A study on fuzzy logic reasoning with residual implication and Frank's t-norm

Authors:
Yahachiro Tsukamoto
Affiliations:
Department of Information Engineering, Faculty of Science and Technology, Meijo University, Nagoya, Japan
Venue:
FUZZ-IEEE'09 Proceedings of the 18th international conference on Fuzzy Systems
Year:
2009

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Abstract

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[12], we here consider a case in which the universe is an infinite set, providing several examples clarifying the meaning of this.