Generalized Additive Weighted Multifactorial Function and its Applications to Fuzzy Inference and Neural Networks

In this chapter, a new family of multifactorial function, called generalized additive weighted multifactorial function, is proposed and discussed in detail. First, its properties in n-dimensional space are discussed and then our results are extended to the infinite dimensional space. Second, the implication of its constant coefficients is explained by fuzzy integral. Finally, its application in fuzzy inference is discussed and we show that it is a usual kind of composition operator in fuzzy neural networks.