Joint Proceedings of the 19th World Congress of the International Fuzzy Systems Association (IFSA), the 12th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT), and the 11th International Summer School on Aggregation Operators (AGOP)

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Aggregation of Operators of Fuzzy Relational Mathematical Morphology: Erosion and Dilation

Authors
Alexander Šostak, Ingrīda Uļjane
Corresponding Author
Alexander Šostak
Available Online 30 August 2021.
DOI
10.2991/asum.k.210827.090How to use a DOI?
Keywords
structured fuzzy relational erosion, structured fuzzy relational dilation, aggregation, duality, adjunction
Abstract

Revising the definitions of fuzzy relational erosion and dilation introduced by N. Madrid et al. (L-fuzzy relational mathematical morphology based on adjoint triples. Inf. Sci. 474, 75–89, 2019), we define the structured versions of these operators and study their basic properties. Our principal interest is aggregation of fuzzy relational, specifically structured, erosions and dilations. We base such aggregation on a dual pair of binary operators (♢, ☉) (e.g. a t-norm and the t-conorm); ♢ is applied for aggregation of erosions and ☉ for aggregation of dilations.

Copyright
© 2021, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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Volume Title
Joint Proceedings of the 19th World Congress of the International Fuzzy Systems Association (IFSA), the 12th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT), and the 11th International Summer School on Aggregation Operators (AGOP)
Series
Atlantis Studies in Uncertainty Modelling
Publication Date
30 August 2021
ISBN
978-94-6239-423-0
ISSN
2589-6644
DOI
10.2991/asum.k.210827.090How to use a DOI?
Copyright
© 2021, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

risenwbib
TY  - CONF
AU  - Alexander Šostak
AU  - Ingrīda Uļjane
PY  - 2021
DA  - 2021/08/30
TI  - Aggregation of Operators of Fuzzy Relational Mathematical Morphology: Erosion and Dilation
BT  - Joint Proceedings of the 19th World Congress of the International Fuzzy Systems Association (IFSA), the 12th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT), and the 11th International Summer School on Aggregation Operators (AGOP)
PB  - Atlantis Press
SP  - 667
EP  - 674
SN  - 2589-6644
UR  - https://doi.org/10.2991/asum.k.210827.090
DO  - 10.2991/asum.k.210827.090
ID  - Šostak2021
ER  -