Transitivity of parametric family of cardinality-based fuzzy similarity measures using Lukasiewicz t-norm

In fuzzy logic, where members of a set might be linguistic terms, the degree of reflexivity might be in unit interval [0,1] instead of {0,1}. This behaviour of a fuzzy set plays an important role especially in the field of inclusion and similarity measure. This paper is aimed at discovering the relations between the parameters of Lukasiewicz transitive members of a family of cardinality-based fuzzy measure.