A new method for fuzzy group decision making based on α-level cut and similarity

Authors:
Jibin Lan;Liping He;Zhongxing Wang
Affiliations:
,School of Economics and Management, Southwest Jiaotong University, Chengdu, Sichuan, P.R. China;School of Mathematics and Information Science, Guangxi University, Nanning, Guangxi, P.R. China;School of Mathematics and Information Science, Guangxi University, Nanning, Guangxi, P.R. China
Venue:
FSKD'05 Proceedings of the Second international conference on Fuzzy Systems and Knowledge Discovery - Volume Part II
Year:
2005

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Abstract

Let opinions of experts among group decision making be represented as L-R fuzzy numbers. The difference of two experts' opinions is reflected by two distances, which are called the left-hand side distance and the right-hand side one. A method to calculate two types of distances based on the same α-level is presented. Then the distances are employed to construct a new similarity function to measure the similarity degrees of both sides which represent the pessimistic and optimistic similarity degrees between the experts, respectively. The degree of importance of each expert among group decision making is obtained by employing Saaty's analytic hierarchy process (AHP). The method of aggregating individual fuzzy opinions into a group consensus opinion by combining similarity degrees and the degree of importance of each expert is proposed. Finally some properties of the proposed similarity measure are proved and some numeric examples are shown to illustrate our method.