A method to multi-attribute decision making with picture fuzzy information based on Muirhead mean

Abstract

The recently proposed picture fuzzy set (PFS) is a powerful tool for handling fuzziness and uncertainty. PFS is characterized by a positive membership degree, a neutral membership degree, and a negative membership degree, making it more suitable and useful than the intuitionistic fuzzy set (IFS) when dealing with multi-attribute decision making (MADM). The aim of this paper is to develop some aggregation operators for fusing picture fuzzy information. Considering the Muirhead mean (MM) is an aggregation technology which can consider the interrelationship among all aggregated arguments, we extend MM to picture fuzzy context and propose a family of picture fuzzy Muirhead mean operators. In addition, we investigate some properties and special cases of the proposed operators. Further, we develop a novel method to MADM in which the attribute values take the form of picture fuzzy numbers (PFNs). Finally, a numerical example is provided to illustrate the validity of the proposed method.

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