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Random fuzzy bilevel linear programming through possibility-based value at risk model

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Abstract

This article considers bilevel linear programming problems where random fuzzy variables are contained in objective functions and constraints. In order to construct a new optimization criterion under fuzziness and randomness, the concept of value at risk and possibility theory are incorporated. The purpose of the proposed decision making model is to optimize possibility-based values at risk. It is shown that the original bilevel programming problems involving random fuzzy variables are transformed into deterministic problems. The characteristic of the proposed model is that the corresponding Stackelberg problem is exactly solved by using nonlinear bilevel programming techniques under some convexity properties. A simple numerical example is provided to show the applicability of the proposed methodology to real-world hierarchical problems.

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Authors and Affiliations

  1. Faculty of Engineering, Hiroshima University, 1-4-1, Kagamiyama, Higashi-Hiroshima, 739-8527, Japan

    Hideki Katagiri

  2. Institute of Socio-Arts and Sciences, The University of Tokushima, 1-1, Minamijosanjima-cho, Tokushima, Tokushima, 770-8502, Japan

    Takeshi Uno

  3. Faculty of Applied Information Science, Hiroshima Institute of Technology, 2-1-1 Miyake, Saeki-ku, Hiroshima, 731-5193, Japan

    Kosuke Kato

  4. Faculty of Science and Engineering, Doshisha University, Tatara Miyakodani 1-3, Kyotanabe, 610-0394, Japan

    Hiroshi Tsuda

  5. The Institute of Statistical Mathematics, 10-3 Midori-cho, Tachikawa, Tokyo, 190-8562, Japan

    Hiroe Tsubaki

Authors
  1. Hideki Katagiri
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  2. Takeshi Uno
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  3. Kosuke Kato
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  4. Hiroshi Tsuda
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  5. Hiroe Tsubaki
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Correspondence to Hideki Katagiri.

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Katagiri, H., Uno, T., Kato, K. et al. Random fuzzy bilevel linear programming through possibility-based value at risk model. Int. J. Mach. Learn. & Cyber. 5, 211–224 (2014). https://doi.org/10.1007/s13042-012-0126-4

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  • DOI: https://doi.org/10.1007/s13042-012-0126-4

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