An algorithmic approach for finding minimum spanning tree in a intuitionistic fuzzy graph

Abstract

The minimum spanning tree (MST) problem is a well known optimization problem in graph theory that has been used to model many real life problems, e.g., telecommuni- cations,transportation network, routing and water supply network. The MST problems with deterministic edge costs have been worked intensively and the MST of a connected weighted graph can be determined using many efficient algorithms introduced by outstand- ing scientists. However, in real life scenarios, several types of uncertainties are generally encountered, because of insufficient information, imperfect information, failure or other reasons. In this paper, we concentrate on a MST problem of a undirected connected fuzzy graph in which a intuitionistic fuzzy numbers, instead of a crisp (real) number, is used to each edge as edge weight. We define this problem as intuitionistic minimum spanning tree (IMST) problem. We introduce an algorithmic approach for designing the IMST of a fuzzy. The Bor ̊uvka’s algorithm is a popular greedy algorithm for designing a MST in a graph. Here, we have modified the classical Bor ̊uvka’s algorithm to generate the IMST of fuzzy graph. The water distribution system is the lifeline of any city. We also describe the utility of IMST in a water distribution network. A numerical example is worked out to illustrate our proposed algorithm.