Universal Approximation and Its Realization of Generalized Mamdani Fuzzy System Based on K-integral Norms
Gui Wang · Acta Automatica Sinica · 2014
Firstly, the definition of a K-integral norm is given by introducing the quasi-subtraction operator, and the input space of a generalized Mamdani fuzzy system is divided by equidistant partition. Secondly, applying some properties of a piecewise linear function(PLF), universal approximation of a generalized Mamdani fuzzy system is proved structurally in the sense of a K-integral norms. Furthermore, the capability of the fuzzy systems to approximate the space of continuous functions is extended into that to a kind of space of integrable functions class. Finally, the universal approximation and its realization of generalized Mamdani fuzzy system to a given integrable function are showed by means of a simulation example.