Three-Way Decisions Based on Q-Rung Orthopair Fuzzy 2-Tuple Linguistic Sets with Generalized Maclaurin Symmetric Mean Operators

Miin-Shen Yang,Tahir Mahmood,Zeeshan Ali

doi:10.3390/math9121387

Abstract

As a typical model of three-way decisions (3WD), decision-theoretic rough sets (DTRS), have gained attention from scholars in decision-making problems. The q-rung orthopair fuzzy 2-tuple linguistic variable (QROF2-TLV) is a mixture of two different notions, q-rung orthopair fuzzy sets (QROFS) and 2-tuple linguistic variables (2-TLV), and is an extensive and proficient technique for coping with awkward and complicated information in realistic decision-making. In this paper, we first propose a DTRS model for 3WD based on QROF2-TLV that gives a new method for evaluating loss functions (LF) of DTRS. We further present the q-rung orthopair fuzzy 2-tuple linguistic generalized Maclaurin symmetric mean (QROF2-TLGMSM) and weighted QROF2-TLGMSM operators and then provide the LFs of DTRS based on QROF2-TLV with the values aggregated by the QROF2-TLGMSM operator. Thus, we propose the q-rung orthopair fuzzy 2-tuple linguistic variable DTRS (QROF2-TLV-DTRS) model. Subsequently, a technique for concluding another DTRS model, which can give the related semantic translation of the decision consequences of every other option, is presented. The model is applied to expound the proposed technique in detail, and the impacts of various conditional probabilities on decision outcomes are discussed. A comparative analysis of the proposed approach is also conducted to examine the proficiency of the proposed method.

Highlights

Multi-attribute decision making (MADM) can be delineated as a method for choosing the most ideal alternative(s) among the accessible choices
The 3WD technique based on intuitionistic fuzzy sets [40] discussed supporting and supporting against of the loss functions (LF) with a condition, such that the sum of both is not exceeded from the unit interval
The 3WD technique based on Pythagorean fuzzy sets discussed supporting and supporting against of the LF with a condition such that the sum of the squires of both is not exceeded from the unit interval [9]

Summary

Introduction

Multi-attribute decision making (MADM) can be delineated as a method for choosing the most ideal alternative(s) among the accessible choices. Because of the increase in volume and multifaceted nature of the ongoing data, the q-rung orthopair FSs (QROFS) were considered by Yager [12] with a modified condition where the sum of the q-powers of the satisfactory and dissatisfactory grades was limited to the unit interval Both IFSs and PFSs are exceptional instances of QROFSs. We contend that QROFSs are sufficiently broad in light of the fact that the satisfactory space of the orthopair increments, and a greater number of orthopairs, meet the limited condition. In this paper, we propose a 3WD model based on QROF2-TLV that gives a novel tool for examining the properties and fundamental operational laws of loss functions (LF) of DTRS.

Preliminaries with Definitions and Review of a DTRS Model for 3WD

Conclusions