模糊度量空间中的有界集

Bounded Sets of Fuzzy Metric Spaces

研究了Gregori和Veeramani意义下的模糊度量空间的有界性问题.提出了模糊强有界集和模糊弱有界集的概念.利用割度量和邻域等方法,得到了模糊强有界、模糊有界、模糊弱有界和模糊无界等性质的若干刻画,进一步深化了模糊度量空间的理论.

This paper is designed to study systematically the boundedness on fuzzy metric spaces,in the sense of Gregori and Veeramani.The new concepts of strong boundedness and weak boundedness are introduced.By using the methods such as cut distance and neighborhood,the properties of strongly bounded fuzzy sets,bounded fuzzy sets,weakly bounded fuzzy sets and unbounded fuzzy sets are characterized.The obtained results deepen the theoretical researches on fuzzy metric spaces.