Proceedings of the 7th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-11)

R-implications and the Exchange Principle:A Complete Characterization

Authors
Balasubramaniam Jayaram, Michal Baczynski, Radko Mesiar
Corresponding Author
Balasubramaniam Jayaram
Available Online August 2011.
DOI
https://doi.org/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).
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Proceedings
Proceedings of the 7th conference of the European Society for Fuzzy Logic and Technology
Part of series
Advances in Intelligent Systems Research
Publication Date
August 2011
ISBN
978-90-78677-00-0
DOI
https://doi.org/10.2991/eusflat.2011.63How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

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
PB  - Atlantis Press
SP  - 223
EP  - 229
UR  - https://doi.org/10.2991/eusflat.2011.63
DO  - https://doi.org/10.2991/eusflat.2011.63
ID  - Jayaram2011/08
ER  -