Inclusion measure and similarity measure of intuitionistic and interval-valued fuzzy sets

We begin the paper studying the axioms that the inclusion measure of an element in another element of a lattice and the similarity measure between two elements should satisfy. Next, we present a series of expressions of inclusion measures, mrst for intuitionistic values and then for intuitionistic fuzzy sets ( or interval-valued, since intuitionistic fuzzy set(IFS) and interval-valued fuzzy set (IV FS) have a strong connection), discussing in both cases their properties. Then we discuss similarity measure which can be transformed by the proposed inclusion mea- sure based on their axiomatic denitions. The similarity measures denied by the proposed inclusion measures of IFSs are seem reasonable by the analysis in [Similarity measures between intuitionistic fuzzy (vague) sets: a comparative analysis, Pattern Recognition Letters 28 (2007) 278-285].