An Approach Towards Decision-Making and Shortest Path Problems Based on T-Spherical Fuzzy Information

Abstract

In this paper, we propose some developments in fuzzy graph theory. An original notion of a T-spherical fuzzy graph is presented as a commonality of fuzzy graph, an intuitionistic fuzzy graph and a picture fuzzy graph. The originality, the imperativeness and the importance of this notion are discussed by showing some results, giving examples and graphical analysis. Some theoretical terms of graphs such as a T-spherical fuzzy subgraph, a complement of T-SFG, degree of T-SFG are clarified and their attributes and aspects are analyzed. Interestingly, three types of decision-making problems using the framework of T-SFGs are studied. These problems include the problem of the shortest path, the safe root for an airline journey and the problem of supply chain management in a T-spherical fuzzy network. The comparison of this new approach towards these problems with existing approaches is also established. A new algorithm is put forward in the event of T-SFGs and is used to seek out the shortest path problem. The overall analysis of the suggested notion under the prevailing theory is conducted. The advantages of the proposed approach are discussed based on the existing tools and a short comparison of the new with existing tools is established.