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Fuzzy matroid sums and a greedy algorithm. (English) Zbl 0789.05018
The results of this paper follow the line of other publications of the authors in the same journal (see volumes 27, 31, 36, 37 and 51). Ten definitions fix the basic ideas related with the theory of fuzzy matroids (fm). A theorem establishes the role of the cardinality of a fm. The main result of this paper is provided by Theorem 4.1. A sufficient condition for the relation of the weights $$w(\alpha) \geq w(\beta)$$, for each basis, is derived. Theorems 4.2 and 4.5 prove that this relationship holds for elementary fm sums in reduced form, when $$\alpha$$ is selected for a certain greedy algorithm.