Fuzzy shortest path problem

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

“…SP could be p 1 13 or p 2 13 because L min (p rv ) could be along path p 1 13 or p 2 13 . Hence, it is not correct that FSPL is (4,5,11) by the fuzzy ranking methods.…”

“…There were several methods reported to solve the SP problem in the open literature [3][4][5][6][7][8][9][10][11]. Among them, only Refs.…”

“…Among them, only Refs. [2][3][4][5]10] are related to the fuzzy SP problem in spite of their potential applications. Dubois and Prade [5] ÿrst treated the fuzzy SP problem.…”

Z-Dijkstra’s Algorithm to solve Shortest Path Problem in a Z-Graph

“…Lin and Chen 36 found the fuzzy shortest path length in a network by means of a fuzzy linear programming approach. Okada and Soper [39][40][41][42][43][44][45] proposed a fuzzy algorithm, which was based on multiple-labelling methods to offer non-dominated paths to a decision maker. Chuang and Kung 20 proposed a fuzzy shortest path length procedure that can find a fuzzy shortest path length among all possible paths in a network.…”

“…The Fuzzy Shortest Path Problem (FSPP) 18,23,25,[33][34][35][36][37][39][40][41][42][43][44][45][46][47][48] is a generalization of the classical SPP for applications in ill-defined environment and has been found important to many applications such as Communication or Transportation Network, Computational Geometry, Graph Algorithms, Geographical Information Systems (GIS), Network Optimization, etc. In traditional shortest path problems, the arc length of the network takes precise numbers, but in the real-world problem, the arc length may represent transportation time or cost which can be known only approximately due to vagueness of information, and hence it can be considered a fuzzy number or an intuitionistic fuzzy number.…”