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首页> 外文期刊>International journal of nonlinear sciences and numerical simulation >On Fixed Point Theorems in Intuitionistic Fuzzy Metric Spaces
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On Fixed Point Theorems in Intuitionistic Fuzzy Metric Spaces

机译：直觉模糊度量空间中的不动点定理

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Recently, C. Alaca, D. Turkoglu and C. Yildiz [Chaos, Solitons and Fractals, 29, 2006, 1073-1078 to appear] have proved intuitionistic fuzzy versions of the celebrated Banach fixed point theorem and Edelstein fixed point theorem respectively, by means of a notion of intuitionistic fuzzy metric space which is based on the concept of fuzzy metric space due to I. Kramosil and J. Michalek [Kybernetika, 1975]. In this paper we observe that each intuitionistic fuzzy metric space generates a (metrizable) topology that coincides with the topology generated by the associated fuzzy metric space. Furthermore, completeness (respectively, compactness) of the intuitionistic fuzzy metric space is equivalent to completeness (respectively, compactness) of its associated fuzzy metric space and then we deduce that such fixed point theorems are immediate consequences of well-known fixed point theorems for fuzzy metric spaces proved by M. Grabiec [Fuzzy Sets and Systems, 1988].
机译：最近，C。Alaca，D。Turkoglu和C. Yildiz [Chaos，Solitons and Fractals，29，2006，1073-1078出现]分别证明了著名的Banach不动点定理和Edelstein不动点定理的直觉模糊形式。一种直观的模糊度量空间概念的方法，该概念基于I. Kramosil和J. Michalek [Kybernetika，1975]提出的模糊度量空间的概念。在本文中，我们观察到每个直觉的模糊度量空间都会生成（可度量的）拓扑，该拓扑与关联的模糊度量空间生成的拓扑一致。此外，直觉模糊度量空间的完备性（分别为紧致性）等于其关联的模糊度量空间的完备性（分别为紧致性），然后我们得出这样的定点定理是众所周知的模糊定点定理的直接结果。 M. Grabiec [Fuzzy Sets and Systems，1988]证明了度量空间。

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