篇名 | On Interval-Valued Fuzzy Metric Spaces |
---|---|
卷期 | 14:1 |
作者 | Yonghong Shen 、 Haifeng Li 、 Faxing Wang |
頁次 | 035-044 |
關鍵字 | Interval numbers 、 Interval-valued fuzzy sets 、 Interval-valued t-norm 、 Interval-valued fuzzy metric spaces 、 Topology 、 Complete 、 EI 、 SCI 、 SCIE 、 Scopus |
出刊日期 | 201203 |
In this paper, following the ideas of (continuous) t-norm and interval numbers, a concept of (continuous) interval-valued t-norm is proposed. Based on the interval-valued fuzzy set and the continuous interval- valued t-norm, we propose a notion of interval- valued fuzzy metric space, which is a generalization of fuzzy metric space in the sense of George and Veeramani [Fuzzy Sets and Systems 64 (1994): 395-399]. Meanwhile, we show that each metric induces an interval-valued fuzzy metric in certain conditions. Finally, we define a Hausdorff topology on an interval-valued fuzzy metric space and generalize some well-known conclusions of general metric spaces.