• 제목/요약/키워드: Intuitionistic Fuzzy Metric Space

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Some Properties on Intuitionistic Fuzzy Metric Space

  • Park, Jong-Seo;Kwun, Young-Chel;Park, Jin-Han
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • 제10권2호
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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.

직관적 퍼지거리공간에 관하여 (On the Intuitionistic Fuzzy Metric Spaces)

  • Park Jin Han;Saadati R,
    • 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.

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A Fixed Point for Pair of Maps in Intuitionistic Fuzzy Mtric Space

  • Park, Jong-Seo;Kim, Seon-Yu
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • 제7권3호
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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].

Common fixed point theorem for a sequence of mappings in intuitionistic fuzzy metric space

  • Park, Jong-Seo;Kang, Hong-Jae
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • 제7권1호
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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].

Some Common Fixed Points for Type(β) Compatible Maps in an Intuitionistic Fuzzy Metric Space

  • Park, Jong Seo
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • 제13권2호
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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.

On Fixed Point Theorem of Weak Compatible Maps of Type(γ) in Complete Intuitionistic Fuzzy Metric Space

  • Park, Jong-Seo
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • 제11권1호
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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].

Fixed Point Theorem for Compatible Maps with Type(I) and (II) in Intuitionistic Fuzzy Metric Space

  • Park, Jong-Seo
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • 제10권3호
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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.

On Some Results for Five Mappings using Compatibility of Type(α) in Intuitionistic Fuzzy Metric Space

  • Park, Jong-Seo;Park, Jin-Han;Kwun, Young-Chel
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • 제8권4호
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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].

A common fixed point theorem in the intuitionistic fuzzy metric space

  • Park Jong-Seo;Kim Seon-Yu;Kang Hong-Jae
    • 한국지능시스템학회논문지
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    • 제16권3호
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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.