Implications generated from additive generators of representable uninorms: (h, e)-implications

Abstract

A new class of fuzzy implications called (h, e)-implications is introduced. They are implications generated from an additive generator of a representable uninorm in a similar way of Yager's f- and g-implications which are generated from additive generators of continuous Archimedean t-norms and t-conorms, respectively. In addition, they satisfy a classical property of some types of implications derived from uninorms that is I(e, y) = y for all y ∈ [0, 1] and they are another example of a fuzzy implication satisfying the exchange principle but not the law of importation for any t-norm, in fact for any function F : [0, 1] <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> → [0, 1]. Other properties of these implications are studied in detail such as other classical tautologies: contrapositive symmetry and distributivity. Finally, it is proved that they do not intersect with any of the most used classes of implications.