• 한국수학교육학회지시리즈B:순수및응용수학
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• 제18권1호
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• pp.41-50
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• 2011

Based on the theory of falling shadows and fuzzy sets, the notion of a falling fuzzy commutative ideal of a BCK-algebra is introduced. Relations between falling fuzzy commutative ideals and falling fuzzy ideals are investigated.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2002년도 추계학술대회 및 정기총회
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• pp.67-70
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• 2002

We study some relations between separability in fuzzy topological spaces and one in fuzzy hyperspaces. And we investigate some properties of axiom of countability in fuzzy hyperspaces.

• 대한수학회논문집
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• 제15권3호
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• pp.499-509
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• 2000

In [9], the concept of fuzzy sets is applied to the theory of Ζ-ideals in a BCI-semigroup (it was renamed as an IS-algebra for the convenience of study), and a characterization of fuzzy Ζ-ideals by their level Ζ-ideals was discussed. In this paper, we study further properties of fuzzy Ζ-ideals. We prove that the homomorphic image and preimage of a fuzzy Ζ-ideal are also fuzzy Ζ-ideals.

• 호남수학학술지
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• 제44권2호
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• pp.148-164
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• 2022

The main purpose of this paper is to apply the notion of hesitant fuzzy sets to an algebraic structure, so called a BCI-algebra. The primary goal of the study is to define hesitant fuzzy p-ideals and hesitant fuzzy quasi-associative ideals in BCI-algebras, and to investigate their properties and relations.

• Journal of Applied and Pure Mathematics
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• 제5권5_6호
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• pp.347-362
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• 2023

We introduce an algebraic structure induced by a fuzzy bipartial order on a complete residuated lattices with the double negative law. We undertake an investigation into the properties of fuzzy bi-partial orders, including their various characteristics and features. We demonstrate that the two families of l-stable and r-stable fuzzy sets can be regarded as complete lattices, and we establish that these two families are anti-isomorphic. Furthermore, we provide two examples related to them.

• 호남수학학술지
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• 제32권3호
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• pp.413-439
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• 2010

W. A. Dudek, M. Shabir and M. Irfan Ali discussed the properties of (${\alpha},{\beta}$)-fuzzy ideals of hemirings in [9]. In this paper, we discuss the generalization of their results on (${\alpha},{\beta}$)-fuzzy ideals of hemirings. As a generalization of the notions of $({\alpha},\;\in{\vee}q)$-fuzzy left (right) ideals, $({\alpha},\;\in{\vee}q)$-fuzzy h-ideals and $({\alpha},\;\in{\vee}q)$-fuzzy k-ideals, the concepts of $({\alpha},\;\in{\vee}q_m)$-fuzzy left (right) ideals, $({\alpha},\;\in{\vee}q_m)$-fuzzy h-ideals and $({\alpha},\;\in{\vee}q_m)$-fuzzy k-ideals are defined, and their characterizations are considered. Using a left (right) ideal (resp. h-ideal, k-ideal), we construct an $({\alpha},\;\in{\vee}q_m)$-fuzzy left (right) ideal (resp. $({\alpha},\;\in{\vee}q_m)$-fuzzy h-ideal, $({\alpha},\;\in{\vee}q_m)$-fuzzy k-ideal). The implication-based fuzzy h-ideals (k-ideals) of a hemiring are considered.

• Korean Journal of Mathematics
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• 제4권2호
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• pp.95-100
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• 1996

In this note, the notion of fuzzy almost s-continuity is introduced and some results related to this notion are obtained.

• 호남수학학술지
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• 제25권1호
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• pp.131-139
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• 2003

The notion of intuitionistic fuzzy ${\alpha}$-continuity is introduced, and its characterization is given.

• 호남수학학술지
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• 제26권3호
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• pp.355-364
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• 2004

In this paper, we consider fuzzy integrals defined by max-measures and discuss some properties of these fuzzy integrals of measurable functions.

• Journal of applied mathematics & informatics
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• 제28권1_2호
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• pp.99-107
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• 2010

This paper is a study about the relationships among topologies and intuitionistic fuzzy topology induced, respectively, by approximation operators and an intuitionistic fuzzy approximation operator associated with an approximation space (X, R), when the relation R on X is precisely reflexive and transitive. In particular, we consider an intuitionistic fuzzy approximation operator on an approximation space X (i.e., a set X with a reflexive and transitive relation on it), which turns out to be an intuitionistic fuzzy closure operator. This intuitionistic fuzzy closure operator gives rise to two saturated fuzzy topologies on X and it turns out that all the level topologies of one of the fuzzy topology coincide and equal to the topology analogously induced on X by a crisp approximation operator. These observations are then applied to intuitionistic fuzzy automata.