Degrees of \(M\)-fuzzy families of independent \(L\)-fuzzy sets. (English) Zbl 1429.05033
Summary: The present paper studies fuzzy matroids in view of degree. First, we generalize the notion of \((L,M)\)-fuzzy independent structure by introducing the degree of \(M\)-fuzzy family of independent \(L\)-fuzzy sets with respect to a mapping from \(L^X\) to \(M\). Such kind of degrees is proved to satisfy some axioms similar to those satisfied by \((L,M)\)-fuzzy independent structure. Then, we define and study some special degrees (e.g., quotient degrees and isomorphism degrees) with respect to mappings between two \((L,M)\)-fuzzy matroid-like spaces in details. Finally we give characterizations of these degrees and investigate relationships between them.
MSC:
| 05B35 | Combinatorial aspects of matroids and geometric lattices |
| 03E72 | Theory of fuzzy sets, etc. |
Keywords:
degree of \(M\)-fuzzy family of independent \(L\)-fuzzy sets; \(M\)-fuzzy family of independent \(L\)-fuzzy sets; \((L,M)\)-fuzzy matroidReferences:
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