Shortest Path Problem Based on Interval-Valued Fuzzy Numbers and Signed Distance Defuzzification Method

This study investigates finding a fuzzy shortest path based on interval-valued fuzzy numbers and signed distance ranking defuzzification method. In this problem, we consider each edge weight of the network as unknown, which means that the precise value for each edge weight is not known at all, but some sample data are available. We propose an approach to combine statistics with fuzzy sets and then use level (1-ß, 1-¿) interval-valued fuzzy numbers that based on past statistical data for obtaining a fuzzy shortest path for this problem. We conclude that the shortest paths in the fuzzy sense obtained from the proposed theorem correspond to the actual paths in the network, and the fuzzy shortest-path problem is an extension of the crisp problem.