• International Journal of Fuzzy Logic and Intelligent Systems
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• v.10 no.2
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• pp.152-156
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• 2010

We define some terminologies on intuitionistic fuzzy metric space and prove that the topology generated by any intuitionistic fuzzy metric space is metrizable. Also, we show that if the intuitionistic fuzzy metric space is complete, then the generated topology is completely metrizable, a Baire space, and that an intuitionistic fuzzy metric space is precompact if and only if every sequence has a Cauchy subsequence.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2005.04a
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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.

• 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.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.7 no.3
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• pp.159-164
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• 2007

Park, Park and Kwun[6] is defined the intuitionistic fuzzy metric space in which it is a little revised from Park[5]. According to this paper, Park, Kwun and Park[11] Park and Kwun[10], Park, Park and Kwun[7] are established some fixed point theorems in the intuitionistic fuzzy metric space. Furthermore, Park, Park and Kwun[6] obtained common fixed point theorem in the intuitionistic fuzzy metric space, and also, Park, Park and Kwun[8] proved common fixed points of maps on intuitionistic fuzzy metric spaces. We prove a fixed point for pair of maps with another method from Park, Park and Kwun[7] in intuitionistic fuzzy metric space defined by Park, Park and Kwun[6]. Our research are an extension of Vijayaraju and Marudai's result[14] and generalization of Park, Park and Kwun[7], Park and Kwun[10].

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.7 no.1
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• pp.30-33
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• 2007

Park and Kim [4], Grabiec [1] studied a fixed point theorem in fuzzy metric space, and Vasuki [8] proved a common fixed point theorem in a fuzzy metric space. Park, Park and Kwun [6] defined the intuitionistic fuzzy metric space in which it is a little revised in Park's definition. Using this definition, Park, Kwun and Park [5] and Park, Park and Kwun [7] proved a fixed point theorem in intuitionistic fuzzy metric space. In this paper, we will prove a common fixed point theorem for a sequence of mappings in a intuitionistic fuzzy metric space. Our result offers a generalization of Vasuki's results [8].

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.13 no.2
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• pp.147-153
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• 2013

Previously, Park et al. (2005) defined an intuitionistic fuzzy metric space and studied several fixed-point theories in this space. This paper provides definitions and describe the properties of type(${\beta}$) compatible mappings, and prove some common fixed points for four self-mappings that are compatible with type(${\beta}$) in an intuitionistic fuzzy metric space. This paper also presents an example of a common fixed point that satisfies the conditions of Theorem 4.1 in an intuitionistic fuzzy metric space.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.11 no.1
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• pp.38-43
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• 2011

In this paper, we give definitions of compatible mappings of type(${\gamma}$) in intuitionistic fuzzy metric space and obtain common fixed point theorem under the conditions of weak compatible mappings of type(${\gamma}$) in complete intuitionistic fuzzy metric space. Our research generalize, extend and improve the results given by Sedghi et.al.[12].

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.10 no.3
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• pp.194-199
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• 2010

In this paper, we give definitions of compatible mappings of type(I) and (II) in intuitionistic fuzzy metric space and obtain common fixed point theorem and example under the conditions of compatible mappings of type(I) and (II) in complete intuitionistic fuzzy metric space. Our research generalize, extend and improve the results given by many authors.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.8 no.4
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• pp.299-305
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• 2008

The object of this paper is to introduce the notion of compatible mapping of type(${\alpha}$) in intuitionistic fuzzy metric space, and to establish common fixed point theorem for five mappings in intuitionistic fuzzy metric space. Our research are an extension for the results of [1] and [7].

• Journal of the Korean Institute of Intelligent Systems
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• v.16 no.3
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• pp.321-325
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• 2006

The purpose of this paper is to establish the common fixed point theorem in the intuitionistic fuzzy metric space in which it is a little revised in Park [11]. Our research are an extension of Jungck's common fixed point theorem [8] in the intuitionistic fuzzy metric space.