In this paper, the notion of closure operators of matroids  is generalized to fuzzy setting  which is called $M$-fuzzifying closure operators, and some properties of $M$-fuzzifying closure operators are discussed. The $M$-fuzzifying matroid induced by an $M$-fuzzifying closure operator can induce an $M$-fuzzifying closure operator. Finally, the characterizations of $M$-fuzzifying acyclic matroi...

this paper presents characterizations of m-fuzzifying matroids bymeans of two kinds of fuzzy operators, called m-fuzzifying derived operatorsand m-fuzzifying difference derived operators.

an l-fuzzifying matroid is a pair (e, i), where i is a map from2e to l satisfying three axioms. in this paper, the notion of closure operatorsin matroid theory is generalized to an l-fuzzy setting and called l-fuzzifyingclosure operators. it is proved that there exists a one-to-one correspondencebetween l-fuzzifying matroids and their l-fuzzifying closure operators.

An L-fuzzifying matroid is a pair (E, I), where I is a map from2E to L satisfying three axioms. In this paper, the notion of closure operatorsin matroid theory is generalized to an L-fuzzy setting and called L-fuzzifyingclosure operators. It is proved that there exists a one-to-one correspondencebetween L-fuzzifying matroids and their L-fuzzifying closure operators.

This paper presents characterizations of M-fuzzifying matroids bymeans of two kinds of fuzzy operators, called M-fuzzifying derived operatorsand M-fuzzifying difference derived operators.

This paper considers fuzzifying topologies, a special case of I-fuzzy topologies (bifuzzy topologies), introduced by Ying [25]. It investigates topological notions defined by means of  -open sets when these are planted into the framework of Ying’s fuzzifying topological spaces (by Łukasiewicz logic in [0, 1]). In this paper we introduce some sorts of operations, called general fuzzifying opera...

in this paper, by presenting some notions and theorems, we obtaindifferent types of fuzzy topologies. in fact, we obtain somelowen-type  and chang-type fuzzy topologies on general fuzzyautomata. to this end, first we define a kuratowski fuzzy interioroperator which induces a  lowen-type  fuzzy topology on the  set ofstates of a max- min general   fuzzy automaton. also by  provingsome theorems, ...

In this paper, new definitions of $L$-fuzzy closure operator, $L$-fuzzy interior operator, $L$-fuzzy remote neighborhood system, $L$-fuzzy neighborhood system and $L$-fuzzy quasi-coincident neighborhood system are proposed. It is proved that the category of $L$-fuzzy closure spaces, the category of $L$-fuzzy interior spaces, the category of $L$-fuzzy remote neighborhood spaces, the category of ...

in this paper, new definitions of $l$-fuzzy closure operator, $l$-fuzzy interior operator, $l$-fuzzy remote neighborhood system, $l$-fuzzy neighborhood system and $l$-fuzzy quasi-coincident neighborhood system are proposed. it is proved that the category of $l$-fuzzy closure spaces, the category of $l$-fuzzy interior spaces, the category of $l$-fuzzy remote neighborhood spaces, the category of ...

The concept of a fuzzifying topology was given in [1] under the name L-fuzzy topology. Ying studied in [9, 10, 11] the fuzzifying topologies in the case of L = [0,1]. A classical topology is a special case of a fuzzifying topology. In a fuzzifying topology τ on a set X , every subset A of X has a degree τ(A) of belonging to τ, 0 ≤ τ(A) ≤ 1. In [4], we defined the degrees of compactness, of loca...