Moment Method Using Fuzzy Basis Functions

The paper introduces the use of fuzzy basis function (FBF) in moment method. Fuzzy logic systems (FLS) are universal function approximators, which can approximate any function to an arbitrary degree of accuracy. In the FLS, the user´s insight can be taken into consideration easily and systematically resulting in a better approximation. Moreover, there are many choices in making a FLS depending on the problem. Options include the type of fuzzification, membership functions, composition, inference, and defuzzification, which show the richness of the FL technique. Many of the currently used basis functions in Moment Method could be viewed as special cases of fuzzy basis functions (FBF´s). The method has been applied to the analysis of a parallel plate capacitor with holes to find the charge density on the plates and the capacitance as a result. The results are compared with conventional basis functions demonstrating the validity of the approach.