Algorithms for Multipolar Interval-Valued Neutrosophic Soft Set with Information Measures to Solve Multicriteria Decision-Making Problem.

Rana Muhammad Zulqarnain,Imran Siddique,Aiyared Iampan,Ebenezer Bonyah

doi:10.1155/2021/7211399

Abstract

Similarity measures (SM) and correlation coefficients (CC) are used to solve many problems. These problems include vague and imprecise information, excluding the inability to deal with general vagueness and numerous information problems. The main purpose of this research is to propose an m-polar interval-valued neutrosophic soft set (mPIVNSS) by merging the m-polar fuzzy set and interval-valued neutrosophic soft set and then study various operations based on the proposed notion, such as AND operator, OR operator, truth-favorite, and false-favorite operators with their properties. This research also puts forward the concept of the necessity and possibility operations of mPIVNSS and also the m-polar interval-valued neutrosophic soft weighted average operator (mPIVNSWA) with its desirable properties. Cosine and set-theoretic similarity measures have been proposed for mPIVNSS using Bhattacharya distance and discussed their fundamental properties. Furthermore, we extend the concept of CC and weighted correlation coefficient (WCC) for mPIVNSS and presented their necessary characteristics. Moreover, utilizing the mPIVNSWA operator, CC, and SM developed three novel algorithms for mPIVNSS to solve the multicriteria decision-making problem. Finally, the advantages, effectiveness, flexibility, and comparative analysis of the developed algorithms are given with the prevailing techniques.

Highlights

Multicriteria decision-making (MCDM) is an essential condition for decision scientific discipline. e decisionmaker should judge the choices stated by the diverse forms of distinguishing perspectives. ough, in quite a lot of situations, it is tough for someone to undertake it because of numerous uncertainties in the data
We prove that under any appropriate circumstances, different hybrid structures comprehending fuzzy set (FS) will be transformed into distinct privileges of m-polar interval-valued neutrosophic soft set (mPIVNSS). is study will be the utmost versatile form that can be used to merge data in daily life complications. e organization of the current research is such as follows: some basic concepts are presented in Section 2, which helps us to construct the structure of the following study
A novel hybrid structure has been established by merging two independent structures m-polar fuzzy set and interval-valued neutrosophic soft set which is known as mPIVNSS

Summary

Introduction

Multicriteria decision-making (MCDM) is an essential condition for decision scientific discipline. e decisionmaker should judge the choices stated by the diverse forms of distinguishing perspectives. ough, in quite a lot of situations, it is tough for someone to undertake it because of numerous uncertainties in the data. Zadeh introduced the notion of the fuzzy set (FS) [1] to resolve complex problems that contain vagueness and uncertainty. FS is unable to handle the environment when any expert considers the membership (Mem) grade of any object in the intervals form. To overawed such states, Turksen [2] proposed the idea of interval-valued fuzzy sets (IVFS). E idea proposed by Atanassov involves only underconsidered data as well as Mem and Nmem values. The IFS theory is unable to cope with overall incompatibility and inaccurate data. To resolve the challenge of incompatibility and incorrect data, Smarandache [4] planned the theory of NS. Molodtsov [5] presented a universal accurate tool for addressing uncertain environments renowned as soft set (SS)

Methods

Discussion

Conclusion