The Riemann-Lebesgue Integral of Interval-Valued Multifunctions

Autor: Danilo Costarelli, Anca Croitoru, Alina Gavriluţ, Alina Iosif, Anna Rita Sambucini
Jazyk: angličtina
Rok vydání: 2020
Předmět:
Zdroj: Mathematics, Vol 8, Iss 12, p 2250 (2020)
Druh dokumentu: article
ISSN: 2227-7390
DOI: 10.3390/math8122250
Popis: We study Riemann-Lebesgue integrability for interval-valued multifunctions relative to an interval-valued set multifunction. Some classic properties of the RL integral, such as monotonicity, order continuity, bounded variation, convergence are obtained. An application of interval-valued multifunctions to image processing is given for the purpose of illustration; an example is given in case of fractal image coding for image compression, and for edge detection algorithm. In these contexts, the image modelization as an interval valued multifunction is crucial since allows to take into account the presence of quantization errors (such as the so-called round-off error) in the discretization process of a real world analogue visual signal into a digital discrete one.
Databáze: Directory of Open Access Journals
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