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The Shape of the Optimal Value of a Fuzzy Linear Programming Problem

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Fuzzy Logic in Intelligent System Design (NAFIPS 2017)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 648))

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Abstract

We investigate the shape of the optimal value of a linear programming problem with fuzzy-number coefficients. We build on the classical and also very recent results from interval linear programming as well as from parametric programming. We show that under general assumptions the optimal value is a well-defined fuzzy number. Its shape is piecewise polynomial provided the shape of the input fuzzy coefficients are polynomial. We also show in particular that the optimal value shape is triangular as long as the following conditions are satisfied: the input fuzzy numbers are triangular and affect only the objective function or the right-hand side, and the problem is so called basis stable.

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Acknowledgements

M. Hladík was supported by the Czech Science Foundation Grant P402/13-10660S, and M. Černý by the Grant P403/16-00408S.

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Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Mathematics and Physics, Charles University, Malostranské nám. 25, 11800, Prague, Czech Republic

    Milan Hladík

  2. Department of Econometrics, University of Economics in Prague, Winston Churchill Square 4, 13067, Prague 3, Czech Republic

    Michal Černý

Authors
  1. Milan Hladík
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  2. Michal Černý
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Corresponding author

Correspondence to Milan Hladík .

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Editors and Affiliations

  1. Division of Graduate Studies and Research, Tijuana Institute of Technology, Tijuana, Baja California, Mexico

    Patricia Melin

  2. Division of Graduate Studies and Research, Tijuana Institute of Technology, Tijuana, Baja California, Mexico

    Oscar Castillo

  3. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Janusz Kacprzyk

  4. Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Alberta, Canada

    Marek Reformat

  5. Laboratory of Computational Intelligence and Automation, University of Waterloo, Waterloo, Ontario, Canada

    William Melek

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Hladík, M., Černý, M. (2018). The Shape of the Optimal Value of a Fuzzy Linear Programming Problem. In: Melin, P., Castillo, O., Kacprzyk, J., Reformat, M., Melek, W. (eds) Fuzzy Logic in Intelligent System Design. NAFIPS 2017. Advances in Intelligent Systems and Computing, vol 648. Springer, Cham. https://doi.org/10.1007/978-3-319-67137-6_31

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  • DOI: https://doi.org/10.1007/978-3-319-67137-6_31

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-67136-9

  • Online ISBN: 978-3-319-67137-6

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