Fuzzy Relational Mathematical Morphology: Erosion and Dilation

In the recent years, the subject if fuzzy mathematical morphology entered the field of interest of many researchers. In our recent paper [23], we have developed the basis of the (unstructured) L-fuzzy relation mathematical morphology where L is a quantale. In this paper we extend it to the structure...

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Autores principales: Šostak, Alexander, Uljane, Ingrīda, Eklund, Patrik
Formato: Online Artículo Texto
Lenguaje:English
Publicado: 2020
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7274683/
http://dx.doi.org/10.1007/978-3-030-50153-2_52
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author Šostak, Alexander
Uljane, Ingrīda
Eklund, Patrik
author_facet Šostak, Alexander
Uljane, Ingrīda
Eklund, Patrik
author_sort Šostak, Alexander
collection PubMed
description In the recent years, the subject if fuzzy mathematical morphology entered the field of interest of many researchers. In our recent paper [23], we have developed the basis of the (unstructured) L-fuzzy relation mathematical morphology where L is a quantale. In this paper we extend it to the structured case. We introduce structured L-fuzzy relational erosion and dilation operators, study their basic properties, show that under some conditions these operators are dual and form an adjunction pair. Basing on the topological interpretation of these operators, we introduce the category of L-fuzzy relational morphological spaces and their continuous transformations.
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spelling pubmed-72746832020-06-08 Fuzzy Relational Mathematical Morphology: Erosion and Dilation Šostak, Alexander Uljane, Ingrīda Eklund, Patrik Information Processing and Management of Uncertainty in Knowledge-Based Systems Article In the recent years, the subject if fuzzy mathematical morphology entered the field of interest of many researchers. In our recent paper [23], we have developed the basis of the (unstructured) L-fuzzy relation mathematical morphology where L is a quantale. In this paper we extend it to the structured case. We introduce structured L-fuzzy relational erosion and dilation operators, study their basic properties, show that under some conditions these operators are dual and form an adjunction pair. Basing on the topological interpretation of these operators, we introduce the category of L-fuzzy relational morphological spaces and their continuous transformations. 2020-05-16 /pmc/articles/PMC7274683/ http://dx.doi.org/10.1007/978-3-030-50153-2_52 Text en © Springer Nature Switzerland AG 2020 This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.
spellingShingle Article
Šostak, Alexander
Uljane, Ingrīda
Eklund, Patrik
Fuzzy Relational Mathematical Morphology: Erosion and Dilation
title Fuzzy Relational Mathematical Morphology: Erosion and Dilation
title_full Fuzzy Relational Mathematical Morphology: Erosion and Dilation
title_fullStr Fuzzy Relational Mathematical Morphology: Erosion and Dilation
title_full_unstemmed Fuzzy Relational Mathematical Morphology: Erosion and Dilation
title_short Fuzzy Relational Mathematical Morphology: Erosion and Dilation
title_sort fuzzy relational mathematical morphology: erosion and dilation
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7274683/
http://dx.doi.org/10.1007/978-3-030-50153-2_52
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AT uljaneingrida fuzzyrelationalmathematicalmorphologyerosionanddilation
AT eklundpatrik fuzzyrelationalmathematicalmorphologyerosionanddilation

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