• 한국지능시스템학회논문지
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• 제17권1호
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• pp.100-111
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• 2007

We introduce the concept of intuitionistic fuzzy G-equivalence relations (congruence), and we obtain some results. Furthermore, we prove that $IFC_G(K)$ is isomorphic to $IFN^*(K)$ for any group K. Also, we prove that($IFC_{G,({\lambda},{\mu})}/{\sim},\;*$) and ($IFNG_{({\lambda},{\mu})}(K),\;{\circ}$) are isomorphic.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제6권3호
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• pp.240-246
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• 2006

We introduce the concept of level subgroups of an intuitionistic fuzzy subgroup and study some of it's properties. These level subgroups in turn play an important role in the characterization of all intuitionistic fuzzy subgroup of a prime cyclic group.

• Journal of Information Processing Systems
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• 제13권1호
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• pp.57-67
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• 2017

In this paper, Atanassov's intuitionistic fuzzy set theory is used to handle the uncertainty of students' knowledgeon domain concepts in an E-learning system. Their knowledge on these domain concepts has been collected from tests that were conducted during their learning phase. Atanassov's intuitionistic fuzzy user model is proposed to deal with vagueness in the user's knowledge description in domain concepts. The user model uses Atanassov's intuitionistic fuzzy sets for knowledge representation and linguistic rules for updating the user model. The scores obtained by each student were collected in this model and the decision about the students' knowledge acquisition for each concept whether completely learned, completely known, partially known or completely unknown were placed into the information table. Finally, it has been found that the proposed scheme is more appropriate than the fuzzy scheme.

• Journal of applied mathematics & informatics
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• 제20권1_2호
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• pp.315-325
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• 2006

The notion of intuitionistic fuzzy finite switchboard state machines and (strong) homomorphisms of intuitionistic fuzzy finite state machines are introduced, and related properties are investigated. After we give a congruence relation on the set of all words of elements of X of finite length, the quotient structure is discussed. We show that the family of equivalence classes is a finite semigroup with identity.

• 한국지능시스템학회논문지
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• 제22권1호
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• pp.126-134
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• 2012

By using the concept of intuitionistic interval-valued fuzzy sets, we introduce the notion of intuitionistic interval-valued fuzzy topology. And we study some fundamental properties of intuitionistic interval-valued fuzzy topological spaces: First, we obtain analogues[see Theorem 3.11 and 3.12] of neighborhood systems in ordinary topological spaces. Second, we obtain the result[see Theorem 4.9] corresponding to "the 14-set Theorem" in ordinary topological spaces. Finally, we give the initial structure on intuitionistic interval-valued fuzzy topologies[see Theorem 5.9].

• 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.

• 한국지능시스템학회논문지
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• 제20권6호
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• pp.875-883
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• 2010

We introduce the concept of intuitionistic smooth topology in Lowen's sense and we prove that the family IST(X) of all intuitionistic smooth topologies on a set is a meet complete lattice with least element and the greatest element [Proposition 3.6]. Also we introduce the notion of level fuzzy topology on a set X with respect to an intuitionistic smooth topology and we obtain the relation between the intuitionistic smooth topology $\tau$ and the intuitionistic smooth topology $\eta$ generated by level fuzzy topologies with respect to $\tau$ [Theorem 3.10].

• Journal of applied mathematics & informatics
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• 제22권1_2호
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• pp.411-424
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• 2006

The purpose of this paper, using the idea of intuitionistic fuzzy set due to Atanassov [2], we define the notion of intuitionistic fuzzy metric spaces (see, [1]) due to Kramosil and Michalek [17] and Jungck's common fixed point theorem ([11]) is generalized to intuitionistic fuzzy metric spaces. Further, we first formulate the definition of weakly commuting and R-weakly commuting mappings in intuitionistic fuzzy metric spaces and prove the intuitionistic fuzzy version of Pant's theorem ([21]).

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2004년도 춘계학술대회 학술발표 논문집 제14권 제1호
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• pp.359-362
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• 2004

Using the idea of intuitionistic fuzzy set due to Atanassov, we define the notion of intuitionistic fuzzy metric spaces as a natural generalization of fuzzy metric spaces due to George and Veeramani and prove some known results of metric spaces including Baire's theorem and the Uniform limit theorem for intuitionistic fuzzy metric spaces.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제8권3호
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• pp.207-219
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• 2008

We give some properties of intuitionistc fuzzy left, right, and two-sided ideals and bi-ideals of a semigroup. And we characterize a regular semigroup, a semigroup that is a lattice of left(right) simple semigroups, a semigroup that is a semilattice of left(right) groups and a semigroup that is a semilattice of groups in terms of intuitionistic fuzzy ideals and intuitionistic fuzzy bi-ideals.