A Model of Fuzzy Shortest Path by Possibility Measure

Abstract

For shortest path problems, the distances associated with networks are assumed to be constant. But, in the real world, such case is rare. This paper formulates the problem in which such distances are L-R fuzzy numbers. The aim is to find the path which the corresponding possibility that its distance is larger than a certain threshold is maximum. That is, we introduce a fuzzy goal, and attempt to maximize the possibility measure, which is a kind of fuzzy measure. Further, we propose an efficient algorithm solving the problem by extending {bf Dijkstra}'s algorithm.