R-implications and the Exchange Principle:A Complete Characterization

DOI

10.2991/eusflat.2011.63How to use a DOI?

Keywords

R-implication, t-norm, exchange principle, fuzzy implication.

Abstract

It is well-known that the residual IT of a leftcontinuous t-norm T satisfies the exchange principle (EP), viz., IT (x, IT (y, z)) = IT (y, IT (x, z)) for all x, y, z [0, 1]. However, the left-continuity of T is only sufficient and not necessary, as many examples in the literature illustrate. In this work we study the necessary conditions on a t-norm T for its residual to satisfy (EP). The work presents a complete characterization of the class of t-norms whose residuals satisfy (EP).

Copyright

© 2011, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Balasubramaniam Jayaram
AU  - Michal Baczynski
AU  - Radko Mesiar
PY  - 2011/08
DA  - 2011/08
TI  - R-implications and the Exchange Principle:A Complete Characterization
BT  - Proceedings of the 7th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-11)
PB  - Atlantis Press
SP  - 223
EP  - 229
SN  - 1951-6851
UR  - https://doi.org/10.2991/eusflat.2011.63
DO  - 10.2991/eusflat.2011.63
ID  - Jayaram2011/08
ER  -