Distributive equation of implications based on continuous triangular norms

DOI

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.

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  - 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 (EUSFLAT-11)
PB  - Atlantis Press
SP  - 246
EP  - 253
SN  - 1951-6851
UR  - https://doi.org/10.2991/eusflat.2011.26
DO  - 10.2991/eusflat.2011.26
ID  - Qin2011/08
ER  -