Degrees of M-fuzzy families of independent L-fuzzy sets

The present paper studies fuzzy matroids in view of degree. First wegeneralize the notion of (L,M)-fuzzy independent structure byintroducing the degree of M-fuzzy family of independent L-fuzzysets with respect to a mapping from L^X to M. Such kind ofdegrees is proved to satisfy some axioms similar to those satisfiedby (L,M)-fuzzy independent structure. Then we define and studysome special degrees (e.g. quotient degrees and isomorphism degrees)with respect to mappings between two (L,M)-fuzzy matroid-likespaces in details. Finally we give characterizations of thesedegrees and investigate relationships between them.

Keywords:

Degree of M-fuzzy family of independent L-fuzzy sets , M-fuzzy family of independent L-fuzzy sets , (L , M)-fuzzy matroid