| Autor: |
Carlos Bejines, Sergio Ardanza-Trevijano, Jorge Elorza |
| Jazyk: |
angličtina |
| Rok vydání: |
2021 |
| Předmět: |
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| Zdroj: |
Axioms, Vol 10, Iss 3, p 201 (2021) |
| Druh dokumentu: |
article |
| ISSN: |
2075-1680 |
| DOI: |
10.3390/axioms10030201 |
| Popis: |
Preservation of structures under aggregation functions is an active area of research with applications in many fields. Among such structures, min-subgroups play an important role, for instance, in mathematical morphology, where they can be used to model translation invariance. Aggregation of min-subgroups has only been studied for binary aggregation functions. However, results concerning preservation of the min-subgroup structure under binary aggregations do not generalize to aggregation functions with arbitrary input size since they are not associative. In this article, we prove that arbitrary self-aggregation functions preserve the min-subgroup structure. Moreover, we show that whenever the aggregation function is strictly increasing on its diagonal, a min-subgroup and its self-aggregation have the same level sets. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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