On strict T-power invariant implications: Properties and intersections

Abstract

The invariance property of fuzzy implication functions with respect to powers of t-norms is an interesting property in approximate reasoning. Although those fuzzy implication functions satisfying it have been recently fully characterized, the fulfillment of other important additional properties has not been investigated yet. As a first step in this line of research, in this paper the so-called strict T-power invariant implications, those implications which are invariant with respect to powers of a strict t-norm, are analyzed. From this study, it is proved that there are members of this family satisfying important properties such as the exchange principle, the law of importation or the iterative Boolean law, among others. This analysis leads to the characterization of the intersection of this family with the most usual classes of fuzzy implication functions.