title: |
Distributive equation of implications based on continuous triangular norms |
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publication: |
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part of series: |
Advances in Intelligent Systems Research | |
| pages: | 246 - 253 | |
DOI: |
To be assigned soon (how to use a DOI) | |
author(s): |
Feng Qin, Michal Baczyski, Aifang Xie |
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publication date: |
July 2011 |
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keywords: |
Combs methods, functional equations,
fuzzy implication, t-norm, continuous t-norm. |
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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. |
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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: |