Abstract
Muirhead mean (MM) is a well-known aggregation operator which can consider interrelationships among any number of arguments assigned by a variable vector. Besides, it is a universal operator since it can contain other general operators by assigning some special parameter values. However, the MM can only process the crisp numbers. Inspired by the MM’ advantages, the aim of this paper is to extend MM to process the intuitionistic fuzzy numbers (IFNs) and then to solve the multi-attribute group decision making (MAGDM) problems. Firstly, we develop some intuitionistic fuzzy Muirhead mean (IFMM) operators by extending MM to intuitionistic fuzzy information. Then, we prove some properties and discuss some special cases with respect to the parameter vector. Moreover, we present two new methods to deal with MAGDM problems with the intuitionistic fuzzy information based on the proposed MM operators. Finally, we verify the validity and reliability of our methods by using an application example, and analyze the advantages of our methods by comparing with other existing methods.
Highlights
Multi-attribute decision making (MADM) and multi-attribute group decision making (MAGDM) are the important aspects of decision sciences, and they can give the ranking results for the finite alternatives or select best choice from them according to the attribute values of different alternatives [1]
Group Decision Making Method Based on Muirhead Mean Operators for Intuitionistic Fuzzy Numbers and MAGDM methods for intuitionistic fuzzy set (IFS), such as TOPSIS method [13,14], VIKOR method [15], GRA method [16], PROMETHE [17], ELECTRE [18], TODIM method [19], DEMATEL method [20] and so on; (3) the MADM and MAGDM methods based on intuitionistic fuzzy aggregation operators
The aggregation operators can aggregate the evaluation information of individual decision maker to collective one, and/or aggregate all attribute values to the comprehensive value, to rank the alternatives by the comprehensive value of alternatives, while the extended traditional decision methods can only rank the alternatives based on some decision principles, for example, TOPSIS can give the ranking results based on the relative closeness
Summary
Multi-attribute decision making (MADM) and MAGDM are the important aspects of decision sciences, and they can give the ranking results for the finite alternatives or select best choice from them according to the attribute values of different alternatives [1]. Because IFS can express the fuzzy information, the researches on intuitionistic fuzzy aggregation operators have made many achievements, for example, arithmetic and geometric operators for IFNs [27,28], distance operator [29], neutral averaging operators [30], generalized operators [31], and so on. Except this basic function of aggregation operators which can aggregate a collection of data to one, some aggregation operators can achieve some special functions. Power operators [25,26,32,33] and dependent aggregation operators [34,35] which can relieve the influences of some unreasonable data give by biased decision makers, Bonferroni mean (BM) [36,37,38,39] and the Heronian mean (HM) [24,40,41], which consider interrelationships of aggregated arguments
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