A Fuzzy Spanning Tree Problem Based on Possibility and Necessity

Abstract

This paper considers a minimum spanning tree problem with fuzzy costs. Based on possibility theory, the problem is formulated as a fuzzy mathematical programming problem, and is to find the spanning tree which maximizes the possibility measure or the necessity measure with respect to a fuzzy goal. First, we consider a fuzzy spanning tree problem where the edge costs are L-R fuzzy numbers and construct a polynomial order algorithm. Next, we investigate the fuzzy spanning tree problem where a set of the edge costs is a possibilistic variable with a quadratic possibility distribution, and improve the proposed algorithm for solving the problem.