title: |
R-implications and the Exchange Principle:A Complete Characterization |
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publication: |
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part of series: |
Advances in Intelligent Systems Research | |
| pages: | 223 - 229 | |
DOI: |
To be assigned soon (how to use a DOI) | |
author(s): |
Balasubramaniam Jayaram, Michal Baczyski, Radko Mesiar |
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publication date: |
July 2011 |
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keywords: |
R-implication, t-norm, exchange principle, fuzzy implication. |
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abstract: |
It is well-known that the residual IT of a leftcontinuous t-norm T satisfies the exchange principle (EP), viz., IT (x, IT (y, z)) = IT (y, IT (x, z)) for
all x, y, z [0, 1]. However, the left-continuity of
T is only sufficient and not necessary, as many examples in the literature illustrate. In this work we
study the necessary conditions on a t-norm T for its
residual to satisfy (EP). The work presents a complete characterization of the class of t-norms whose
residuals satisfy (EP). |
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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: |