Axiomatic considerations of t-norms and R-implications

Authors:
Daowu Pei;Rui Yang
Affiliations:
Faculty of Science, Zhejiang Sci-Tech University, Hangzhou, China;Faculty of Science, Zhejiang Sci-Tech University, Hangzhou, China
Venue:
FSKD'09 Proceedings of the 6th international conference on Fuzzy systems and knowledge discovery - Volume 6
Year:
2009

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Abstract

Triangular norms (t-norms) have been applied to many areas of artificial intelligence. Residual implications (R-implications) induced by t-norms have become important tools in both theoretical and applied researches of nonclassical logics and approximate reasoning. This paper discusses axiomatic characterizations of t-norms and R-implications. The correspondences between properties of t-norms and R-implications are investigated. Some important conclusions are proved first time. Some mistakes in the related literature are corrected, and the proof procedures of some results are simplified.