Standard Fuzzy Sets and some Many - Valued Logics

After Zadeh has introduced his theory, many-valued logic began to have a new interest. Especially, Łukasiewicz logic was enclosed quite closely in fuzzy sets. There is a strong opinion that Łukasiewicz infinite-valued logic has the role as the logic of fuzzy sets, similarly as classical logic has the role as the logic of crisp sets. But actually, it seems that Kleene’s 3-valued logic was the closest logic connecting to fuzzy sets, when Zadeh created his theory. We will discuss this thing later. In the books Rescher (Rescher, 1969) and Bergmann (Bergmann, 2008) descriptions about Kleene’s logic are given.