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

Document Type: Research Paper

Authors

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

10.22111/ijfs.2020.5110

Abstract

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.

Keywords