• Journal of applied mathematics & informatics
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• 제13권1_2호
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• pp.487-500
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• 2003

We investigate categorical relationships between the category of smooth fuzzy topological spaces, the category of intuitionistic fuzzy topological spaces, and the category of intuitionistic fuzzy topological spaces, and the category of intuitioistic fuzzy topological spaces in Sostak's sense.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제15권2호
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• pp.137-144
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• 2015

In this paper, we obtain two types of adjoint functors between the category of intuitionistic fuzzy topological spaces in Mondal and Samanta’s sense, and the category of intuitionistic fuzzy topological spaces in Ŝostak’s sense. Also, we reveal that the category of Chang’s fuzzy topological spaces is a bireflective full subcategory of the category of intuitionistic fuzzy topological spaces in Mondal and Samanta’s sense.

• 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.

• 한국지능시스템학회논문지
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• 제7권3호
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• pp.102-106
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• 1997

We introduce the category [PFSyn] of saturated fuzzy syntopogenous preordered spaces and continuous isotones ans show that the category [PFSyn] is topological and cotopological. Furthermore, to consdier a compatibility between order structures and fuzzy syntopogenous structure, we introduce a category [IPFSyn] of increasing saturated fuzzy syntopogenous spaces and its dual category [IPFSyn] of decreasing fuzzy syntopogenous spaces, and show that [IPFSyn] and [DPFSyn] are both bireflective in the category [PFSyn].

• 한국지능시스템학회논문지
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• 제12권5호
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• pp.487-490
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• 2002

In this paper, we introduce the notion of fuzzy pseudotopological tower and fuzzy pretopological tower And we show that the category FPsTR of fuzzy pseudotopological tower spaces and the category FPrTR of fuzzy pretopological tower spaces are bireflective subcategoies of the category FLTR of fuzzy limit tower spaces.

• 대한수학회논문집
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• 제12권1호
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• pp.113-126
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• 1997

In this paper we introduce a new definition of a lattice fuzzy topology which is a generalization of Lowen's fuzzy topology and show that the category of Lowen's fuzzy topological spaces is a bireflective full subcategory of the category of lattice fuzzy topological spaces.

• Korean Journal of Mathematics
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• 제25권4호
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• pp.579-585
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• 2017

Based on injectivity, we introduce some definitions in the category NFHG of normal fuzzy hypergroups. And we show that a complete normal fuzzy hypergroup is a weakly injective object in NFHG. Also we investigate weak injectivity in the comma category NFHG/K.

• Korean Journal of Mathematics
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• 제17권2호
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• pp.161-167
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• 2009

Category Fuz of fuzzy sets has a similar function to the Category Set. We study injective, absolute retract, enough injectives, injective hulls and essential extension in the Category Fuz of fuzzy sets.

• 호남수학학술지
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• 제33권1호
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• pp.27-41
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• 2011

This paper studies the relationship between L-fuzzy proximities and L-fuzzy topologies by topological fuzzy remote neigh-borhood systems. We will prove that the category of L-fuzzy topo- logical spaces can be embedded in the category of L-fuzzy quasi-proximity spaces as a core ective full subcategory.

• 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.