On Fuzzy Polynomial Implications

Abstract

In this work, the class of fuzzy polynomial implications is introduced as those fuzzy implications whose expression is given by a polynomial of two variables. Some properties related to the values of the coefficients of the polynomial are studied in order to obtain a fuzzy implication. The polynomial implications with degree less or equal to 3 are fully characterized. Among the implications obtained in these results, there are some well-known implications such as the Reichenbach implication. © Springer International Publishing Switzerland 2014.