Behavior of the Soft Constraints Method Applied to Interval Type-2 Fuzzy Linear Programming Problems

  • Juan C. Figueroa-García
  • Germán Hernández
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7996)


This paper presents some considerations when applying the Zimmermann soft constraints method to linear programming with Interval Type-2 fuzzy constraints. A descriptive study of the behavior of the method is performed using an example with an explanation of the obtained results.


Membership Function Linear Programming Model Soft Constraint Fuzzy Constraint Linear Membership Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bellman, R.E., Zadeh, L.A.: Decision-making in a fuzzy environment. Management Science 17(1), 141–164 (1970)MathSciNetGoogle Scholar
  2. 2.
    Figueroa, J.C.: Linear programming with interval type-2 fuzzy right hand side parameters. In: 2008 Annual Meeting of the IEEE North American Fuzzy Information Processing Society (NAFIPS) (2008)Google Scholar
  3. 3.
    Figueroa, J.C.: Solving fuzzy linear programming problems with interval type-2 RHS. In: 2009 Conference on Systems, Man and Cybernetics, pp. 1–6. IEEE (2009)Google Scholar
  4. 4.
    Figueroa, J.C.: Interval type-2 fuzzy linear programming: Uncertain constraints. In: IEEE Symposium Series on Computational Intelligence, pp. 1–6. IEEE (2011)Google Scholar
  5. 5.
    Figueroa, J.C.: A general model for linear programming with interval type-2 fuzzy technological coefficients. In: 2012 Annual Meeting of the North American Fuzzy Information Processing Society (NAFIPS), pp. 1–6. IEEE (2012)Google Scholar
  6. 6.
    Figueroa-García, J.C., Hernandez, G.: Computing Optimal Solutions of a Linear Programming Problem with Interval Type-2 Fuzzy Constraints. In: Corchado, E., Snášel, V., Abraham, A., Woźniak, M., Graña, M., Cho, S.-B. (eds.) HAIS 2012, Part III. LNCS, vol. 7208, pp. 567–576. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  7. 7.
    Figueroa, J.C., Kalenatic, D., Lopez, C.A.: Multi-period mixed production planning with uncertain demands: Fuzzy and interval fuzzy sets approach. Fuzzy Sets and Systems 206(1), 21–38 (2012)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Karnik, N.N., Mendel, J.M.: Operations on type-2 fuzzy sets. Fuzzy Sets and Systems 122, 327–348 (2001)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Karnik, N.N., Mendel, J.M., Liang, Q.: Type-2 fuzzy logic systems. Fuzzy Sets and Systems 17(10), 643–658 (1999)Google Scholar
  10. 10.
    Liang, Q., Mendel, J.M.: Interval type-2 fuzzy logic systems: Theory and design. IEEE Transactions on Fuzzy Systems 8(5), 535–550 (2000)CrossRefGoogle Scholar
  11. 11.
    Melgarejo, M.: Implementing Interval Type-2 Fuzzy processors. IEEE Computational Intelligence Magazine 2(1), 63–71 (2007)CrossRefGoogle Scholar
  12. 12.
    Melgarejo, M.A.: A Fast Recursive Method to compute the Generalized Centroid of an Interval Type-2 Fuzzy Set. In: Annual Meeting of the North American Fuzzy Information Processing Society (NAFIPS), pp. 190–194. IEEE (2007)Google Scholar
  13. 13.
    Mendel, J.M.: Uncertain rule-based fuzzy logic systems: Introduction and new directions. Prentice Hall (1994)Google Scholar
  14. 14.
    Mendel, J.M., John, R.I.: Type-2 fuzzy sets made simple. IEEE Transactions on Fuzzy Systems 10(2), 117–127 (2002)CrossRefGoogle Scholar
  15. 15.
    Mendel, J.M., John, R.I., Liu, F.: Interval type-2 fuzzy logic systems made simple. IEEE Transactions on Fuzzy Systems 14(6), 808–821 (2006)CrossRefGoogle Scholar
  16. 16.
    Zimmermann, H.J.: Fuzzy programming and Linear Programming with several objective functions. Fuzzy Sets and Systems 1(1), 45–55 (1978)MathSciNetzbMATHCrossRefGoogle Scholar
  17. 17.
    Zimmermann, H.J., Fullér, R.: Fuzzy Reasoning for solving fuzzy Mathematical Programming Problems. Fuzzy Sets and Systems 60(1), 121–133 (1993)MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Juan C. Figueroa-García
    • 1
    • 2
  • Germán Hernández
    • 2
  1. 1.Universidad Distrital Francisco José de CaldasBogotáColombia
  2. 2.Universidad Nacional de ColombiaSede BogotáColombia

Personalised recommendations