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A generalization of Hukuhara difference for interval and fuzzy arithmetic

Author

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  • Luciano Stefanini

    () (Department of Economics and Quantitative Methods, University of Urbino (Italy))

Abstract

We propose a generalization of the Hukuhara difference. First, the case of compact convex sets is examined; then, the results are applied to generalize the Hukuhara difference of fuzzy numbers, using their compact and convex level-cuts. Finally, a similar approach is seggested to attempt a generalization of division for real intervals and fuzzy numbers.

Suggested Citation

  • 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.
  • Handle: RePEc:urb:wpaper:08_01
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    File URL: http://www.econ.uniurb.it/RePEc/urb/wpaper/WP_08_01.pdf
    File Function: First version, 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. Sadefo Kamdem, J. & Mbairadjim Moussa, A. & Terraza, M., 2012. "Fuzzy risk adjusted performance measures: Application to hedge funds," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 702-712.
    4. repec:spr:opsear:v:54:y:2017:i:4:d:10.1007_s12597-017-0305-x is not listed on IDEAS
    5. 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.
    6. R. Sujatha & T. M. Rajalaxmi, 2016. "Hierarchical Fuzzy Hidden Markov Chain for Web Applications," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 15(01), pages 83-118, January.
    7. Morteza Pakdaman & Sohrab Effati, 2016. "On fuzzy linear projection equation and applications," Fuzzy Optimization and Decision Making, Springer, vol. 15(2), pages 219-236, June.
    8. 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.
    9. Majumder, Pinki & Mondal, Sankar Prasad & Bera, Uttam Kumar & Maiti, Manoranjan, 2016. "Application of Generalized Hukuhara derivative approach in an economic production quantity model with partial trade credit policy under fuzzy environment," Operations Research Perspectives, Elsevier, vol. 3(C), pages 77-91.
    10. 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.
    11. Debdas Ghosh, 2016. "A Newton method for capturing efficient solutions of interval optimization problems," OPSEARCH, Springer;Operational Research Society of India, vol. 53(3), pages 648-665, September.

    More about this item

    Keywords

    Fuzzy Arithmetic; Interval Arithmetic; Hukuhara difference; Fuzzy Numbers.;

    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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