Two open problems of Jayaram are solved. Firstly, we prove that an Archimedean triangular norm with a strong associated negation is necessarily left-continuous. Secondly, as straightforward consequence of the first result, we show that an Archimedean triangular norm with a strong associated negation is necessarily conditionally cancellative.
T-norms with strong negations: Solution of two open problems
Ghiselli Ricci, Roberto
2018-01-01
Abstract
Two open problems of Jayaram are solved. Firstly, we prove that an Archimedean triangular norm with a strong associated negation is necessarily left-continuous. Secondly, as straightforward consequence of the first result, we show that an Archimedean triangular norm with a strong associated negation is necessarily conditionally cancellative.
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