• 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).

• 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.

• 대한수학회보
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• 제37권1호
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• pp.63-76
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• 2000

In this paper, we introduce the concept of intuitionistic fuzzy points and intuitionistic fuzzy neighborhoods. We investigate the properties of continuous, open and closed maps in the intuitionistic fuzzy topological spaces, and show that the category of Chang's fuzzy topological spaces is a bireflective full subcategory of that of intuitionistic fuzzy topological spaces.

• 충청수학회지
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• 제36권2호
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• pp.135-148
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• 2023

We prove that for any preordered intuitionistic fuzzy approximation space, an intuitionistic fuzzy topology can be created, and conversely, for any intuitionistic fuzzy topology, a reflexive intuitionistic fuzzy relation can be constructed. We also show that there is a relationship, called Galois correspondence, between the functors of these categories. Additionally, by applying certain limitations on the category of intuitionistic fuzzy topological spaces, we obtain an isomorphism between these categories.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제5권1호
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• pp.88-93
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• 2005

Web usage mining is a research field for searching potentially useful and valuable information from web log file. Web log file is a simple list of pages that users refer. Therefore, it is not easy to analyze user's current interest field from web log file. This paper presents web usage mining method for finding users' current interest based on fuzzy categories. We consider not only how many times a user visits pages but also when he visits. We describe a user's current interest with a fuzzy interest degree to categories. Based on fuzzy categories and fuzzy interest degrees, we also propose a method to cluster users according to their interests for user modeling. For user clustering, we define a category vector space. Experiments show that our method properly reflects the time factor of users' web visiting as well as the users' visit number.

• 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.

• 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.

• Korean Journal of Mathematics
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• 제22권4호
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• pp.693-698
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• 2014

Although the category NFHG of normal fuzzy hypergroups is not a topos, it forms a pseudo topos. Also we show that there are pseudo power objects in NFHG.

• 한국지능시스템학회논문지
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• 제17권6호
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• pp.838-842
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• 2007

In this paper, we define that a fuzzy convergence approach limit and a fuzzy approach Chuchy structure on X. And we investigate the relations between the category CAP and the category FCAP. And we show that the categories $FCAP_{RC}$ and $uFACHY_{cpl}$ are isomorphic.

• 호남수학학술지
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• 제42권2호
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• pp.219-234
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• 2020

The fundamental relation on a fuzzy hyperring is defined as the smallest equivalence relation, such that the quotient would be the ring, that is not commutative necessarily. In this paper, we introduce a new fuzzy strongly regular equivalence on fuzzy hyperrings, where the ring is commutative with respect to both sum and product. With considering this relation on fuzzy hyperring, the set of the quotient is a commutative ring. Also, we introduce fundamental functor between the category of fuzzy hyperrings and category of commutative rings and some related properties. Eventually, we introduce α-part in fuzzy hyperring and determine some necessary and sufficient conditions so that the relation α is transitive.