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 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...

This paper deals with closure properties of models of fuzzy attribute implications. Fuzzy attribute implications are particular IF-THEN rules which can be interpreted in data tables with fuzzy attributes and/or ranked data tables over domains with similarity relations. We show that models of any set of fuzzy attribute implications form a fuzzy closure system with hedge. Conversely, we show that...

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...

This paper presents the applications of hierarchical clustering to the generators in a power system. A useful application of fuzzy mathematics is that the correction of clustering results and determination of whether it can obtain correct transitive closure. Thus, the fuzzy transitive closure plays an important role in hierarchical clustering. Based on the fuzzy relation matrix, the hierarchica...

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, we introduce and study the concept of $r$-fuzzy regular semi open (closed) sets in smooth topological spaces. by using $r$-fuzzy regular semi open (closed) sets, we define a new fuzzy closure operator namely $r$-fuzzy regular semi interior (closure) operator. also, we introduce fuzzy regular semi continuous and fuzzy regular semi irresolute mappings. moreover, we investigate the ...

We introduce fuzzy closure systems and fuzzy closure operators as extensions of closure systems and closure operators. We study relationships between fuzzy closure systems and fuzzy closure spaces. In particular, two families F (S) and F (C) of fuzzy closure systems and fuzzy closure operators on X are complete lattice isomorphic.

In this paper, we introduce and study the concept of $r$-fuzzy regular semi open (closed) sets in smooth topological spaces. By using $r$-fuzzy regular semi open (closed) sets, we define a new fuzzy closure operator namely $r$-fuzzy regular semi interior (closure) operator. Also, we introduce fuzzy regular semi continuous and fuzzy regular semi irresolute mappings. Moreover, we investigate the ...