- ISSN: 1796-2021 (Online); 2374-4367 (Print)
- Abbreviated Title: J. Commun.
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- DOI: 10.12720/jcm
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Home > Published Issues > 2013 > Volume 8, No. 9, September 2013 >
The Inverse Spanning Tree of a Fuzzy Graph Based on Credibility Measure
Abstract—An inverse spanning tree problem is to make theleast modification on the edge weights such that apredetermined spanning tree is a minimum spanning tree. In thispaper, based on the notion of fuzzy α-minimum spanning tree,the inverse spanning tree problem with fuzzy edge weights isdiscussed and formulated as a fuzzy programming model withsome chance constraints. It shows that when all the edgeweights are assumed to be independent fuzzy variables withregular credibility distributions, the proposed model can bereformulated into a traditional nonlinear programmingaccording to the equivalent condition of fuzzy α-minimumspanning tree characterized by a set of constraints on non-treeedges and their tree paths. Moreover, if all the fuzzy weights aretriangular fuzzy numbers, a linear programming problem can beobtained and solved efficiently with the help of some welldeveloped software packages.
Cite: Jian Zhou, Qina Wang, and Xiang Zhang, "The Inverse Spanning Tree of a Fuzzy Graph Based on Credibility Measure," Journal of Communications, vol. 8, no. 9, pp. 566-571, 2013. doi: 10.12720/jcm.8.9.566-571