The main purpose of this paper is to introduce a concept of L-fuzzifying topological vector spaces (here L is a completely distributive lattice) and study some of their basic properties. Also, a characterization of such spaces in terms of the corresponding L-fuzzifying neighborhood structure of the zero element is given. Finally, the conclusion that the category of L-fuzzifying topological vect...

The purpose of this paper is to introduce the concept of soft double fuzzy semi-topogenous order. Firstly, we give the definition of soft double fuzzy semi-topogenous order. Secondly, we induce a soft double fuzzy topology from a given soft double fuzzy semi-topogenous order by using soft double fuzzy interior operator.

The aim of this paper is to study the categorical relations between matroids, Goetschel-Voxman’s fuzzy matroids and Shi’s fuzzifying matroids. It is shown that the category of fuzzifying matroids is isomorphic to that of closed fuzzy matroids and the latter is concretely coreflective in the category of fuzzy matroids. The category of matroids can be embedded in that of fuzzifying matroids as a ...

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...

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.

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...

the main purpose of this paper is to introduce and study new classes of soft closed sets like soft regular generalized b-closed sets in soft topological spaces (brie y soft rgb-closed set) moreover, soft rg-closed, soft gpr-closed, soft gb-closed, soft gsp-closed, soft g-closed, soft gb-closed, and soft sgb-closed sets in soft topological spaces are introduced in this paper and we investigat...

In this paper,  we introduce  the notion of $M$-fuzzifying interval spaces, and discuss the relationship between $M$-fuzzifying interval spaces and $M$-fuzzifying convex structures.It is proved that  the category  {bf MYCSA2}  can be embedded in  the category  {bf  MYIS}  as a reflective subcategory, where  {bf MYCSA2} and   {bf  MYIS} denote  the category of $M$-fuzzifying convex structures of...