Skip to main content
SpringerLink
Log in

Solving Interval Bilevel Programming Based on Generalized Possibility Degree Formula

  • Conference paper
  • First Online:
Proceedings of the Fifth Euro-China Conference on Intelligent Data Analysis and Applications (ECC 2018)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 891))

  • 705 Accesses

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  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. Calvete, H.I., Galé, C.: Linear bilevel programming with interval coefficients. J. Comput. Appl. Math. 236(15), 3751–3762 (2012)

    Article  MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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/s13660-017-1384-1

    Article  MathSciNet  MATH  Google Scholar 

  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/s00500-017-2811-4

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  8. Larranaga, P., Lozano, J.A.: Estimation of Distribution Algorithms: A New Tool for Evolutionary Computation. Kluwer Academic Publishers, Norwell (2002)

    Book  Google Scholar 

Download references

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).

Author information

Authors and Affiliations

  1. School of Mathematics and Information Science, Baoji University of Arts and Sciences, Baoji, 721013, Shaanxi, China

    Aihong Ren

  2. College of Information Science and Engineering, Fujian University of Technology, Fuzhou, 350118, Fujian, China

    Xingsi Xue

  3. Intelligent Information Processing Research Center, Fujian University of Technology, Fuzhou, 350118, Fujian, China

    Xingsi Xue

Authors
  1. Aihong Ren
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xingsi Xue
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Aihong Ren .

Editor information

Editors and Affiliations

  1. Department of Computer Science, VSB-Technical University of Ostrava, Ostrava, Czech Republic

    Pavel Krömer

  2. School of Automation, Xi’an University of Posts and Telecommunications, Xi’an, China

    Hong Zhang

  3. College of Computer Science and Engineering, Shandong University of Science and Technology, Qingdao, China

    Yongquan Liang

  4. College of Information Science and Engineering, Fujian University of Technology, Fuzhou, Fujian, China

    Jeng-Shyang Pan

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Ren, A., Xue, X. (2019). Solving Interval Bilevel Programming Based on Generalized Possibility Degree Formula. In: Krömer, P., Zhang, H., Liang, Y., Pan, JS. (eds) Proceedings of the Fifth Euro-China Conference on Intelligent Data Analysis and Applications. ECC 2018. Advances in Intelligent Systems and Computing, vol 891. Springer, Cham. https://doi.org/10.1007/978-3-030-03766-6_44

Download citation

Publish with us

Policies and ethics

Search

Navigation