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arXiv · 2212.03605

Pseudo triangular norms on bounded trellises

Abdelkrim Mehenni·Lemnaouar Zedam
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Abstract

In this paper, we introduce the notion of pseudo-triangular norm (pseudo-t-norm, for short) as a classes of weakly associative operations on trellises and as a generalization of triangular norm (t-norm, for short) on bounded trellises and we investigate their various properties and present some constructions of pseudo-t-norms on bounded trellises. Also, we study the T-distributivity on bounded trellises. Moreover, we show the relationship among pseudo-t-norms and isomorphisms on bounded trellises, which are more complicated in absence of the property of (transitivity) associativity of the trellis meet and join operations.

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Abdelkrim Mehenni, Lemnaouar Zedam. 2022-12-07. Pseudo triangular norms on bounded trellises. https://arxiv.org/abs/2212.03605

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