Some novel point operators and multiple rounds voting process based decision-making algorithm under picture fuzzy set environment

Abstract

Picture fuzzy set (PFS), a generalization of the Atanassov-intuitionistic fuzzy set, is one of the most trustworthy tool to handle the uncertainties in the data during the decision-making process. The objective of this paper is to present some different kinds of the point operators for the PFS. The key feature of the presented point operators is to provide a smaller degree of uncertainty which is equivalent to the corresponding PFS. The desirable properties of the proposed operators are also derived in details. Also, we provide a memoryless multiple rounds voting process under the PFS environment to strength the result, and hence deduce a relationship between the proposed PFS and the existing set. In addition to this, we address the MADM (multiple attribute decision-making) problems by presented an algorithm to solve the problem based on the proposed point operators. The applicability and the superiority of the proposed algorithm are shown through two numerical examples. At last, the validity of the proposed algorithm is tested using different test criteria.