Automorphisms, negations and implication operators

Authors:
H. Bustince;P. Burillo;F. Soria
Affiliations:
Departamento de Automática y Computación, Universidad Pública de Navarra, Campus de Arrosadia, 31006 Pamplona, Spain;Departamento de Automática y Computación, Universidad Pública de Navarra, Campus de Arrosadia, 31006 Pamplona, Spain;Departamento de Automática y Computación, Universidad Pública de Navarra, Campus de Arrosadia, 31006 Pamplona, Spain
Venue:
Fuzzy Sets and Systems - Implication operators
Year:
2003

Citing 17
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Abstract

In this paper we study the conditions in which the implication operators satisfy the property I(x,c(x)) = c(x) for all x ∈ [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.