Principles of inclusion and exclusion for interval-valued fuzzy sets and IF-sets

The principle of inclusion and exclusion is one of basic tools of classical set theory. Many previous papers have presented its generalizations to fuzzy sets or IF-sets (Atanassov's intuitionistic fuzzy sets) with Gödel or product operations. In our previous work we clarified these questions for fuzzy sets with intersections and unions based on continuous triangular norms and conorms. Here we extend these results to interval-valued fuzzy sets and IF-sets.