Distributive equation of implications based on continuous triangular norms
Authors
Feng Qin, Michal Baczynski, Aifang Xie
Corresponding Author
Feng Qin
Available Online August 2011.
- DOI
- https://doi.org/10.2991/eusflat.2011.26How to use a DOI?
- Keywords
- Combs methods, functional equations, fuzzy implication, t-norm, continuous t-norm.
- Abstract
- In order to avoid combinatorial rule explosion in fuzzy reasoning, in this work we explore the distributive equations of implications. In details, by means of the section of I, we give out the sufficient and necessary conditions of solutions for the distributive equation of implication I(x, T1(y, z)) = T2(I(x, y), I(x, z)), when T1 is a continuous but not Archimedean triangular norm, T2 is a continuous Archimedean triangular norm and I is an unknown function. Our methods of proof can be applied to the three other functional equations related closely to the distributive equation of implication.
- Open Access
- This is an open access article distributed under the CC BY-NC license.
Cite this article
TY - CONF AU - Feng Qin AU - Michal Baczynski AU - Aifang Xie PY - 2011/08 DA - 2011/08 TI - Distributive equation of implications based on continuous triangular norms BT - Proceedings of the 7th conference of the European Society for Fuzzy Logic and Technology PB - Atlantis Press SP - 246 EP - 253 SN - 1951-6851 UR - https://doi.org/10.2991/eusflat.2011.26 DO - https://doi.org/10.2991/eusflat.2011.26 ID - Qin2011/08 ER -