• 호남수학학술지
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• 제32권2호
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• pp.307-331
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• 2010

The notion of intuitionistic fuzzy semi-pre interior (semi-pre closure) is introduced, and several related properties are investigated. Characterizations of an intuitionistic fuzzy regular open set, an intuitionistic fuzzy semi-open set and an intuitionistic fuzzy ${\gamma}$-open set are provided. A method to make an intuitionistic fuzzy regular open set (resp. intuitionistic fuzzy regular closed set) is established. A relation between an intuitionistic fuzzy ${\gamma}$-open set and an intuitionistic fuzzy semi-preopen set is considered. A condition for an intuitionistic fuzzy set to be an intuitionistic fuzzy ${\gamma}$-open set is discussed.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제15권1호
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• pp.79-86
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• 2015

This paper is devoted to finding relationship between intuitionistic fuzzy preorders and intuitionistic fuzzy topologies. For any intuitionistic fuzzy preordered space, an intuitionistic fuzzy topology will be constructed. Conversely, for any intuitionistic fuzzy topological space, we obtain an intuitionistic fuzzy preorder on the set. Moreover, we will show that the family of all intuitionistic fuzzy preorders on an underlying set has a very close link to the family of all intuitionistic fuzzy topologies on the set satisfying some extra condition.

• 호남수학학술지
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• 제27권4호
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• pp.525-541
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• 2005

We give the characterization of an intuitionistic fuzzy ideal[resp. intuitionistic fuzzy left ideal, an intuitionistic fuzzy right ideal and an intuitionistic fuzzy bi-ideal] generated by an intuitionistic fuzzy set in a semigroup without any condition. And we prove that every intuitionistic fuzzy ideal of a semigroup S is the union of a family of intuitionistic fuzzy principle ideals of S. Finally, we investigate the intuitionistic fuzzy ideal generated by an intuitionistic fuzzy set in $S^1$.

• Korean Journal of Mathematics
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• 제30권3호
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• pp.443-458
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• 2022

In this paper, we apply the concept of intuitionistic Q-fuzzy set to PMS-algebras. We study the concept of intuitionistic Q-fuzzy PMS-ideals of PMS-algebras and investigate some related properties of intuitionistic Q-fuzzy PMS-ideals of PMS-algebras. We provide the relationship between an intuitionistic Q-fuzzy PMS-subalgebra and an intuitionistic Q-fuzzy PMS-ideal of a PMS-algebra. We establish a condition for an intuitionistic Q-fuzzy set in a PMS-algebra to be an intuitionistic Q-fuzzy PMS-ideal of a PMS-algebra. Characterizations of intuitionistic Q-fuzzy PMS-ideals of PMS-algebras in terms of their level sets are given.

• 한국지능시스템학회논문지
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• 제21권3호
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• pp.389-394
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• 2011

The notion of generalized intuitionistic fuzzy soft set theory is proposed. Our generalized intuitionistic fuzzy soft set theory is a combination of the generalized intuitionistic fuzzy set theory and the soft set theory. In other words, our generalized intuitionistic fuzzy soft set theory is an extension of the intuitionistic fuzzy soft set theory. The complement, "and" and "or" operations are defined on the generalized intuitionistic fuzzy soft sets. Their basic properties for the generalized intuitionistic fuzzy soft sets are also presented and discussed.

• 한국지능시스템학회논문지
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• 제18권3호
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• pp.316-322
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• 2008

본 논문은 구간치 intuitionistic fuzzy soft sets의 개념과 연산을 소개하며 기본적인 성질을 조사한다.

• 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.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2005년도 춘계학술대회 학술발표 논문집 제15권 제1호
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• pp.157-160
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• 2005

In this paper, we define precompact set in intuitionistic fuzzy metric spaces and prove that any subset of an intuitionistic fuzzy metric space is compact if and only if it is precompact and complete. Also we define topologically complete intuitionistic fuzzy metrizable spaces and prove that any $G\delta$ set in a complete intuitionistic fuzzy metric spaces is a topologically complete intuitionistic fuzzy metrizable space and vice versa.

• Korean Journal of Mathematics
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• 제25권1호
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• pp.1-18
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• 2017

In this paper, we introduce the concepts of ([r, s], [t, u])-interval-valued intuitionistic fuzzy generalized preclosed sets and ([r, s], [t, u])-interval-valued intuitionistic fuzzy generalized preopen sets in the interval-valued intuitionistic smooth topological space and ([r, s], [t, u])-interval-valued intuitionistic fuzzy generalized pre-continuous mappings and then investigate some of their properties.

• Journal of applied mathematics & informatics
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• 제35권3_4호
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• pp.331-347
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• 2017

Soft sets are fantastic mathematical tools to handle imprecise and uncertain information in complicated situations. In this paper, we defined the hybrid structure which is the combination of soft set and complex number representation of intuitionistic fuzzy set. We defined basic set theoretic operations such as complement, union, intersection, restricted union, restricted intersection etc. for this hybrid structure. Moreover, we developed this theory to establish some more set theoretic operations like Disjunctive sum, difference, product, conjugate etc.