Belief and Possibility Belief Interval-Valued N-Soft Set and Their Applications in Multi-Attribute Decision-Making Problems.

Shahbaz Ali,Rabia Fayyaz,Qin Xin,Muneeba Kousar,Muhammad Shazib Hameed,Dragan Pamučar

doi:10.3390/e23111498

Abstract

In this research article, we motivate and introduce the concept of possibility belief interval-valued N-soft sets. It has a great significance for enhancing the performance of decision-making procedures in many theories of uncertainty. The N-soft set theory is arising as an effective mathematical tool for dealing with precision and uncertainties more than the soft set theory. In this regard, we extend the concept of belief interval-valued soft set to possibility belief interval-valued N-soft set (by accumulating possibility and belief interval with N-soft set), and we also explain its practical calculations. To this objective, we defined related theoretical notions, for example, belief interval-valued N-soft set, possibility belief interval-valued N-soft set, their algebraic operations, and examined some of their fundamental properties. Furthermore, we developed two algorithms by using max-AND and min-OR operations of possibility belief interval-valued N-soft set for decision-making problems and also justify its applicability with numerical examples.

Highlights

In real life, the limitation of precise research is progressively being recognized in various fields such as economics, social sciences, medical sciences, computer sciences, physical sciences, environmental sciences, management sciences, and engineering
In [15], Molodtsov indicates that there is a difficulty in the fuzzy set and intuitionistic fuzzy set theory, that is, the level of the membership defined by the individual regarded depends on the knowledge received by the individual, in consequence, vulnerable to subjective factors
We present the concept of a possibility belief interval-valued N-soft set, which can be viewable as a possibility belief interval-valued N-soft model

Summary

Introduction

The limitation of precise research is progressively being recognized in various fields such as economics, social sciences, medical sciences, computer sciences, physical sciences, environmental sciences, management sciences, and engineering. Fatimah [45] extended the soft set model under a non-binary evaluation environment and introduced the concept of N-soft set (NSS) and explained the significance of ordered grades in the practical problems They developed decision-making procedures for the N-soft set.

Preliminaries

Operations on BIV NSS

Operations on PBIV NSS

Algorithms

Applications

Conclusions