Automorphisms, negations and implication operators

In this paper we study the conditions in which the implication operators satisfy the property I(x, c(x)) = c(x) for all x E [0, 1], c being any strong negation. This study has led us to present different implication operator characterization theorems from automorphisms, obtaining a theorem similar to the one presented by Smets and Magrez (Internat. J. Approx. Reason. 1 (1987) 327), in which the strong negation c used is not generated by the same automorphism that generates the implication. (C) 2002 Elsevier Science B.V. All rights reserved.