Relevancy transformation operators in the form of polynomial functions

Abstract

Relevancy transformation operators (RET operators) have been widely used in fuzzy systems modelling and the construction of weighted aggregation functions. Several construction methods of RET operators based on different aggregation functions such as t-norm, t-conorm and copula, have been proposed. In this paper, the attention is paid to the expression of RET operators, which is an important feature from an application the point of view. Polynomial RET operators are introduced as those RET operators in the form of polynomial functions of two variables. A complete characterisation of polynomial RET operators of degree less than 4 are presented.