criteria decision support and group decision support systems are typically suitable for such a study [1, 2, 12]. Due to the complexity of this study, different experts will have different views under various uncertain information for different scenarios (S1, S2, …, S8). Experts' views are often expressed in certain linguistic terms and some undetermined values during the evaluation procedure. Hence the integration of multi-criteria decision making, group decision making and fuzzy logic systems is recommended to carry out for this study. Fuzzy multi-criteria decision making (FMCDM) technique has been one of the fastest growing areas in decision making and operations research during the last three decades [7-8, 11, 12]. A major reason behind the development of fuzzy MCDM is due to the large number of criteria that decision makers are expected to incorporate in their actions and the difficulty of expressing decision

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makers’ opinions by crisp values in practice [1, 13-15]. Group decision making takes into account how people work together in reaching a decision. Uncertain factors often appear in a group decision process. Based on giving a rational-political group decision model [4, 7], we identify three main uncertain factors involved in a group decisionmaking process: decision makers’ roles (weights), preferences (scores) for alternatives, and judgments (weights) for criteria. This paper presents a fuzzy multi-criteria group decisionmaking (FMCGDM) method to deal with the three uncertain factors to a multi-level, multi-criteria decision to generate a group satisfactory decision. The solution is in the most acceptable degree of the group. With the help of fuzzy multi-criteria group decision support systems (FMCGDDS), a software package designed to assist multi-criteria decision analysis under uncertainties, a longterm options study for Belgian energy policy is being carried out as a result of the cooperation between the Belgian Nuclear Research Centre (SCK•CEN) and University of Technology, Sydney (UTS). II. FMCGDSS METHOD This section gives a fuzzy multi-criteria group decision method, which deals with two-level criteria for evaluating a number of alternatives by a group. This method is developed based on the previous study [4-6, 9, 10] and described as follows Let P = {P1, P2, …, Pn}, n ≥ 2, be a given finite set of decision makers to select a satisfactory alternative or identify a number of important issues with raking for a decision problem. The proposed method consists of 12 steps within three levels:

management level (say, the leader denoted as E0) before or at the beginning of the decision process. Possible linguistic terms used in the factor are Normal, Important, More important, and Most important. Step 3: Set up weights for all aspects and related criteria Referring to a set of aspects F = (F1 , F2 ,…, Fn ) , let WF = (WF1 ,WF2 ,…,WFn ) be the weights of these aspects, where WFi ∈ {Absolutely unimportant, Unimportant, Less important, Important, More important, Strongly important, Absolutely important}. Those weights are described by fuzzy ~ , a~ ,…, a~ . numbers a 1 2 n For an aspect Fi , let C i = {C i1 , C i 2 , , C it }, i = 1, 2, …, n be a set of the selected criteria with respect to the aspect Fi . Let WCi = {WC i1 , WC i 2 , , WCit }, i = 1,2, … , n , be the weights for the set of criteria, as shown in Table 1, where WC ij will be signed a value from the same linguistic term list as WFi above, which are described by fuzzy numbers i

i

~ c1 , c~2 ,… , c~t . For the example given in Fig. 1, ‘Air

pollution’ is an aspect of performance, two criteria to evaluate it are ‘Impacts of air pollution on human health: mid -term,’ and ‘Impacts of air pollution on human health: long-term.’ Table 1: Linguistic terms and related fuzzy numbers for describing the weights of aspects and criteria

The importance degrees Absolutely unimportant Unimportant

Level one: Alternatives, criteria, and group members set up and all weights generation Step 1: When a decision problem is proposed in a group, each group member can raise one or more possible strategies or alternative solutions. Let p

p

p

p

p

p

S*= {S1 1 , S 2 1 ,....S m1p1 ,......S1 n , S 2 n ,......S m npn } ,

where

p

S j i is the jth alternative for the decision problem raised by

group member pi ’. Through a discussion and summarization, S = {S1, S2, …, Sm}, m ≥ 2 is selected from S* as alternatives for the decision problem. Step 2: As group members play different roles in an organization and therefore have different degrees of influence for the selection of the satisfactory group solution. That means the relative importance of each decision maker may not equal in a decision group. Some members are more important than others for a specific decision problem. Therefore, in the method, each member is assigned with a weight that is described by a linguistic ~ term v k , k = 1, 2, , n . These terms are determined through discussions in the group or assigned by a higher

