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Solving Interval Bilevel Programming Based on Generalized Possibility Degree Formula

  • Aihong RenEmail author
  • Xingsi Xue
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 891)

Abstract

This study proposes a method for dealing with interval bilevel programming. The generalized possibility degree formula is utilized to cope with interval inequality constraints involved in interval bilevel programming. Then several types of equivalent bilevel programming models for interval bilevel programming can be established according to several typical possibility degree formulas which are corresponding to different risk attitudes of decision makers. Finally, a computational example is provided to illustrate the proposed method.

Keywords

Interval number Interval bilevel programming Generalized possibility degree formula 

Notes

Acknowledgments

This work was supported by National Natural Science Foundation of China (No.61602010), Natural Science Basic Research Plan in Shaanxi Province of China (No.2017JQ6046) and Science Foundation of the Education Department of Shaanxi Province of China (No.17JK0047).

References

  1. 1.
    Abass, S.A.: An interval number programming approach for bilevel linear programming problem. Int. J. Manag. Sci. Eng. Manag. 5(6), 461–464 (2010)Google Scholar
  2. 2.
    Calvete, H.I., Galé, C.: Linear bilevel programming with interval coefficients. J. Comput. Appl. Math. 236(15), 3751–3762 (2012)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Nehi, H.M., Hamidi, F.: Upper and lower bounds for the optimal values of the interval bilevel linear programming problem. Appl. Math. Model. 39(5–6), 1650–1664 (2015)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Ren, A.H., Wang, Y.P.: A cutting plane method for bilevel linear programming with interval coefficients. Ann. Oper. Res. 223, 355–378 (2014)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Ren, A.H., Wang, Y.P., Xue, X.X.: A novel approach based on preference-based index for interval bilevel linear programming problem. J. Inequal. Appl. 2017, 112 (2017).  https://doi.org/10.1186/s13660-017-1384-1MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Ren, A.H., Wang, Y.P.: An approach based on reliability-based possibility degree of interval for solving general interval bilevel linear programming problem. Soft Comput. 1–10 (2017).  https://doi.org/10.1007/s00500-017-2811-4CrossRefGoogle Scholar
  7. 7.
    Liu, F., Pan, L.H., Liu, Z.L., Peng, Y.N.: On possibility-degree formulae for ranking interval numbers. Soft Comput. 22, 2557–2565 (2018)CrossRefGoogle Scholar
  8. 8.
    Larranaga, P., Lozano, J.A.: Estimation of Distribution Algorithms: A New Tool for Evolutionary Computation. Kluwer Academic Publishers, Norwell (2002)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of Mathematics and Information ScienceBaoji University of Arts and SciencesBaojiChina
  2. 2.College of Information Science and EngineeringFujian University of TechnologyFuzhouChina
  3. 3.Intelligent Information Processing Research CenterFujian University of TechnologyFuzhouChina

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