On ordinal sums of partially ordered monoids: A unified approach to ordinal sum constructions of t-norms, t-conorms and uninorms

This paper introduces two fundamental types of ordinal sum constructions for partially ordered monoids that are determined by two specific partial orderings on the disjoint union of the partially ordered monoids. Both ordinal sums of partially ordered monoids are generalized with the help of operato...

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Bibliographic Details
Published inFuzzy sets and systems Vol. 446; pp. 4 - 25
Main Authors Dvořák, Antonín, Holčapek, Michal, Paseka, Jan
Format Journal Article
LanguageEnglish
Published Elsevier B.V 05.10.2022
Subjects
Ordinal sum
Partially ordered monoid
Posets
t-conorms
t-norms
Uninorms
Partially ordered monoid
Ordinal sum
t-norms
Posets
t-conorms
Uninorms
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Summary:This paper introduces two fundamental types of ordinal sum constructions for partially ordered monoids that are determined by two specific partial orderings on the disjoint union of the partially ordered monoids. Both ordinal sums of partially ordered monoids are generalized with the help of operators on posets, which combine, in some sense, the properties of interior and closure operators on posets. The proposed approach provides a unified view on several known constructions of ordinal sums of t-norms and t-conorms on posets (lattices) and introduces generalized ordinal sums of uninorms on posets (lattices).
ISSN:0165-0114
1872-6801
DOI:10.1016/j.fss.2021.04.008