• Korean Journal of Mathematics
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• 제21권2호
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• pp.189-195
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• 2013

PosM is a category whose objects are ample spaces and morphisms are possibility mappings. We study some properties of the Category PosM. So we show that Category PosM is a cartesian closed category, and it forms a topos with some condition.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2003년도 춘계 학술대회 학술발표 논문집
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• pp.37-40
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• 2003

We introduce the category IRel (H) consisting of intuitionistic fuzzy relational spaces on sets and we study structures of the category IRel (H) in the viewpoint of the topological universe introduced by L.D.Nel. Thus we show that IRel (H) satisfies all the conditions of a topological universe over Set except the terminal separator property and IRel (H) is cartesian closed over Set.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제10권1호
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• pp.73-81
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• 2010

We introduce the new category VSet(H) consisting of H-fuzzy spaces and H-fuzzy mappings between them satisfying a certain condition, and investigate VSet(H) in the sense of a topological universe. Moreover, we show that VSet(H) is Cartesian closed over Set.

• 한국지능시스템학회논문지
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• 제15권3호
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• pp.389-394
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• 2005

The purpose of this paper is to introduce the notions of L-fuzzy topological towers by using a completely distributive lattic L and show that the category L-FPrTR of L-fuzzy pretopoplogical tower spaces and the category L-FPsTR of L-fuzzy pseudotopological tower spaces are extensional topological constructs. And we show that L-FPsTR is the cartesian closed topological extension of L-FPrTR. Hence we show that L-FPsTR is a topological universe.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 1998년도 The Third Asian Fuzzy Systems Symposium
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• pp.95-100
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• 1998

A notion of 'fuzzy' convergence of filters on a set is introduced. We show that the collection of fuzzy L-limit spaces forms a cartesian closed topological category and obtain an interesting relationship between the notions of 'fuzzy' convergence structure and convergence approach spaces.

• East Asian mathematical journal
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• 제10권1호
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• pp.187-193
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• 1994

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 1997년도 추계학술대회 학술발표 논문집
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• pp.367-369
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• 1997

We introduce a notion of fuzzy L-convergence of filters and show that the collection of fuzzy L-convergence spaces forms a cartesian closed topological category.

• 한국지능시스템학회논문지
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• 제2권3호
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• pp.17-21
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• 1992

In this paper we consider the notion of fuzzy relation as a generalization of that of fuzzy set. For a complete Heyting algebra L. the category set(L) of all L-fuzzy sets is shown to be a bireflective subcategory of the category Rel(L) of all L-fuzzy relations and L-fuzzy relation preserving maps. We investigate categorical structures of subcategories of Rel(L) in view of quasitopos. Among those categories, we include the category L-fuzzy similarity relations with respect to both max-min and max-product compositions, respectively, as a cartesian closed topological category. Moreover, we describe exponential objects explicitly in terms of function space.

• 호남수학학술지
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• 제32권2호
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• pp.333-362
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• 2010

We define H*H-fuzzy set and form a new category Set(H*H) consisting of H*H-fuzzy sets and morphisms between them. First, we study it in the sense of topological universe and obtain an exponential objects of Set(H*H). Second, we investigate some relationships among the categories Set(H*H), Set(H) and ISet(H).

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 1998년도 The Third Asian Fuzzy Systems Symposium
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• pp.219-224
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• 1998

We introduce the notion of ${\gamma}$-fuzzy filter and ${\gamma}$-limit structure to L-fuzzy point. We show that the category ${\gamma}$Lim of ${\gamma}$-limit spaces is a cartesian closed topological construct containing the category LFTop of stratified L-fuzzy topological spaces as a bireflective subcategory.