Fuzzy sets and t -norms in the light of fuzzy logic

The paper is a discussion of the many-valued fuzzy logic, which is syntactico-semantically complete and its impact on the fuzzy set theory, namely on the operations with fuzzy sets. Arguments that all the operations with membership grades must fulfil the so called fitting condition are given. It follows that general t -norms are not suitable to be basis of the operations with fuzzy sets. Some general classes of operations with membership grades are presented.