Jozsef Dombi - Institute of Informatics, University of Szeged, Szeged, Hungary
Tamas Szepe - Department of Technical Informatics, University of Szeged, Szeged, Hungary

Fuzzy control is one of the most important parts of fuzzy theory for which several approaches exist. Mamdani uses \alpha-cuts and builds the union of the membership functions which is called the aggregated consequence function. The resulting function is the starting point of the defuzzification process. In this article, we define a more natural way to calculate the aggregated consequence function via arithmetical operators. Defuzzification is the optimum value of the resultant membership function. The left and right hand sides of the membership function will be handled separately. Here, we present a new ABFC (Arithmetic Based Fuzzy Control) algorithm based on arithmetic operations which use a new defuzzification approach. The solution is much smoother, more accurate, and much faster than the classical Mamdani controller.

Fuzzy controller, Mamdani controller, Defuzzification, Fuzzy arithmetic