R-implications and the Exchange Principle:A Complete Characterization
- Balasubramaniam Jayaram, Michal Baczynski, Radko Mesiar
- Corresponding Author
- Balasubramaniam Jayaram
Available Online August 2011.
- https://doi.org/10.2991/eusflat.2011.63How to use a DOI?
- R-implication, t-norm, exchange principle, fuzzy implication.
- 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).
- 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 SN - 1951-6851 UR - https://doi.org/10.2991/eusflat.2011.63 DO - https://doi.org/10.2991/eusflat.2011.63 ID - Jayaram2011/08 ER -