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In this paper, an extension of matroids is introduced in lattice-valued fuzzy set theory. Such a generalized matroid is a pair made of a finite set and a fuzzy subfamily of its lattice-valued fuzzy subsets satisfying three axioms. It uses two lattices: one for membership grades of elements to fuzzy sets, and another for membership degrees of fuzzy sets in a fuzzy family of fuzzy sets. It is a logical...
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