引用本文:杨浩, 吴健荣.模糊度量空间中的有界集[J].西南大学学报(自然科学版),2019,41(10):45~50
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模糊度量空间中的有界集
杨浩, 吴健荣
苏州科技大学 数理学院, 江苏 苏州 215009
摘要:
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.
关键词:  模糊度量  模糊强有界集  模糊有界集  模糊弱有界集  模糊无界集
DOI:10.13718/j.cnki.xdzk.2019.10.006
分类号:O159
基金项目:国家自然科学基金项目(11371013).
Bounded Sets of Fuzzy Metric Spaces
YANG Hao, WU Jian-rong
School of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou Jiangsu 215009, China
Abstract:
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.
Key words:  fuzzy metric space  strongly bounded fuzzy set  bounded fuzzy set  weakly bounded fuzzy set  unbounded fuzzy set
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