On the distributive equation for t-representable t-norms generated from nilpotent and strict t-norms
Available Online August 2011.
- https://doi.org/10.2991/eusflat.2011.15How to use a DOI?
- Interval-valued fuzzy sets, intuitionistic fuzzy sets, fuzzy implication, triangular norm, distributivity equations, functional equations.
- Recently, in , 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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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 SN - 1951-6851 UR - https://doi.org/10.2991/eusflat.2011.15 DO - https://doi.org/10.2991/eusflat.2011.15 ID - Baczynski2011/08 ER -