New Results in the Calculus of Fuzzy-Valued Functions Using Mid-Point Representations

We present new results in the calculus for fuzzy-valued functions of a single real variable. We adopt extensively the midpoint-radius representation of intervals in the real half-plane and show its usefulness in fuzzy calculus. Concepts related to convergence and limits, continuity, level-wise gH-di...

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Autores principales: Stefanini, Luciano, Sorini, Laerte, Shahidi, Mina
Formato: Online Artículo Texto
Lenguaje:English
Publicado: 2020
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7274666/
http://dx.doi.org/10.1007/978-3-030-50143-3_3
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author Stefanini, Luciano
Sorini, Laerte
Shahidi, Mina
author_facet Stefanini, Luciano
Sorini, Laerte
Shahidi, Mina
author_sort Stefanini, Luciano
collection PubMed
description We present new results in the calculus for fuzzy-valued functions of a single real variable. We adopt extensively the midpoint-radius representation of intervals in the real half-plane and show its usefulness in fuzzy calculus. Concepts related to convergence and limits, continuity, level-wise gH-differentiability of first and second orders have nice and useful midpoint expressions. Using mid-point representation of fuzzy-valued functions, partial orders and properties of monotonicity and convexity are discussed and analysed in detail. Periodicity is easy to represent and identify. Graphical examples and pictures accompany the presentation.
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spelling pubmed-72746662020-06-08 New Results in the Calculus of Fuzzy-Valued Functions Using Mid-Point Representations Stefanini, Luciano Sorini, Laerte Shahidi, Mina Information Processing and Management of Uncertainty in Knowledge-Based Systems Article We present new results in the calculus for fuzzy-valued functions of a single real variable. We adopt extensively the midpoint-radius representation of intervals in the real half-plane and show its usefulness in fuzzy calculus. Concepts related to convergence and limits, continuity, level-wise gH-differentiability of first and second orders have nice and useful midpoint expressions. Using mid-point representation of fuzzy-valued functions, partial orders and properties of monotonicity and convexity are discussed and analysed in detail. Periodicity is easy to represent and identify. Graphical examples and pictures accompany the presentation. 2020-05-15 /pmc/articles/PMC7274666/ http://dx.doi.org/10.1007/978-3-030-50143-3_3 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
Stefanini, Luciano
Sorini, Laerte
Shahidi, Mina
New Results in the Calculus of Fuzzy-Valued Functions Using Mid-Point Representations
title New Results in the Calculus of Fuzzy-Valued Functions Using Mid-Point Representations
title_full New Results in the Calculus of Fuzzy-Valued Functions Using Mid-Point Representations
title_fullStr New Results in the Calculus of Fuzzy-Valued Functions Using Mid-Point Representations
title_full_unstemmed New Results in the Calculus of Fuzzy-Valued Functions Using Mid-Point Representations
title_short New Results in the Calculus of Fuzzy-Valued Functions Using Mid-Point Representations
title_sort new results in the calculus of fuzzy-valued functions using mid-point representations
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7274666/
http://dx.doi.org/10.1007/978-3-030-50143-3_3
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AT sorinilaerte newresultsinthecalculusoffuzzyvaluedfunctionsusingmidpointrepresentations
AT shahidimina newresultsinthecalculusoffuzzyvaluedfunctionsusingmidpointrepresentations

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