title: |
On the distributive equation for t-representable t-norms generated from nilpotent and strict t-norms |
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publication: |
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part of series: |
Advances in Intelligent Systems Research | |
| pages: | 540 - 546 | |
DOI: |
To be assigned soon (how to use a DOI) | |
author(s): |
Michal Baczyski |
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publication date: |
July 2011 |
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keywords: |
Interval-valued fuzzy sets, intuitionistic fuzzy sets, fuzzy implication, triangular norm,
distributivity equations, functional equations. |
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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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copyright: |
©
Atlantis Press. This article is distributed under the
terms of the Creative Commons Attribution License, which permits
non-commercial use, distribution and reproduction in any medium,
provided the original work is properly cited. |
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full text: |