Distance generated by a fuzzy compatibility

Abstract

Our three-dimensional Euclidean space is an example of a common existence of crisp and fuzzy structures. Although we have a crisp distance available, the notion of nearness also makes sense. More precisely, it is possible to distinguish at least two levels of fuzzy structures: nearness of points (that is connected to our perception) and our expressions about the points (that is connected to the language we use). This is a motivation for our work that studies a kind of fuzzy metric based on a given crisp one. The topology naturally induced by this metric is also investigated.