Approximation properties of Łukasiewicz Fuzzy Systems

Approximation properties of fuzzy systems of Mamdani and Takagi Sugeno types were investigated in detail in literature and are widely used in various applications. Fuzzy logic systems based on a t-norm and a fuzzy implications are not studied in such a great detail, despite their strong theoretical motivation rooting back to classical logic. In the present paper we try to reduce this gap in the literature by investigating approximation properties of Fuzzy Systems based on a Łukasiewicz t-norm and a Łukasiewicz implication. We obtain general approximation theorems together with error estimates and smoothness properties. Also, we investigate in detail fuzzy systems of Łukasiewicz type, using them in function approximation example.