A Novel Score Function for Picture Fuzzy Numbers and Its Based Entropy Method to Multiple Attribute Decision-Making

Abstract

AbstractA picture fuzzy set (PFS) is a comprehensive extension of a fuzzy set which permits to express the vagueness inherent in decision-making information. In this paper, we consider a class of multiple attribute decision-making (MADM) problems under the PFS framework, in which attribute weights are completely unknown. In such problems, the attribute values are given in the form of picture fuzzy numbers (PFNs). In the development of a method to solve such MADM problems, firstly, a novel score function is introduced in order to compare the PFNs with a brief study of related properties. This score function defeats the drawbacks of the existing score functions. After that, a new algorithm is proposed to solve a picture fuzzy MADM problem by using the proposed score function, the picture fuzzy weighted geometric (PFWG) operator and the picture fuzzy hybrid geometric (PFHG) operator. An illustrative example is given to show the applicability of the proposed algorithm.KeywordsPicture fuzzy numberMultiple attribute decision-makingPFHG operator