A study on fuzzy logic reasoning with residual implication and Frank´s t-norm

This paper formulates fuzzy reasoning based on residual implications using Frank´s t-norm. The most important of the normative criteria for generalized modus ponens is that the conclusion must not be more informative than the consequent used in the fuzzy implication. Following a recent paper on analysis using a universal set as a finite set from the similar point of view, we here consider a case in which the universe is an infinite set, providing several examples clarifying the meaning of this.