On fuzzy equality and approximation in fuzzy logic
The paper shows that the theory of fuzzy approximation of relations and functions can be elaborated inside the formal theory of fuzzy logic with evaluated syntax. Moreover, it illustrates that fuzzy logic is not only a generalization of classical logic, but that it departs from the latter by solving specific problems which make no sense in classical logic. In detail, the concept of fuzzy equality is discussed, and it is shown that, together with provability degree, it enables one to generalize the concept of fuzzy approximation. Finally, approximation of functions by the Mamdani-Assilian formula based on totally bounded fuzzy equalities is studied.
scientific article; zbMATH DE number 2138690