• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2003.05a
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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.

• Journal of the Korean Institute of Intelligent Systems
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• v.15 no.3
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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.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.10 no.1
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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.

• Honam Mathematical Journal
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• v.32 no.2
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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).

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.10 no.2
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• pp.134-141
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• 2010

We introduce the category IVSet(H) of interval-valued H-fuzzy sets and show that IVSet(H) satisfies all the conditions of a topological universe except the terminal separator property. And we study some relations among IVSet (H), ISet (H) and Set (H).

• The Pure and Applied Mathematics
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• v.12 no.1
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• pp.33-45
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• 2005

We introduce the category ISet(H) of intuitionistic H-fuzzy sets and show that ISet(H) satisfies all the conditions of a topological universe except the terminal separator property. And we study the relation between Set(H) and ISet(H).

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2003.05a
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• pp.29-32
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• 2003

We introduce the subcategories IRe $l_{PR}$ (H), IRe $l_{PO}$ (H) and IRe $l_{E}$(H) of IRe $l_{R}$(H) and study their structures in a viewpoint of the topological universe introduced by L.D.Nel. In particular, the category IRe $l_{R}$(H)(resp. IRe $l_{P}$(H) and IRe $l_{E}$(H)) is a topological universe eve, Set. Moreover, we show that IRe $l_{E}$(H) has exponential objects.ial objects.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2003.05a
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• pp.33-36
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• 2003

We introduce the subcategory IRel$\_$R/ (H) of IRel (H) consisting of intuitionistic H-fuzzy reflexive relational spaces on sets and we study structures of IRel$\_$R/ (H) in a viewpoint of the topological universe introduce by L.D.Nel. We show that IRel$\_$R/ (H) is a topological universe over Set. Moreover, we show that exponential objects in IRel$\_$R/ (H) are quite different from those in IRel (H) constructed in [7].