Picture fuzzy power Muirhead mean operators and their application to multi attribute decision making

Abstract

<p style='text-indent:20px;'>The main objective of this paper is to develop some aggregating operators for Picture fuzzy sets (PFS) by integrating power average (PA) and Muirhead mean (MM) operators. This paper develops Picture fuzzy power Muirhead mean (PFPMM), Picture fuzzy weighted power Muirhead mean (PFWPMM), Picture fuzzy dual power Muirhead mean (PFDPMM) and Picture fuzzy weighted dual power Muirhead mean (PFWDPMM) operators along with some desirable properties and special cases. Some advantages of developed operators are that they define the interrelationship between all aggregated values and lead to a flexible aggregation process through a parameter vector. Further, a multi-attribute decision making (MADM) problem based on proposed operators has been presented. To exemplify the availability and practicability of the proposed study, a financial investment risk problem in an enterprise is solved numerically. A sensitivity analysis is conducted to examine the effect of different values of parameters on aggregated values, while a comparative analysis is carried out to compare the results with some other existing operators.</p>