The Renewable Energy Source Selection by Remoteness Index-Based VIKOR Method for Generalized Intuitionistic Fuzzy Soft Sets

Muhammad Jabir Khan,Wiyada Kumam,Phatiphat Thounthong,Nusrat Shaheen,Zahir Shah,Nasser Aedh Alreshidi,Poom Kumam

doi:10.3390/sym12060977

Abstract

In this paper, we introduce the Euclidean, Hamming, and generalized distance measures for the generalized intuitionistic fuzzy soft sets (GIFSSs). We discuss the properties of the presented distance measures. The numerical example of decision making and pattern recognition is discussed based on the proposed distance measures. We develop a remoteness index-based VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method for GIFSSs. The displaced and fixed ideals intuitionistic fuzzy values (IFVs) are defined. The novel concept of displaced and fixed remoteness indexes for IFVs are discussed. We discuss the methods to obtain the precise and intuitionistic fuzzy (IF) weights. The several displaced and fixed ranking indexes are defined based on the precise and IF weights. The remoteness indexes based VIKOR methods are proposed in the form of four algorithms. In the end, the selection of renewable energy sources problem is solved by using the four remoteness index-based VIKOR methods.

Highlights

In the fuzzy sets theory, the membership function is used to represents the information [1].Real-life uncertainties handle effectively by fuzzy set theory
This paper aims to discuss the selection of renewable energy sources for under developing countries using the remoteness index-based VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method for generalized intuitionistic fuzzy soft sets (GIFSSs)
We have introduced the Euclidean, Hamming, and generalized distance measures for GIFSSs and discussed their properties

Summary

Introduction

In the fuzzy sets theory, the membership function is used to represents the information [1].Real-life uncertainties handle effectively by fuzzy set theory. Molodtsov soft set theory deals with uncertainties effectively by considering the parametric point of view, that is, each element is judged by some criteria of attributes. The membership and non-membership functions assign the values from the unit interval [0, 1] with the condition that their sum is less than or equal to one, i.e., if we represent the membership and non-membership functions by ξ and ν, respectively, than 0 ≤ ξ + ν ≤ 1. This condition specifies a range of ξ and ν. The condition 0 ≤ ξ q + νq ≤ 1, where q > 1 is any real number, specifies the range of membership and non-membership functions

Objectives

Methods

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Conclusion