Skip to main content
SpringerLink
Log in

An Analysis of Bilevel Linear Programming Solving Parameters Based on Factoraggregation Approach

  • Conference paper
Aggregation Functions in Theory and in Practise

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 228))

Abstract

We introduce the notion of factoraggregation,which is a special construction of general aggregation operators, and apply it for an analysis of optimal solution parameters for bilevel linear programming problems. The aggregation observes lower level objective functions considering the classes of equivalence generated by an objective function on the upper level. The proposed method is illustrated with numerical and graphical examples.

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 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Calvo, T., Mayor, G., Mesiar, R.: Aggregation Operators. Physical-Verlag, Heidelberg (2002)

    Book  MATH  Google Scholar 

  2. Detyniecki, M.: Fundamentals on Aggregation Operators, Berkeley (2001)

    Google Scholar 

  3. Figueroa-Garcia, J.C., Kalenatic, D., Lopez-Bello, C.A.: Multi-period mixed production planning with uncertain demands: fuzzy and interval fuzzy sets approach. Fuzzy Sets and Systems 206, 21–38 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  4. Grabisch, M., Marichal, J.-L., Mesiar, R., Pap, E.: Aggregation Functions. Cambridge University Press (2009)

    Google Scholar 

  5. Jiménez, M., Bilbao, A.: Pareto-optimal solutions in fuzzy multi-objective linear programming. Fuzzy Sets and Systems 160, 2714–2721 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  6. Klement, E.P., Mesiar, R., Pap, E.: Triangular Norms. Kluwer Academic Publishers, Dordrecht (2000)

    Book  MATH  Google Scholar 

  7. Sakawa, M., Nishizaki, I.: Interactive fuzzy programming for decentralized two-level linear programming problems. Fuzzy Sets and Systems 125, 301–315 (2000)

    Article  MathSciNet  Google Scholar 

  8. Sakawa, M., Nishizaki, I., Uemura, Y.: Interactive fuzzy programming for multi-level linear programming problems. Comput. Math. Appl. 36, 71–86 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  9. Takaci, A.: General aggregation operators acting on fuzzy numbers induced by ordinary aggregation operators. Novi. Sad. J. Math. 33(2), 67–76 (2003)

    MATH  MathSciNet  Google Scholar 

  10. Zimmermann, H.J.: Fuzzy programming and linear programming with several objective functions. Fuzzy Sets and Systems 1, 45–55 (1978)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Latvia, Zellu street 8, Riga, LV-1002, Latvia

    Pavels Orlovs, Olga Montvida & Svetlana Asmuss

Authors
  1. Pavels Orlovs
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Olga Montvida
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Svetlana Asmuss
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Pavels Orlovs .

Editor information

Editors and Affiliations

  1. Department of Automatica y Computacion, Universidad Publica de Navarra, Pamplona, Spain

    Humberto Bustince

  2. Department of Automatica y Computacion, Universidad Publica de Navarra, Pamplona, Spain

    Javier Fernandez

  3. Department of Mathematics and, Slovak University of Technology, Bratislava, Slovakia

    Radko Mesiar

  4. Department of Computer Science, Universidad de Alcalá de Henares, Madrid, Spain

    Tomasa Calvo

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Orlovs, P., Montvida, O., Asmuss, S. (2013). An Analysis of Bilevel Linear Programming Solving Parameters Based on Factoraggregation Approach. In: Bustince, H., Fernandez, J., Mesiar, R., Calvo, T. (eds) Aggregation Functions in Theory and in Practise. Advances in Intelligent Systems and Computing, vol 228. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39165-1_34

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-39165-1_34

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39164-4

  • Online ISBN: 978-3-642-39165-1

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation