## The minimal tree problem for fuzzy graphs. (El problema del árbol minimal para grafos difusos.)(Spanish. English summary)Zbl 0648.90085

Summary: On the basis of previous definitions, the problem of spanning a fuzzy tree is analyzed. First we treat its existence and then the spanning of a fuzzy tree of minimum cost is found by means of an $$\alpha$$-out decomposition. We have done this with two different assumptions about the cost structure.

### MSC:

 90C35 Programming involving graphs or networks 03E72 Theory of fuzzy sets, etc.

### Keywords:

spanning a fuzzy tree; $$\alpha$$-out decomposition
Full Text:

### References:

 [1] BERGE, C. (1958):Theorie des graphes et ses applications, París, Dunod. [2] BORTOLAN, G., y DEGANI, R. (1985): “A review of sime methods for ranking fuzzy subsets{”,Fuzzy Sets and Systems, 15, 1–19.} · Zbl 0567.90056 · doi:10.1016/0165-0114(85)90012-0 [3] CHRISTOFIDES, N. (1975):Graph Theory. An Algorithmic Approach, Londres, Academic Press. · Zbl 0321.94011 [4] DUBOIS, D., y PRADE, H. (1978): “Fuzzy real algebra{”,Fuzzy Sets and Systems 2, 327–348.} · Zbl 0412.03035 · doi:10.1016/0165-0114(79)90005-8 [5] – (1980):Fuzzy Sets and Sytems. Theory and Applications, Nueva York, Academic Press. [6] DELGADO, M.; VERDEGAY, J. L. y VILA, M. A. (1985): “On fuzzy tree definition{”European J. Oper. Res., 22, 2, 243–249.} · Zbl 0596.05059 · doi:10.1016/0377-2217(85)90232-2 [7] ROSENFELD, A. (1975): “Fuzzy graph{”., enFuzzy Sets and Their Applications to Cognitive and Decision Processes (L. A. Zadeh, K. S. Fu, K. Tanaka y M. Shimura, eds.), Nueva York, Academic Press, 77–97.} [8] VILA, M. A. (1984):Algunas cuestiones sobre la teoría de grafos difusos y sus aplicaciones, Proc. FISAL-83, Palma de Mallorca, 167–177.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.