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 (ℱð’®ð’¢ð’®) as a generalization of fuzzy soft graphs. We define and explain the notions of ℱð’®ð’¢ð’®, strong ℱð’®ð’¢ð’®, complete ℱð’®ð’¢ð’®, uniform vertex ℱð’®ð’¢ð’®, uniform edge ℱð’®ð’¢ð’®, complement of ℱð’®ð’¢ð’®, -complement of ℱð’®ð’¢ð’®, regular ℱð’®ð’¢ð’® and totally regular ℱð’®ð’¢ð’®. The paper also investigates some basic properties of these notions and provides examples to illustrate them. Moreover, we discuss an application of ℱð’®ð’¢ð’® 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.