Skip to main content

Approaching Fuzzy Integer Linear Programming Problems

  • Chapter
Interactive Fuzzy Optimization

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 368))

Abstract

Integer Programming problems in which they exists some lack of precision of a vague nature in their formulation are considered. It is also provided a classification of this kind of problems, and a description for each of them is carried out. In particular, we focuse on the fuzzy boolean case for which a solution method is shown.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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. Bellman, R.E. and Zadeh, L.A. (1970): Decision Making in a Fuzzy Environment. Man. Sci. 17 (B), 4, 141–164.

    Google Scholar 

  2. Delgado, M., J.L. Verdegay and M.A. Vila (1989): A General Model for Fuzzy Linear Programming. Fuzzy Sets and Systems 29, 21–29.

    Article  Google Scholar 

  3. Fabian, C. and M. Stoica (1984): Fuzzy Integer Programming. In Fuzzy Sets and Decision Analysis. H.J. Zimmermann, L. A. Zadeh and B. R. Gaines (Eds). North-Holland, 123-131.

    Google Scholar 

  4. Gal, T. (1979): Postoptimal Analyses, Parametric Programming and Related Topics. McGraw Hill.

    Google Scholar 

  5. Garfinkel, R.S and Nemhauser, G.L. (1972): Integer Programming. Wiley Interscience.

    Google Scholar 

  6. Geoffrion, A. M. and R. Nauss (1977): Parametric and Postoptimality Analysis in Integer Linear Programming. Management Science 23, 453–466.

    Article  Google Scholar 

  7. Marsten, R.E. and Morin, T.L. (1977): Parametric Integer Programming: The Right-Hand-Side Case. Annals of Discrete Math. 1, 375–390.

    Article  Google Scholar 

  8. Nauss, R. M. (1979): Parametric Integer Programming. University of Missouri Press.

    Google Scholar 

  9. Negoita, C.V. and D.A. Ralescu (1975): Applications of Fuzzy Sets to Systems Analysis. Birkhauser.

    Google Scholar 

  10. Orlovski, S.A. (1977): On Programming with Fuzzy Constraint Sets. Kybernetes 6, 197–201.

    Article  Google Scholar 

  11. Taha, H.A. (1975): Integer Programming. Theory, Applications and Computations. Academic Press.

    Google Scholar 

  12. Verdegay, J.L. (1982): Fuzzy Mathematical Programming. In Fuzzy Information and Decision Processes. M.M. Gupta and E. Sanchez (Eds). North-Holland, 231-237.

    Google Scholar 

  13. Yager, R.R. (1988): A Mathematical Programming Approach to Inference with the Capability of Implementing Default Rules. Int. J. of Man-Machine Studies 29, 685–714.

    Article  Google Scholar 

  14. Zadeh, L.A. (1978): Fuzzy Sets as a Basis for a Theory of Possibility. Fuzzy Sets and Systems, 1, 3–28.

    Article  Google Scholar 

  15. Zadeh, L. A. (1979): Calculus of Fuzzy Restrictions. In Fuzzy Sets and their Applications to Cognitive and Decision Processes. L.A. Zadeh, K.S. Fu, K. Tanaka and M. Shimura, (Eds.), Academic Pres, 1-40.

    Google Scholar 

  16. Zimmermann, H.J. and M.A. Pollatschek (1984): Fuzzy 0-1 Linear Programs. In Fuzzy Sets and Decision Analysis. H. J. Zimmermann, L.A. Zadeh and B. R. Gaines (Eds). North-Holland, 133-145.

    Google Scholar 

  17. Zimmermann, H.J. (1987): Fuzzy Sets, Decision Making and Expert Systems. Kluwer Academic Publishers.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Herrera, F., Verdegay, J.L. (1991). Approaching Fuzzy Integer Linear Programming Problems. In: Fedrizzi, M., Kacprzyk, J., Roubens, M. (eds) Interactive Fuzzy Optimization. Lecture Notes in Economics and Mathematical Systems, vol 368. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45700-5_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-45700-5_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54577-4

  • Online ISBN: 978-3-642-45700-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics