On ordinal sums of partially ordered monoids: A unified approach to ordinal sum constructions of t-norms, t-conorms and uninorms
| Autor: | Michal Holčapek, Antonín Dvořák, Jan Paseka |
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| Rok vydání: | 2022 |
| Předmět: |
Disjoint union
Logic 010102 general mathematics Closure (topology) 02 engineering and technology 16. Peace & justice 01 natural sciences Combinatorics Artificial Intelligence 0202 electrical engineering electronic engineering information engineering 020201 artificial intelligence & image processing Ordinal sum 0101 mathematics Mathematics |
| Zdroj: | Fuzzy Sets and Systems. 446:4-25 |
| ISSN: | 0165-0114 |
| DOI: | 10.1016/j.fss.2021.04.008 |
| Popis: | 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). |
| Databáze: | OpenAIRE |
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