On Self-Aggregations of Min-Subgroups

 

Abstract

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.

Citation

Please, cite this work as:

[BAE21] C. Bejines, S. Ardanza-Trevijano, and J. Elorza. “On Self-Aggregations of Min-Subgroups”. In: Axioms 10.3 (2021), p. 201. DOI: 10.3390/AXIOMS10030201. URL: https://doi.org/10.3390/axioms10030201.

BibTeX

@Article{DBLP:journals/axioms/BejinesAE21,
     author = {Carlos Bejines and Sergio Ardanza-Trevijano and Jorge Elorza},
     title = {On Self-Aggregations of Min-Subgroups},
     journal = {Axioms},
     volume = {10},
     number = {3},
     pages = {201},
     year = {2021},
     url = {https://doi.org/10.3390/axioms10030201},
     doi = {10.3390/AXIOMS10030201},
     timestamp = {Mon, 28 Aug 2023 21:28:02 +0200},
     biburl = {https://dblp.org/rec/journals/axioms/BejinesAE21.bib},
     bibsource = {dblp computer science bibliography, https://dblp.org},
}

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Papers citing this work

The following is a non-exhaustive list of papers that cite this work:

[1] S. Ardanza-Trevijano, M. Chasco, J. Elorza, et al. “Aggregation of T-subgroups”. In: Fuzzy Sets and Systems 463 (Jul. 2023), p. 108390. ISSN: 0165-0114. DOI: 10.1016/j.fss.2022.08.022. URL: http://dx.doi.org/10.1016/j.fss.2022.08.022.

[2] C. Bejines. “Aggregation of fuzzy vector spaces”. In: Kybernetika (Dec. 2023), p. 752–767. ISSN: 1805-949X. DOI: 10.14736/kyb-2023-5-0752. URL: http://dx.doi.org/10.14736/kyb-2023-5-0752.

[3] F. J. Talavera, C. Bejines, S. Ardanza-Trevijano, et al. “Aggregation of fuzzy graphs”. In: International Journal of Approximate Reasoning 172 (Sep. 2024), p. 109243. ISSN: 0888-613X. DOI: 10.1016/j.ijar.2024.109243. URL: http://dx.doi.org/10.1016/j.ijar.2024.109243.