Inclusion measure for intuitionistic fuzzy sets and embedding of intervals

Comparison of measuring the degree of inclusion for two intuitionistic fuzzy sets (IF-sets) and measuring the degree of embedding of two intervals is considered. Embedding is understood as the classical inclusion of intervals. Inclusion of IF-sets is based on a specific order. In case that the nonmebership function does not exceed the membership function in an IF set, and we replace formally the IF-set by an interval-valued fuzzy set, then the inclusion of IF-sets corresponds to an embedding of interval-valued sets. The embedding measure for interval-valued fuzzy sets was defined previously and we compare the concept of embedding with the inclusion of IF-sets.