On the Additional Properties of Fuzzy Polynomial Implications of Degree 4

Abstract

It is well known that fuzzy implication functions have a very flexible definition that encompasses lots of different potential families. Therefore, the additional properties that the family members fulfill define the behavior these operators will have when modeling fuzzy conditionals or applied to any other application. In this way, in this paper, we study the additional properties of fuzzy polynomial implications of degree 4, a recent family of fuzzy implications which has been recently introduced as a family whose members have a simple expression, appealing for applied researchers. It is proved that members of this family fulfill some of the additional essential properties of fuzzy implication functions.