Membership functions a1 a2

Less important

a3

Important

a4

More important

a5

Strongly important

a6

Absolutely important

a7

Level two: Individual Preference Generation Step 4: Set up the relevance degree of each alternative on each criterion Let A = ( A1 , A2 , … , Am ) be a set of alternatives, ACik = { ACik1 , ACik2 , , ACitk } be the relevance degree of alternative Ak on criterion Ci , i = 1,2, … , n , k = 1,2, … , m , where ACijk ∈ {Lowest, Very low, Low, Medium, High, Very high, Highest}, as shown in Table 2, which are described by ~ ~ ~ fuzzy numbers b1 , b2 , … , bk . Table 3 further describes the relationships among these aspects, criteria, alternatives, their weights, and decision makers’ evaluation values (scores).

497

i

Table 2: Linguistic terms for preference of alternatives

Linguistic terms Very low (VL) Low (L) Medium low (ML) Medium (M) Medium high (MH) High (H) Very high (VH)

v~k , k = 1, 2,

Fuzzy numbers b1 b2 b3 b4 b5 b6 b7

is obtained: V = { v~k , k = 1, 2,

WF

F1

1

…

… WF

Fn

n

C11 …

WC11 …

C1t1

WC1t1

AC11t1

… Cn1 …

… WCn1 …

…

Cntn

... …

Am AC11m …

…

AC1mt1

AC AC

(

…

m n1

AC

…

…

WCnt n

Step 10: Considering the normalized weights of all group members, we can construct a weighted normalized fuzzy decision vector  b11 b21 bm1   2  2 bm2  (~r1 , ~r2 , , ~rm ) = v~1* , ~v2* , , ~vn*  b1 b2 ,   b n b n bmn  2  1 n ~* k where ~ r = v b .

…

1 n1

1 ntn

…

ACntmn

j

i = 1,2, … , n are normalized and denoted as WC ij

where the Cij 0R

, for j = 1,2,

∑ WCij 0 is the right end of 0-cutset. R

, t i , i = 1, 2,

, n.

The positive and negative solution distances between each ~ r j and r*, ~ r j and r- can be calculated [4, 7] as: d *j = d (~ r j , r * ) and

i

based on FAk = {FA1k , FA2k , , FAnk }, k = 1,2, … , m . FA =

FAik R

∑i =1 FAik 0 n

, for i = 1, 2,

, n, k = 1, 2,

, m.

n

k

j = 1, 2,

, m,

where d (.,.) is the distance measurement between two fuzzy numbers. Step 12: A closeness coefficient is defined to determine *

−

the ranking order of all alternatives once the d j and d j of

CC j =

alternatives Ak , k = 1,2, … , m is calculated by using k

d −j = d (~ r j , r − ),

each Sj (j = 1, 2, ..., m) are obtained. The closeness coefficient of each alternative is calculated based on [1]:

Step 8: Calculate the aspect relevance degrees The relevance degree S k of the aspects F on the S k = FA × WF = ∑i=1 FAi × WFi

j

r * = 1 and r − = 0.

Step 6: Calculate the relevance degrees The relevance degree FAik of the aspect Fi on the alternatives Ak , i = 1,2, …, n, k = 1,2, … , m, are calculated by using FAik = WCi* × AC ik = ∑tj =1WCij* × ACijk , i = 1,2, …, n, k = 1, 2,…, m. Step 7: Normalise the relevance degrees The relevance degrees FAik of the aspect Fi on the alternatives Ak , i = 1,2, … , n , k = 1,2, … , m are normalized k i

k

positive fuzzy numbers and their ranges belong to the closed interval [0, 1]. We can then define a fuzzy positive-ideal solution (FPIS, r*) and a fuzzy negative-ideal solution (FNIS, r-) as:

i

ti j =1

∑k =1

)

Step 11: In the weighted normalized fuzzy decision vector the elements v~j , j = 1,2, , m , are normalized as

Step 5: Normalise the weights for criteria The weights for the criteria WCi = {WCi1 , WCi 2 , , WCit },

WC ij* =

, n }.

