Title :
Approximation properties and continuous differentiability of a class of SISO fuzzy systems
Author :
Bede, B. ; Peterson, Matthew P.
Author_Institution :
Dept. of Math., DigiPen Inst. of Technol., Redmond, WA, USA
Abstract :
The goal of the present paper is to investigate approximation and smoothness properties of Larsen type single input single output (SISO) fuzzy systems, that is, fuzzy logic systems using the maximum as aggregation for the individual rule outputs, product (Goguen) t-norm as the conjunctive operator and center of gravity defuzzification. We prove that the function providing the output of the above considered Larsen type fuzzy system is capable of approximating any continuous function. Also, it is continuously differentiable under very relaxed conditions as e.g. continuous differentiability of the antecendents except at their core, and continuous differentiability of the consequences of fuzzy rules except at their core and the enpoints of their support. We show practical examples regarding the approximation and smoothness of the Larsen type operators, showing also by an example that the conditions on the antecedent part cannot be in general weakened further without loosing continuous differentiability. The present paper provides a theoretical background for claims in literature stating that the output of a fuzzy control system of this type is smooth.
Keywords :
approximation theory; continuous systems; fuzzy control; fuzzy logic; fuzzy systems; Goguen t-norm; Larsen type fuzzy system; Larsen type operators; Larsen type single input single output fuzzy systems; SISO fuzzy systems; approximation property; center of gravity defuzzification; conjunctive operator; continuous differentiability; continuous function; fuzzy control system; fuzzy logic systems; product t-norm; smoothness property; Accuracy; Approximation methods; Fuzzy systems; Gravity; Informatics; Splines (mathematics);
Conference_Titel :
Applied Computational Intelligence and Informatics (SACI), 2013 IEEE 8th International Symposium on
Conference_Location :
Timisoara
Print_ISBN :
978-1-4673-6397-6
DOI :
10.1109/SACI.2013.6608949