Aggregating Intuitionistic Fuzzy Preference Relations with Symmetrical Intuitionistic Fuzzy Bonferroni Mean Operators in
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Aggregating Intuitionistic Fuzzy Preference Relations with Symmetrical Intuitionistic Fuzzy Bonferroni Mean Operators in Group Decision Making Wei Yang1,2
•
Seong Tae Jhang2 • Shao Guang Shi1 • Zhen Ming Ma1,3
Received: 27 February 2020 / Revised: 25 May 2020 / Accepted: 5 September 2020 Ó Taiwan Fuzzy Systems Association 2020
Abstract As a useful aggregation technique, the Bonferroni mean can capture the interrelationship between input arguments and has been a hot research topic, especially, in intuitionistic fuzzy environment. In this paper, it is pointed out by an example that the existing intuitionistic fuzzy Bonferroni mean (IFBM) operators fail to satisfy the need in group decision making with intuitionistic fuzzy preference relations (IFPRs). Then, symmetrical intuitionistic fuzzy Bonferroni mean (SIFBM) operator and weighted SIFBM operator are developed to settle the above issue and some desirable properties of them are provided. Furthermore, an acceptable group multiplicative consistency of the IFPRs is introduced and a novel algorithm is established to jointly and stepwisely reach the acceptable group multiplicative consistency and consensus of IFPRs in group decision making. Finally, numerical examples are given to illustrate the effectiveness of the proposed method and
& Wei Yang [email protected] Seong Tae Jhang [email protected] Shao Guang Shi [email protected] Zhen Ming Ma [email protected] 1
School of Mathematics and Statistics, Linyi University, Linyi 276005, China
2
Department of Computer Science, The University of Suwon, Wau-ri, Bongdam-eup, Hwaseongsi 445-743, Gyeonggi-do, South Korea
3
Key Laboratory of Complex Systems and Intelligent Computing in Universities of Shandong (Linyi University), Linyi 276005, China
comparisons with the existing methods are made to demonstrate the advantages of the proposed method. Keywords Symmetrical intuitionistic fuzzy Bonferroni mean operator Group decision making Acceptable group multiplicative consistency Intuitionistic fuzzy preference relation
1 Introduction Group decision making problem with preference relations are to select the optimal alternative(s) from a given set of finite feasible alternatives by several decision makers has been widely used in various fields such as politics, social psychology, engineering, management, business and economics, etc. Among the procedure for group decision making with preference relations, checking and reaching the consistency and consensus are crucial without which unreasonable result could be derived. Although preference relations with a certain degree have been extensively investigated [1–8], they don’t always meet the real decision making problems, because the decision makers may not be able to provide their preferences for alternatives to a such certain degree due to lack of precise or sufficient level of knowledge related to the problems, or the difficulty in explaining explicitly the degree to which one alternative is better than others [9]. In these situations, there is usually a degree of u
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