Generalized path-finding algorithms on semirings and the fuzzy shortest path problem

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摘要

A new dioı̈d structure 〈Ωk,⊕,⊗,ε,e〉 is proposed to solve a path-finding problem in a fuzzy graph. This algebraic structure is adapted precisely to solve the problem of the K-best fuzzy shortest paths. We demonstrate that the generalized Gauss–Seidel's algorithm always converges for the solving of the K-best fuzzy shortest paths problem on a valued fuzzy graph without cycles of negative weight. This work starts a safe extension of the path algebra paradigm to valued fuzzy graphs for the shortest path-finding problem.

论文关键词:Fuzzy graphs,Path algebra,Dioı̈ds,K-Best fuzzy shortest paths,Generalized Gauss–Seidel's algorithm

论文评审过程:Received 30 November 2001, Revised 10 November 2002, Available online 24 October 2003.

论文官网地址:https://doi.org/10.1016/j.cam.2003.08.027