Soft Rough q-Rung Orthopair m-Polar Fuzzy Sets and q-Rung Orthopair m-Polar Fuzzy Soft Rough Sets and Their Applications

Jingshui Ping,Ahmed Mostafa Khalil,Nasruddin Hassan,Mohammed Atef,Muhammad Riaz

doi:10.1109/access.2021.3118055

Abstract

The notion of a q-rung orthopair fuzzy soft rough set ( $^{q}ROFSRS$ ) appeared as an extension of q-rung orthopair fuzzy set ( $^{q}ROFS$ ) and q-rung orthopair fuzzy soft set ( $^{q}ROFSS$ ) with the aid of rough set (RS) definition. Thus, $^{q}ROFSRS$ and m-polar fuzzy set ( $_{m}PFS$ ) are convenient to deal with uncertain knowledge which helps us to solve many problems in decision making. In this paper, we define the soft rough q-rung orthopair m-polar fuzzy sets ( $^{\text {q}}RO_{\text {m}}PFS$ ) and q-rung orthopair m-polar fuzzy soft rough sets ( $^{q}RO_{\text {m}}PFSRS$ ) through crisp soft and q- rung orthopair (q-RO) m-polar fuzzy soft approximation space. The related characteristics of these models are also studied. Then, we construct two new algorithms for these models to solve MADM issues. The successful application and corresponding comparative analyses proves that our proposed models are rational and effective.

Highlights

T HE rapid of research articles become very huge, especially in mathematics
Dubious et al [4] combine the notion of Rough Sets (RS) and FS, to form rough fuzzy sets and fuzzy rough sets
We intend to develop a hybrid of SRS and qROmP F S and put forward a new model called q-rung orthopair m-polar fuzzy soft rough sets and soft rough q-rung orthopair fuzzy sets (SRqROmP F S)

Summary

INTRODUCTION

T HE rapid of research articles become very huge, especially in mathematics. Numerous suggestions were made to solve real-world problems using mathematical techniques by way of appropriate equations or formulas in helping decision makers to make their best decisions. Using the notions of SS, SRS, and qROF S, Hussain et al [52] proposed the q-rung orthopair fuzzy soft sets and their application. Riaz et al [54] introduced the notion of soft rough q-rung orthopair fuzzy sets and some of their properties were discussed. Thereafter, many researchers studied SRS, SS, and their applications such as [55]–[60], [64] From these interesting studies, we intend to develop a hybrid of SRS and qROmP F S and put forward a new model called q-rung orthopair m-polar fuzzy soft rough sets (qROmP F SRS) and soft rough q-rung orthopair fuzzy sets (SRqROmP F S).

PRELIMINARIES

SRqROmP F S APPROACH

CONCLUSION