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

Document Type : Research Paper


School of Mathematics and Information Science, ShaanXi Normal university, 710119 ShaanXi, P.R. China


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.