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

On the distributive equation for t-representable t-norms generated from nilpotent and strict t-norms

Authors
Michal Baczynski
Corresponding Author
Michal Baczynski
Available Online August 2011.
DOI
https://doi.org/10.2991/eusflat.2011.15How to use a DOI?
Keywords
Interval-valued fuzzy sets, intuitionistic fuzzy sets, fuzzy implication, triangular norm, distributivity equations, functional equations.
Abstract
Recently, in [4], we have discussed the following distributive equation of implications I(x, T1(y, z)) = T2(I(x, y), I(x, z)) over t-representable t-norms, generated from strict t-norms, in interval-valued fuzzy sets theory. In this work we continue these investigations, but with the assumption that T1 is generated from nilpotent t-norms, while T2 is generated from strict t-norms. As a byproduct result we show all solutions for the following functional equation f(min(u1 +v1, a), min(u2 +v2, a)) = f(u1, u2) + f(v1, v2) related to this case.
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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.2011.15How 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  - Michal Baczynski
PY  - 2011/08
DA  - 2011/08
TI  - On the distributive equation for t-representable t-norms generated from nilpotent and strict t-norms
BT  - Proceedings of the 7th conference of the European Society for Fuzzy Logic and Technology
PB  - Atlantis Press
SP  - 540
EP  - 546
UR  - https://doi.org/10.2991/eusflat.2011.15
DO  - https://doi.org/10.2991/eusflat.2011.15
ID  - Baczynski2011/08
ER  -