University of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065417120200201Degrees of M-fuzzy families of independent L-fuzzy sets5364511010.22111/ijfs.2020.5110ENS. Y.ZhangSchool of Mathematics and Information Science, ShaanXi Normal university, 710119 ShaanXi, P.R. ChinaS. G.LiSchool of Mathematics and Information Science, ShaanXi Normal university, 710119 ShaanXi, P.R. ChinaJournal Article20200118The present paper studies fuzzy matroids in view of degree. First we<br />generalize the notion of $(L,M)$-fuzzy independent structure by<br />introducing the degree of $M$-fuzzy family of independent $L$-fuzzy<br />sets with respect to a mapping from $L^X$ to $M$. Such kind of<br />degrees is proved to satisfy some axioms similar to those satisfied<br />by $(L,M)$-fuzzy independent structure. Then we define and study<br />some special degrees (e.g. quotient degrees and isomorphism degrees)<br />with respect to mappings between two $(L,M)$-fuzzy matroid-like<br />spaces in details. Finally we give characterizations of these<br />degrees and investigate relationships between them.https://ijfs.usb.ac.ir/article_5110_2fec6c357594b46207d0d0444db616b1.pdf