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

Authors:
A. Boulmakoul
Affiliations:
LIST Laboratory, Computer Sciences Department, Faculty of Sciences and Technology of Mohammedia, B.P. 146, Mohammedia, Morocco
Venue:
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the international conference on linear algebra and arithmetic, Rabat, Morocco, 28-31 May 2001
Year:
2004

Citing 6
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Abstract

A new dioïd 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.