On Interval-Valued Fuzzy Metric Spaces
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.
interval-valued fuzzy metric spaces interval numbers interval-valued t-norm interval-valued fuzzy sets topology complete