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Lemnaouar Zedam

Publications and source records attributed to Lemnaouar Zedam.

2 recordsLinked to original sources
arXiv2023

Pseudo triangular norms on bounded trellises

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.

math.RA↗
arXiv2023

Triangular norms on bounded trellises

In this paper, we introduce the notion of a t-norm on bounded pseudo-ordered sets and in particular on bounded trellises (also known as weakly associative lattices), and provide some basic examples. The impact of abandoning transitivity is considerable: on a proper bounded trellis, the meet operation is not a t-norm, and there might actually exist no or even multiple maximal t-norms. We provide a first generic construction method that allows to extend a t-norm on an interior range of a given $\meet$-semi-trellis to the entire $\meet$-semi-trellis. Also, we discuss at length an instantiation of this method based on a particular interior range, namely a finite sub-trellis of the set of right-transitive elements of a given trellis. We pay specific attention to bounded pseudo-chains and modular trellises.

math.RA↗