Fuzzy Calculus by RBF Neural Networks

The paper presents novel modeling of fuzzy inference system by using the ‘fuzzified’ radial basis function (RBF) neural network (NN). RBF NN performs the mapping of the antecedent fuzzy numbers (a.k.a. membership functions, attributes, possibilities degrees) into the consequent ones. In this way, an RBF NN is capable of performing the rigorous calculus with fuzzy numbers. Prior the mapping, both the antecedents and the consequents are discretized and transferred into the n-dimensional and m-dimensional ‘fuzzy’ vectors. These vectors present the training inputs and outputs of an RBF NN and, in this way, an RBF network performs an exact R n → R m mapping. The generalization capacity of such a neural implementation is superior to the ability of the original fuzzy model.