On the characterizations of (S,N)-implications

Authors:
Michał Baczyński;Balasubramaniam Jayaram
Affiliations:
Institute of Mathematics, University of Silesia, 40-007 Katowice, ul. Bankowa 14, Poland;Department of Mathematics and Computer Sciences, Sri Sathya Sai University, Prasanthi Nilayam, Andhra Pradesh 515134, India
Venue:
Fuzzy Sets and Systems
Year:
2007

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Abstract

The characterization of S-implications generated from strong negations presented firstly by Trillas and Valverde in 1985 is well-known in the literature. In this paper we show that some assumptions are needless and present two characterizations of S-implications with mutually independent requirements. We also present characterizations of (S,N)-implications obtained from continuous fuzzy negations or strict negations. Besides these main results some new facts concerning fuzzy implications, fuzzy negations and laws of contraposition are proved.