• Korean Journal of Mathematics
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• v.31 no.4
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• pp.485-494
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• 2023

The degree of hesitancy of a vertex in a hesitancy fuzzy graph depends on the degree of membership and non-membership of the vertex. We define a new class of hesitancy fuzzy graph, the intuitionistic hesitancy fuzzy graph in which the degree of hesitancy of a vertex is independent of the degree of its membership and non-membership. We introduce the idea of β-product of a pair of hesitancy fuzzy graphs and intuitionistic hesitancy fuzzy graphs and prove certain results based on this product.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.9 no.2
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• pp.137-140
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• 2009

In this paper, we introduce and formulate the definitions of Banach operator type k and Banach operator pair on intuitionistic fuzzy metric space. Thereafter we prove some properties and theorems on intuitionistic fuzzy metric space.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.10a
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• pp.64-69
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• 1998

In this paper, we introduce the concept of the intuitionistic fuzzy proximity space as a generalization of a fuzzy proximity space, and investigate some of their properties. Also we study the relations between intuitionistic fuzzy proximity spaces and intuitionistic fuzzy topological spaces.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2002.05a
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• pp.114-118
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• 2002

As a generalization of fuzzy sets, the concept of intuitionistic fuzzy sets was introduced by Atanassov [1]. By using intuitionistic fuzzy sets, we introduce and study the concept of intuitionistic fuzzy filters and define the concept of Hausdorffness on intuitionistic fuzzy filters, which can not be defined in crisp theory of filters, and study their properties for some extent.

• Bulletin of the Korean Mathematical Society
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• v.44 no.2
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• pp.291-308
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• 2007

The motivation of this paper is to present a new and interesting notion of intuitionistic fuzzy n-normed linear space. Cauchy sequence and convergent sequence in intuitionistic fuzzy n-normed linear space are introduced and we provide some results onit. Furthermore we introduce generalized cartesian product of the intuitionistic fuzzy n-normed linear space and establish some of its properties.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2004.10a
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• pp.351-354
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• 2004

Using the idea of generalized intuitionistic fuzzy set, we study the notion of generalized intuitionistic fuzzy matrices as a generalization of fuzzy matrices, We show that some properties of a square generalized intuitionistic fuzzy matrix such as reflexivity, transitivity and circularity are carried over to the adjoint generalized intuitionistic fuzzy matrix.

• Journal of the Korean Institute of Intelligent Systems
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• v.17 no.1
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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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• v.6 no.3
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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.

• The Pure and Applied Mathematics
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• v.14 no.3
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• pp.139-151
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• 2007

We introduce the concept of intuitionistic fuzzy semiprimality of a semigroup which is an extension of semiprimality in it. And we obtain a characterization of a semigroup that is a semilattice of simple semigroups in terms of intuitionistic fuzzy semiprime interior ideals.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.14 no.3
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• pp.181-187
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• 2014

Dealing with uncertainty is always a challenging problem. Intuitionistic fuzzy sets was presented to manage situations in which experts have some membership and non-membership value to assess an alternative. Hesitant fuzzy sets was used to handle such situations in which experts hesitate between several possible membership values to assess an alternative. In this paper, the concept of intuitionistic hesitant fuzzy set is introduced to provide computational basis to manage the situations in which experts assess an alternative in possible membership values and non-membership values. Distance measure is defined between any two intuitionistic hesitant fuzzy elements. Fuzzy technique for order preference by similarity to ideal solution is developed for intuitionistic hesitant fuzzy set to solve multi-criteria decision making problem in group decision environment. An example is given to illustrate this technique.