In this paper, we introduce the concept of linear v{C}ech closure spaces and establish the properties of open sets in linear v{C}ech closure spaces (Lv{C}CS). Here, we observe that the concept of linearity is preserved by semi-open sets, g-semi open sets, $gamma$-open sets, sgc-dense sets and compact sets in Lv{C}CS. We also discuss the concept of relative v{C}ech closure operator, meet and pro...

the aim of this paper is to introduce $(l,m)$-fuzzy closurestructure where $l$ and $m$ are strictly two-sided, commutativequantales. firstly, we define $(l,m)$-fuzzy closure spaces and getsome relations between $(l,m)$-double fuzzy topological spaces and$(l,m)$-fuzzy closure spaces. then, we introduce initial$(l,m)$-fuzzy closure structures and we prove that the category$(l,m)$-{bf fc} of $(l,m...

The aim of this paper is to introduce $(L,M)$-fuzzy closurestructure where $L$ and $M$ are strictly two-sided, commutativequantales. Firstly, we define $(L,M)$-fuzzy closure spaces and getsome relations between $(L,M)$-double fuzzy topological spaces and$(L,M)$-fuzzy closure spaces. Then, we introduce initial$(L,M)$-fuzzy closure structures and we prove that the category$(L,M)$-{bf FC} of $(L,M...

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 ...

in this paper, we introduce the concepts of norm and inner prod- uct on fuzzy linear spaces over fuzzy elds and discuss some fundamental properties.

Violator Spaces were introduced by J. Matoušek et al. in 2008 as generalization of Linear Programming problems. Convex geometries were invented by Edelman and Jamison in 1985 as proper combinatorial abstractions of convexity. Convex geometries are defined by antiexchange closure operators. We investigate an interrelations between violator spaces and closure spaces and show that violator spaces ...