2022/12/07 by Mehenni, Abdelkrim, Zedam, Lemnaouar
#FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2212.03605
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.