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The Riemann-Lebesgue Integral of Interval-Valued Multifunctions

Author

Listed:
  • 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)

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.

Suggested Citation

  • Danilo Costarelli & Anca Croitoru & Alina Gavriluţ & Alina Iosif & Anna Rita Sambucini, 2020. "The Riemann-Lebesgue Integral of Interval-Valued Multifunctions," Mathematics, MDPI, vol. 8(12), pages 1-17, December.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:12:p:2250-:d:465366
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    References listed on IDEAS

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    1. Zhou, Yi-Ming & Zhang, Chao & Zhang, Zeng-Ke, 2009. "An efficient fractal image coding algorithm using unified feature and DCT," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1823-1830.
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    Cited by:

    1. Anca Croitoru & Alina Gavriluţ & Alina Iosif & Anna Rita Sambucini, 2023. "Inequalities in Riemann–Lebesgue Integrability," Mathematics, MDPI, vol. 12(1), pages 1-12, December.

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