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

DOI

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.

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/).

Download article (PDF)

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 (EUSFLAT-11)
PB  - Atlantis Press
SP  - 540
EP  - 546
SN  - 1951-6851
UR  - https://doi.org/10.2991/eusflat.2011.15
DO  - 10.2991/eusflat.2011.15
ID  - Baczynski2011/08
ER  -