Fuzzy Soft Graph Structure with Application

Fuzzy Soft Graph Structure

Abstract

Graph structure provides a valuable framework for examining combinatorial issues in various areas of artificial intelligence and computer systems. The fuzzy graph structure is a development of the fuzzy graph. In this research work, we introduce the concept of a fuzzy soft graph structure (ℱ𝒮𝒢𝒮) as a generalization of fuzzy soft graphs. We define and explain the notions of ℱ𝒮𝒢𝒮, strong ℱ𝒮𝒢𝒮, complete ℱ𝒮𝒢𝒮, uniform vertex ℱ𝒮𝒢𝒮, uniform edge ℱ𝒮𝒢𝒮, complement of ℱ𝒮𝒢𝒮, -complement of ℱ𝒮𝒢𝒮, regular ℱ𝒮𝒢𝒮 and totally regular ℱ𝒮𝒢𝒮. The paper also investigates some basic properties of these notions and provides examples to illustrate them. Moreover, we discuss an application of ℱ𝒮𝒢𝒮 in decision-making problems, such as the identification of the best courier service. Further, we introduce an algorithm to express the general steps of our application. The current study was introduced to make routine life more effective and productive.