The Riemann-Lebesgue Integral of Interval-Valued Multifunctions

Danilo Costarelli, Anca Croitoru, Alina Gavriluţ, Alina Iosif and Anna Rita Sambucini
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Danilo Costarelli: Department of Mathematics and Computer Sciences, University of Perugia, 1, Via Vanvitelli, 06123 Perugia, Italy
Anca Croitoru: Faculty of Mathematics, University Alexandru Ioan Cuza, Bd. Carol I, No. 11, 700506 Iaşi, Romania
Alina Gavriluţ: Faculty of Mathematics, University Alexandru Ioan Cuza, Bd. Carol I, No. 11, 700506 Iaşi, Romania
Alina Iosif: Department of Computer Science, Information Technology, Mathematics and Physics, Petroleum-Gas University of Ploieşti, Bd. Bucureşti, No. 39, 100680 Ploieşti, Romania
Anna Rita Sambucini: Department of Mathematics and Computer Sciences, University of Perugia, 1, Via Vanvitelli, 06123 Perugia, Italy

Mathematics, 2020, vol. 8, issue 12, 1-17

Abstract: We study Riemann-Lebesgue integrability for interval-valued multifunctions relative to an interval-valued set multifunction. Some classic properties of the R L 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.

Keywords: Riemann-Lebesgue integral; interval valued (set) multifunction; non-additive set function; image processing (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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