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Generalized Hukuhara Differentiability of Interval-valued Functions and Interval Differential Equations

Author

Listed:
  • Luciano Stefanini

    () (Dipartimento di Economia e Metodi Quantitativi, Università di Urbino (Italy))

  • Barnabas Bede

    () (Department of Mathematics, University of Texas-Pan American, Edimburg, Texas (USA))

Abstract

In the present paper we introduce and study a generalization of the Hukuhara differ- ence and also generalizations of the Hukuhara differentiability to the case of interval valued functions. We consider several possible definitions for the derivative of an interval valued function and we study connections between them and their proper- ties. Using these concepts we study interval differential equations. Local existence and uniqueness of two solutions is obtained together with characterizations of the solutions of an interval differential equation by ODE systems and by differential algebraic equations. We also show some connection with differential inclusions. The thoretical results are turned into practical algorithms to solve interval differential equations.

Suggested Citation

  • Luciano Stefanini & Barnabas Bede, 2008. "Generalized Hukuhara Differentiability of Interval-valued Functions and Interval Differential Equations," Working Papers 0803, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2008.
  • Handle: RePEc:urb:wpaper:08_03
    as

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    File URL: http://www.econ.uniurb.it/RePEc/urb/wpaper/WP_08_03.pdf
    File Function: First version, 2008
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    References listed on IDEAS

    as
    1. Luciano Stefanini, 2008. "A generalization of Hukuhara difference for interval and fuzzy arithmetic," Working Papers 0801, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2008.
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    Citations

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    Cited by:

    1. Luciano Stefanini & Barnabás Bede, 2012. "Some notes on generalized Hukuhara differentiability of interval-valued functions and interval differential equations," Working Papers 1208, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2012.
    2. Luciano Stefanini & Barnabás Bede, 2012. "Generalized Fuzzy Differentiability with LU-parametric Representation," Working Papers 1210, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2012.
    3. Y. Chalco-Cano & W. A. Lodwick & R. Osuna-Gómez & A. Rufián-Lizana, 2016. "The Karush–Kuhn–Tucker optimality conditions for fuzzy optimization problems," Fuzzy Optimization and Decision Making, Springer, vol. 15(1), pages 57-73, March.
    4. repec:spr:opsear:v:54:y:2017:i:4:d:10.1007_s12597-017-0305-x is not listed on IDEAS
    5. Sankar Prasad Mondal, 2016. "Differential equation with interval valued fuzzy number and its applications," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 7(3), pages 370-386, September.
    6. Barnabás Bede & Luciano Stefanini, 2012. "Generalized Differentiability of Fuzzy-valued Functions," Working Papers 1209, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2012.
    7. Luhandjula, M.K. & Rangoaga, M.J., 2014. "An approach for solving a fuzzy multiobjective programming problem," European Journal of Operational Research, Elsevier, vol. 232(2), pages 249-255.
    8. Jianke Zhang & Qinghua Zheng & Xiaojue Ma & Lifeng Li, 2016. "Relationships between interval-valued vector optimization problems and vector variational inequalities," Fuzzy Optimization and Decision Making, Springer, vol. 15(1), pages 33-55, March.

    More about this item

    Keywords

    Interval Arithmetic; Interval Differentiability; Hukuhara Difference; Hukuhara Derivative; Interval Differential Equations.;

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C88 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Other Computer Software
    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General

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