• 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.

• East Asian mathematical journal
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• v.18 no.2
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• pp.183-193
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• 2002

The aim of this paper is to prove a common fixed point theorem from the class of compatible maps to larger class of weakly compatible maps without appeal to continuity in fuzzy metric spaces.

• Korean Journal of Mathematics
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• v.14 no.2
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• pp.241-248
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• 2006

We define a G-fuzzy congruence, which is a generalized fuzzy congruence, and characterize the G-fuzzy congruence generated by a left and right compatible fuzzy relation on a semigroup.

• Communications of the Korean Mathematical Society
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• v.23 no.3
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• pp.427-446
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• 2008

In this paper, we give some new definitions of compatible mappings in intuitionistic fuzzy metric spaces and we prove a common fixed point theorem for four mappings under the condition of compatible mappings of type (I) and of type (II) in complete intuitionistic fuzzy metric spaces.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.11 no.2
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• pp.108-112
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• 2011

Kaneko et a1.[4] etc many authors extended with multi-valued maps for the notion of compatible maps in complete metric space. Recently, O'Regan et a1.[5] presented fixed point and homotopy results for compatible single-valued maps on complete metric spaces. In this paper, we will establish some common fixed point theorems using compatible maps in 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.

• Communications of the Korean Mathematical Society
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• v.25 no.1
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• pp.59-68
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• 2010

In this paper, we prove common fixed point theorems for semi-compatible mappings on intuitionistic fuzzy metric space with different some conditions of Park and Kim [10]. This research extended and generalized the results of Singh and Chauhan [14].

• Communications of the Korean Mathematical Society
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• v.24 no.2
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• pp.197-214
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• 2009

In this paper, we formulate the definition of compatible mappings of type (I) and (II) in intuitionistic fuzzy metric spaces and prove a common fixed point theorem by using the conditions of compatible mappings of type (I) and (II) in complete intuitionistic fuzzy metric spaces. Our results intuitionistically fuzzify the result of Cho, Sedghi, and Shobe [4].

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.11 no.3
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• pp.149-152
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• 2011

In this paper, we obtain common fixed point theorem for common property(E.A.) and weakly compatible functions in intuitionistic fuzzy metric space.