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

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.
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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.2011.26How 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  - 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
UR  - https://doi.org/10.2991/eusflat.2011.26
DO  - https://doi.org/10.2991/eusflat.2011.26
ID  - Qin2011/08
ER  -