L-fuzzy relational mathematical morphology based on adjoint triples
Result description
We propose an alternative to the standard structure of L-fuzzy Mathematical Morphology (MM) by, on the one hand, considering L-fuzzy relations as structuring elementsand, on the other hand, by using adjoint triples to handle membership values. Those modifications lead to a framework based on set-theoretical operations where we can prove a representation theorem for algebraic morphological erosions and dilations. In addition, we also present some new results concerning duality and transformation invariance.Concerning duality, we show that duality and adjointness can coexist in this L-fuzzy relational MM; concerning transformation invariance, we show sufficient conditionsto guarantee the invariance of morphological operators under arbitrary transformations.
Keywords
Fuzzy Mathematical MorphologyAlgebraic Mathematical MorphologyFuzzy SetsAdjoint triples
The result's identifiers
Result code in IS VaVaI
Result on the web
https://www.sciencedirect.com/science/article/pii/S002002551830728X
DOI - Digital Object Identifier
Alternative languages
Result language
angličtina
Original language name
L-fuzzy relational mathematical morphology based on adjoint triples
Original language description
We propose an alternative to the standard structure of L-fuzzy Mathematical Morphology (MM) by, on the one hand, considering L-fuzzy relations as structuring elementsand, on the other hand, by using adjoint triples to handle membership values. Those modifications lead to a framework based on set-theoretical operations where we can prove a representation theorem for algebraic morphological erosions and dilations. In addition, we also present some new results concerning duality and transformation invariance.Concerning duality, we show that duality and adjointness can coexist in this L-fuzzy relational MM; concerning transformation invariance, we show sufficient conditionsto guarantee the invariance of morphological operators under arbitrary transformations.
Czech name
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Czech description
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Classification
Type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
GA18-06915S: New approaches to aggregation operators in analysis and processing of data
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Information Sciences
ISSN
0020-0255
e-ISSN
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Volume of the periodical
474
Issue of the periodical within the volume
2
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
15
Pages from-to
75-89
UT code for WoS article
000449567200005
EID of the result in the Scopus database
2-s2.0-85054071888
Basic information
Result type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
OECD FORD
Pure mathematics
Year of implementation
2019