A Minimum Trust Discount Coefficient Model for Incomplete Information in Group Decision Making with Intuitionistic Fuzzy
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A Minimum Trust Discount Coefficient Model for Incomplete Information in Group Decision Making with Intuitionistic Fuzzy Soft Set Xiao-guo Chen1 • Gao-feng Yu1 • Jian Wu2,3
•
Yue Yang1
Received: 22 July 2019 / Revised: 27 September 2019 / Accepted: 22 January 2020 Taiwan Fuzzy Systems Association 2020
Abstract This article proposes a framework to deal with incomplete information in multiple criteria group decision making with intuitionistic fuzzy soft set. To do that, the weighted sum method for choice values and simple mathematical expectation method are extended to the case of obtained fuzzy soft set, and they are proved to have the same result in estimating the incomplete information. In order to reduce the system error in the estimating process cause by multiple decision information, a minimum trust discount coefficient model is established according to the relevant methods of evidence theory. Then, a new definition of entropy for intuitionistic fuzzy sets is introduced to determine the weights of group experts. Therefore, individual decision-making matrices are integrated into a comprehensive decision-making matrix by the integration operation formula of intuitionistic fuzzy soft matrix. The decision making is realized according to the difference of the score values of objects. Finally, the steps of this method are concluded, and one example is given to explain the application of this method. Keywords Group decision making Intuitionistic fuzzy soft set Incomplete information Evidence theory
& Jian Wu [email protected] 1
School of Information Engineering, Sanming University, Sanming 365004, China
2
School of Economic and Management, Sanming University, Sanming 365004, China
3
School of Economics and Management, Shanghai Maritime University, Shanghai 201306, China
1 Introduction Multiple criteria decision making (MCDM) is a frequently used decision-making method in our daily life such as construction scheme optimization, medical diagnosis, mine disaster relief optimization, and all systems efficiency evaluation [1]. However, due to the increasing complexity of decision-making problem, it is impossible for single decision maker (DM) to satisfy the requirements of reliability on decision-making results [2–8]. Therefore, the multiple criteria group decision making (MCGDM) methods are receiving more and more attention from researchers [9–16]. In traditional MCGDM problem [17–21], decision makers are assumed that they can express all of their preferences by crisp number, fuzzy numbers, or linguistic values. However, in some realistic situations, the decision maker (DM) may not express his/her complete preference relations because of the complexity of decision-making problem and the knowledge limitation of themselves. Therefore, one key issue in multiple criteria group decision making (MCGDM) with incomplete information is how to estimate the missing preference relations [22–26]. Xu [27] defined various types of incomplete uncertain judgment matrices. He applied continuous interval argument C-OWA oper
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