The origin of my idea of intuitionistic fuzziness was a happenstance – as a mathematical game. I read the Russian translation of A. Kaufmann’s book [301] and decided to add to the definition, a second degree (degree of nonmembership) and studied the properties of a set with both degrees. Of course, I observed that the new set is an extension of the ordinary fuzzy set, but I did not immediately notice that it has essentially different properties. So the first research works of mine in this area followed, step-by-step, the existing results in fuzzy sets theory. Of course, some concepts are not so difficult to extend formally. It is interesting to show that the respective extension has specific properties, absent in the basic concept.