G-normal fuzzy relational models are universal approximators

Abstract

Making a fuzzy relational model (FRM) g-normal by a specific configuration of the FRM and putting some constraints on both its fuzzifier and its fuzzy relational matrix, results in some favorite features at the expense of loosing some degrees of freedom. In this paper, we show that the g-normal fuzzy relational modeling structure has the universal approximation property despite all the constraints that makes the model g-normal. Indeed, we prove that any real function in Lp (including continuous functions) can be modeled by a g-normal model with any arbitrary accuracy when the universe of discourse is a compact set.