Descriptive-complexity based distance for fuzzy sets

The notion of distance between two objects is very general. Distance metrics and distances have now become an essential tool in many areas of mathematics and its applications including geometry, probability, statistics, coding/graph theory, data analysis, pattern recognition. For a comprehensive source on this subject see [4]. The notion of a fuzzy set was introduced by [8]. It is a class of objects with continuous values of membership and hence extends the classical definition of a set (to distinguish it from a fuzzy set we refer to it as a crisp set).