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

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 LX 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.