Intuitionistic fuzzy sets and some of their so-called extensions

In the present paper we investigate the relationship between intuitionistic fuzzy sets, interval-valued intuitionistic fuzzy sets and some proposed extensions of fuzzy sets, intuitionistic fuzzy sets, and sets that have similar structure. In many cases we establish that the proposed concepts claiming to be extensions of the intuitionistic fuzzy sets are either incorrect in their definitions or offer nothing new compared to the already existing notions. Finally, we formulate four requirements that must be observed so that a new concept claiming to extend an existing one can be considered legitimate and viable, expanding the boundaries of the existing mathematical theory in a meaningful way.