A solution approach to minimum spanning tree problem under fermatean fuzzy environment

Abstract

In classical graph theory, the minimal spanning tree (MST) is a subgraph with no cycles that connects each vertex with minimum edge weights. Calculating minimum spanning tree of a graph has always been a common problem throughout ages. Fuzzy minimum spanning tree (FMST) is able to handle uncertainty existing in edge weights for a fuzzy graph which occurs in real world situations. In this article, we have studied the MST problem of a directed and undirected fuzzy graph whose edge weights are represented by fermatean fuzzy numbers (FFN). We focus on determining an algorithmic approach for solving fermatean fuzzy minimum spanning tree (FFMST) using the modified Prim’s algorithm for an undirected graph and modified optimum branching algorithm for a directed graph under FFN environment. Since the proposed algorithm includes FFN ranking and arithmetic operations, we use FFNs improved scoring function to compare the weights of the edges of the graph. With the help of numerical examples, the solution technique for the proposed FFMST model is described.