Temporal Intuitionistic Fuzzy Metric Spaces

Abstract

In this study temporal intuitionistic fuzzy metric space is defined to obtain a dynamic measure that expresses distances between the spatio-temporal points whose positions change over time and also between the data represented by these points. In order to define this new approach, the concepts of temporal fuzzy t-norm, temporal fuzzy t-conorm and temporal fuzzy negation, which do not exist in the literature, are defined and some basic features of these concepts are examined. The concept of temporal intuitionistic fuzzy metric spaces is defined with a new approach on the basis of the idea that the degrees of nearness and non-nearness change over time. On the other hand, the fundamental topological properties of temporal intuitionistic fuzzy metric space are also examined. We show that the fundamental properties provided by classical and fuzzy metric spaces are also preserved by this new temporal metric space. Thus, a new and more general and more dynamic metric topology is obtained, in which the basic topological properties of fuzzy and intuitionistic fuzzy metric spaces are preserved.