The normalized weight of a decision maker Pk (k = 1, 2, ..., n) is denoted as ~ v v~k* = n k , for k = 1, 2, , n. ∑i =1 vi 0R

Table 3: The relationships among the aspects, criteria, alternatives, their weights, and evaluation values

A1 1 AC11 …

, n as shown in Table 3. A weight vector

k = 1,2, … , m. Here, S k is

still a fuzzy number. Level three: Group Aggregation Step 9: Each member Pk has been assigned with a weight already that is described by a linguistic term

(

)

1 − d j + (1 − d *j ) , 2

j = 1, 2,

, m.

The alternative Sj that corresponds to the Max (CCj, j =1, 2, …, m) is the best satisfactory solution of the decision group, and the top N issues that correspond to the top N higher raking CCj are the critical issues to consider for the decision problem. III. A CASE STUDY: LONG-TERM OPTIONS FOR BELGIAN ENERGY POLICY Among the four important issues of the long-term options for Belgian energy policy evaluation, the issue of

498

Environmental and human health & safety (also see Figure 1) involves seven aspects. Each aspect has multiple evaluation criteria, and these aspects and criteria have different important degrees. Totally, 14 criteria are listed in the hierarchy (also see Figure 1). All options of this issue can be seen as alternatives. Since the judgments from the ten assessment members (experts) are usually vague rather than crisp, and hence can be better described by linguistic terms. It is a typical fuzzy multi-criteria group decision making (FMCGDM) problem. A. FMCGDSS System Structure There are four components on the FMCGDSS software: (1) Presentation, (2) Aggregation, (3) Model management, and (4) Data management. In addition, there are three bases: (a) Database, (b) Method-base, and (c) Model-base. These bases are linked to the corresponding management components, respectively. The FMCGDM method is in the model base and all data about the environment healthy is in the database. Figure 2 shows the structure of the FMCGDSS software. Database

Data management component

Method-base Aggregation component

Fig. 3 Setting up a group

Step 2: Input names of all experts, and titles of aspects and criteria (Figure 4).

Model-base

Model management component

Fig. 4 An example of aspects

Presentation

Group member

……

Then a tree structure of criteria is generated. Figure 5 shows the main interface of the FMCGDSS with the left part as the two-level structure of the problem.

Group member

Fig. 2 The structure of FMCGDSS

B. System Working Process Main steps for this case study are described as follows: Step 1: Get all ten group members (experts)’ survey forms. Input the description of the evaluation issue, and the number of experts, alternatives and evaluation aspects (Figure 3).

Fig. 5 Structure of the problem

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Step 3: input weights for experts, aspects, and criteria, respectively in Figure 6.

Fig. 6. The weights of group members, the aspects (higher lever) and criteria (low level)

Step 4: Fill the belief level matrix (scores) by all experts. Based on the criteria and alternatives, every expert fills a belief level matrix to express the possibility of selecting an option under some criteria as shown in Figure 7 for Expert 2.

IV. CONCLUSIONS The software FMCGDSS provides a helpful tool to analysis long terms options of Belgian energy policy. It can accept input data (from interviews and questionnaires from various sources) with or without uncertainties: numerical, linguistic, or missing values from a group of experts whose views may not agree with each others. From the input data, FMCGDSS can generate overall evaluation and any individual expert evaluation in any category or subcategory. All the outcomes can be displayed graphically. If there are different weights assigned to criteria, alternatives, and experts, FMCDSS can automatically deal with all conflict situations. In this paper, we provided a case study on longterms options of Belgian energy policy to illustrate how FMCDSS can be used for societal policy support with various uncertainties. We strongly believe the FMCDSS tool will be useful for the social-economic analysis of nuclear systems in particular and for any complex evaluation systems in general. ACKNOWLEDGMENT This work was supported in part by Australian Research Council (ARC) under discovery grants DP0559213

REFERENCES [1] [2] [3] [4] [5] [6] [7] [8] Fig.7 Expert 2’s input for all alternatives under all criteria by linguistic terms. ‘Cannot be determined’ is one more linguistic term allowed in the system

[9]

Steps 5-12: calculate and generate the final result of the problem. Finally, the option 7 (S7) is chosen by aggregating the ten experts' results as it received the highest closeness coefficient value. In the left part of Figure 8 is the group’s result and the right part is Expert 8’s detailed solution for the eight alternatives.

[10]

[11] [12] [13]

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Fig. 8 Final result of the group and all individuals

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