Information Sciences ( IF 8.1 ) Pub Date : 2020-01-07 , DOI: 10.1016/j.ins.2020.01.007 Jing-Feng Tian , Ming-Hu Ha , Da-Zeng Tian
One of the most important topics of research in fuzzy sets is to get an appropriate notion of fuzzy metric space (FMS), in the paper we propose a new FMS–tripled fuzzy metric space (TFMS), which is a new generalization of George and Veeramani’s FMS. Then we present some related examples, topological properties, convergence of sequences, Cauchy sequence (CS) and completeness of the TFMS. Moreover, we introduce two kinds of notions of generalized fuzzy ψ-contractive (Fψ-C) mappings, and derive a fixed point theorem (FPT) on the mappings in the space.
中文翻译:
三重模糊度量空间和不动点定理
模糊集研究中最重要的主题之一就是要获得适当的模糊度量空间(FMS)概念,在本文中,我们提出了一种新的FMS三重模糊度量空间(TFMS),它是George和Veeramani的FMS。然后我们给出一些相关的例子,拓扑性质,序列的收敛性,柯西序列(CS)和TFMS的完整性。此外,我们介绍两种广义模糊的概念的ψ -contractive(F ψ -C)的映射,并且导出在所述空间中的映射的固定点定理(FPT)。