Pythagorean Fuzzy Linguistic Power Generalized Maclaurin Symmetric Mean Operators and Their Application in Multiple Attribute Group Decision-Making

Abstract

As an extension of Pythagorean fuzzy sets and linguistic term sets, Pythagorean fuzzy linguistic sets (PFSs) are powerful to describe decision-making information quantificational and qualitatively, which have received much scholars’ attention. The purpose of this paper is to propose a new multiple attribute group decision-making (MAGDM) approach with Pythagorean fuzzy linguistic (PFL) information. To this end, we firstly analyze the drawbacks of existing operations of PFL numbers and propose new operational rules based on linguistic scale function. The power average (PA) operator is famous for its capacity of reducing the negative influence of unreasonable evaluation values provided by prejudiced decision makers on the decision results. The generalized Maclaurin symmetric mean (GMSM) can not only capture the interrelationship among multiple inputs but also manipulate the effect of related properties by adjusting the parameters. When considering aggregation operators of PFL numbers, we combine PA with GMSM and propose the PFL power generalized Maclaurin symmetric and the PFL power generalized weighted Maclaurin symmetric operators. We also study important properties and special cases of these operators. We continue to investigate MAGDM problems with PFL decision information and propose a novel method to determine the optimal alternative. Finally, we conduct numerical examples to demonstrate the effectiveness of our proposed method. We also attempt to illustrate the advantages and superiorities of the proposed method via comparative analysis.

Keywords

• Pythagorean fuzzy linguistic sets
• linguistic scale function
• power average operator
• generalized Maclaurin symmetric mean
• multiple attribute group decision making