2022/12/05 by Lemnaouar Zedam, Zedam, Lemnaouar, De Baets, Bernard
Computer Science · Decision Sciences · #Advanced Algebra and Logic #FOS: Mathematics #Fuzzy and Soft Set Theory #Rings and Algebras (math.RA) #Rough Sets and Fuzzy Logic
paper · pdf · doi:10.48550/arxiv.2212.02655
openalex publication_date 2022/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.