The Application of Energy and Laplacian Energy of Hesitancy Fuzzy Graph Based on Similarity Measures in Decision Making Problems

TL;DR

This paper introduces a novel hesitancy fuzzy similarity measure and an algorithm for classifying hesitancy fuzzy graphs, with applications in decision making and expert reputation scoring.

Contribution

It develops a new hesitancy fuzzy similarity measure and a classification algorithm for hesitancy fuzzy graphs, enhancing decision-making processes.

Findings

Validated with real-time numerical examples

Effective classification of hesitancy fuzzy graphs

Improved estimation of expert reputation scores

Abstract

In this article, a new hesitancy fuzzy similarity measure is defined and then used to develop the matrix of hesitancy fuzzy similarity measures, which is subsequently used to classify hesitancy fuzzy graph using the working procedure. We build a working procedure (Algorithm) for estimating the eligible reputation scores values of experts by applying hesitancy fuzzy preference relationships (HFPRs) and the usual similarity degree of one distinct HFPRs to each other's. As the last step, we provide real time numerical examples to demonstrate and validate our working procedure.