Categories of bi-fuzzy pre-matroids

In this paper, the concept of (L,M)(L,M)-fuzzy weak mappings is introduced as a generalization of weak mappings. Matroids and weak mappings form a category which is denoted by M. Fuzzifying matroids and fuzzifying weak mappings form a category which is denoted by FYM. [0,1][0,1]-pre-matroids and [0,1][0,1]-weak mappings form a category which is denoted by IM. Bi-fuzzy pre-matroids and bi-fuzzy weak mappings form a category which is denoted by IIFM. We study the relations among M, FYM, IM and IIFM.