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Generalized Differentiability of Fuzzy-valued Functions

Author

Listed:
  • Barnab?s Bede

    (Department of Mathematics, DigiPen Institute of Technology, Redmond,Washington, USA)

  • Luciano Stefanini

    (Department of Economics, Society & Politics, Università di Urbino "Carlo Bo")

Abstract

In the present paper, using novel generalizations of the Hukuhara difference for fuzzy sets, we introduce and study new generalized differentiability concepts for fuzzy valued functions. Several properties of the new concepts are investigated and they are compared to similar fuzzy differentiabilities finding connections between them. Characterization and relatively simple expressions are provided for the new derivatives.

Suggested Citation

  • Barnab?s 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.
    • Handle: RePEc:urb:wpaper:12_09
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    File URL: http://www.econ.uniurb.it/RePEc/urb/wpaper/WP_12_09.pdf
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    References listed on IDEAS

    as
    1. Luciano Stefanini & Barnab?s 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 & 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.
    3. 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.
    4. Luciano Stefanini & Maria Letizia Guerra, 2007. "On Fuzzy Arithmetic Operations: Some Properties and Distributive Approximations," Working Papers 0703, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2007.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Beatriz Hernández-Jiménez & Gabriel Ruiz-Garzón & Antonio Beato-Moreno & Rafaela Osuna-Gómez, 2021. "A Better Approach for Solving a Fuzzy Multiobjective Programming Problem by Level Sets," Mathematics, MDPI, vol. 9(9), pages 1-14, April.
    2. Luciano Stefanini & Barnab?s 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. Omid Solaymani Fard & Mohadeseh Ramezanzadeh, 2017. "On Fuzzy Portfolio Selection Problems: A Parametric Representation Approach," Complexity, Hindawi, vol. 2017, pages 1-12, September.
    4. Saed Mallak & Doa’a Farekh & Basem Attili, 2021. "Numerical Investigation of Fuzzy Predator-Prey Model with a Functional Response of the Form Arctan ( ax )," Mathematics, MDPI, vol. 9(16), pages 1-22, August.
    5. Nadeem Salamat & Muhammad Mustahsan & Malik M. Saad Missen, 2019. "Switching Point Solution of Second-Order Fuzzy Differential Equations Using Differential Transformation Method," Mathematics, MDPI, vol. 7(3), pages 1-19, March.
    6. A. Rufián-Lizana & Y. Chalco-Cano & G. Ruiz-Garzón & H. Román-Flores, 2014. "On some characterizations of preinvex fuzzy mappings," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 771-783, July.
    7. Hsien-Chung Wu, 2020. "Arithmetics of Vectors of Fuzzy Sets," Mathematics, MDPI, vol. 8(9), pages 1-42, September.
    8. Tofigh Allahviranloo & Zahra Noeiaghdam & Samad Noeiaghdam & Juan J. Nieto, 2020. "A Fuzzy Method for Solving Fuzzy Fractional Differential Equations Based on the Generalized Fuzzy Taylor Expansion," Mathematics, MDPI, vol. 8(12), pages 1-24, December.
    9. Animesh Mahata & Sankar Prasad Mondal & Ali Ahmadian & Fudiah Ismail & Shariful Alam & Soheil Salahshour, 2018. "Different Solution Strategies for Solving Epidemic Model in Imprecise Environment," Complexity, Hindawi, vol. 2018, pages 1-18, May.
    10. Nguyen Dinh Phu, 2016. "On Nonlocal Initial Problems for Fuzzy Differential Equations and Environmental Pollution Problems," Academic Journal of Applied Mathematical Sciences, Academic Research Publishing Group, vol. 2(8), pages 77-92, 08-2016.

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    More about this item

    Keywords

    Fuzzy-valued function; Strongly generalized differentiability; Generalized Hukuhara differentiability; Generalized fuzzy derivative.;
    All these keywords.

    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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