On Soft Rough Topology with Multi-Attribute Group Decision Making

Muhammad Riaz,Florentin Smarandache,Atiqa Firdous,Atiqa Fakhar

doi:10.3390/math7010067

Muhammad Riaz, Florentin Smarandache + Show 2 more

Open Access

https://doi.org/10.3390/math7010067

Copy DOI

Journal: Mathematics	Publication Date: Jan 9, 2019
Citations: 28	License type: CC BY 4.0

Affiliation: University of the Punjab, University of New Mexico

Abstract

Rough set approaches encounter uncertainty by means of boundary regions instead of membership values. In this paper, we develop the topological structure on soft rough set ( SR -set) by using pairwise SR -approximations. We define SR -open set, SR -closed sets, SR -closure, SR -interior, SR -neighborhood, SR -bases, product topology on SR -sets, continuous mapping, and compactness in soft rough topological space ( SRTS ). The developments of the theory on SR -set and SR -topology exhibit not only an important theoretical value but also represent significant applications of SR -sets. We applied an algorithm based on SR -set to multi-attribute group decision making (MAGDM) to deal with uncertainty.

Highlights

The problem of imperfect knowledge has been the center of attention for many years.In the field of mathematics, computer science, and artificial intelligence, researchers have used different methods to tackle the problem of uncertain and incomplete data, including probability theory, fuzzy set [1], and rough set [2,3] and soft set techniques [4,5,6]
We present some new results of SR-set theory and SR-topology
Soft rough set with the topology τSR is called a topological SR-set

Summary

Introduction

The problem of imperfect knowledge has been the center of attention for many years. In the field of mathematics, computer science, and artificial intelligence, researchers have used different methods to tackle the problem of uncertain and incomplete data, including probability theory, fuzzy set [1], and rough set [2,3] and soft set techniques [4,5,6]. Soft set with decision making have studied by many researchers [7,8,9,10,11]. Introduced fuzzy parameterized fuzzy soft set (fpfs-set), fpfs-topology, and fpfs-compact spaces, with some important applications of fpfs-set to decision-making problems. They presented fns-mappings and fixed points of fns-mapping. Neutrosophic set and rough sets with decision making problems have studied by many researchers [34,35,36,37,38,39,40].

Preliminaries

Topological Structure of SR-Sets

Continuity in SR-Sets

Compactness in SR-Set

Application of SR-Set in Multi-Attribute Group Decision Making

1: Graphical representation of Algorithm

Conclusions