A fuzzy aggregation approach to group decision-making based on centroid measurement

Abstract

Abstract: In group decision-making situations, the decision-makers’ opinions are generally characterized bysubjectivity, imprecision and vagueness. Such opinions can be represented by fuzzy numbers such as positivetrapezoidalfuzzynumbers.Severalaggregationmethodshavebeenproposedpreviously;however,therearestilldeficits which limit their applications. This paper proposes an aggregation method based on centroidmeasurement which aims to overcome some of the shortcomings. In the paper, a number of axioms areproposed. A numerical example is given at the end to illustrate the application of the proposed aggregationmethod.Keywords: fuzzy opinions, fuzzy numbers, group decision-making, aggregation 1. IntroductionIn multiple-criteria group decision-making sit-uations, group members’ opinions or evalua-tions are based on a certain set of criteria. Theopinions may vary due to different perspectiveson both criteria and alternatives (Xu, 1988,1990; Feng & Xu, 1999a, 1999b; Qiu et al.,2003; Zhang & Lu, 2003; Zhang et al., 2003;Zhang & Jiang, 2006). Aggregating individualopinions to form an opinion with group con-sensus is an important consideration in groupdecision-making.The consensus opinion can be obtained bycalculating the weighted sum ofindividual opin-ions. One way to assign the weights is to esti-mate the relative importance of an individualbased on the criterion of authority. In theprocess of group decision-making, individualmembers’ opinions usually involve subjectivity,imprecision and vagueness (Hsu & Chen, 1996;Lee, 2002). Bardossy et al. (1993) suggest that asubjectiveestimatecanberepresentedbyafuzzynumber. The concept of fuzzy numbers was firstproposed by Dubois and Prade (1978). In theexisting literature, positive trapezoidal or trian-gular fuzzy numbers are employed to representfuzzy opinions (Olcer & Odabasi, 2005). Anumerical approximation technique has beenproposed to convert linguistic terms to theircorresponding fuzzy numbers (Chen et al.,1992). Kacprzyk et al. (1992) showed how lin-guisticquantifierscanbeusedingroupdecision-making. Some aggregation approaches dealingwith fuzzy numbers have been proposed forforming opinions with group consensus.Hsu and Chen (1996) proposed a similarityaggregation method in which the weight indexesconsist of two facets: the degree of relativeimportance of the individual and the degree ofsimilarity of opinion among group members.