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On the distributive equation of implication based on a continuous t-norm and a continuous Archimedean t-conorm

2011 4th International Conference on Biomedical Engineering and Informatics (BMEI), 2011
In order to avoid combinatorial rule explosion in fuzzy reasoning, in this work we explore the distributive equation of implication I(T(x, y), z) = S(I(x, z), I(y, z)). In detail, by means of the sections of I, we give out the sufficient and necessary conditions of solutions for the distributive equation of implication I(T (x, y), z) = S(I(x, z), I(y ...
Feng Qin
exaly   +2 more sources

Reconstruction of Additive Generators from Partial Derivatives of Continuous Archimedean t-Norms

2010 40th IEEE International Symposium on Multiple-Valued Logic, 2010
The paper shows a direct correspondence between the first partial derivatives of a continuous Archimedean triangular norm and the first derivatives of its additive generator. An explicit formula for the additive generator is obtained. Application of the result is demonstrated on the problem of convex combinations of strict triangular norms.
Mirko Navara   +2 more
exaly   +3 more sources

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