The fuzzy shortest path length and the corresponding shortest path in a network

The fuzzy shortest path (SP) problem aims at providing decision makers with the fuzzy shortest path length (FSPL) and the SP in a network with fuzzy arc lengths. In this paper, each arc length is represented as a triangular fuzzy set and a new algorithm is proposed to deal with the fuzzy SP problem. First, we proposed a heuristic procedure to find the FSPL among all possible paths in a network. It is based on the idea that a crisp number is a minimum number if and only if any other number is larger than or equal to it. It owns a firm theoretic base in fuzzy sets theory and can be implemented effectively. Second, we propose a way to measure the similarity degree between the FSPL and each fuzzy path lengths. The path with the highest similarity degree is the SP. An illustrative example is given to demonstrate our proposed approach.