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.