ABSTRACT
In this chapter, the authors propose a new family of multifactorial function that is called generalized additive weighted multifactorial function. They discuss its properties in n-dimensional space and extend their results to the infinite dimensional space. The authors explain the implication of its constant coefficients by fuzzy integral. They also discuss application in fuzzy inference and show that it is a usual kind of composition operator in fuzzy neural networks. Mulitfactorial functions, which can be used to compose the “states”, are very effective methods in multi-criteria fuzzy decision-making. In addition, the multifactorial function is used to define fuzzy perturbation function. The simple additive weighted aggregation operator is a usual Additive Standard Multifactorial-function and is used widely in many aspects.
