Advertisement

A Transportation Model with Interval Type-2 Fuzzy Demands and Supplies

  • Juan C. Figueroa-García
  • Germán Hernández
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7389)

Abstract

This paper presents a basic transportation model (TM) where its demands and supplies are defined as Interval Type-2 Fuzzy sets (IT2FS). This kind of constraints involves uncertainty to the membership function of a fuzzy set, so we called this model as Interval Type-2 Transportation Model (IT2TM). Using convex optimization techniques, a global solution of this problem can befound. To do so, we define a general model for IT2TM and then we present an application example to illustrate how the algorithm works.

Keywords

Membership Function Transportation Model Uncertain Demand Fuzzy Linear Programming Fuzzy Linear Programming Problem 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    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
  2. 2.
    Figueroa, J.C.: Solving Fuzzy Linear Programming Problems with Interval Type-2 RHS. In: 2009 Conference on Systems, Man and Cybernetics. IEEE (2009)Google Scholar
  3. 3.
    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
  4. 4.
    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 I. LNCS, vol. 7208, pp. 567–576. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  5. 5.
    Klir, G.J., Yuan, B.: Fuzzy Sets and Fuzzy Logic: Theory and Applications. Prentice Hall (1995)Google Scholar
  6. 6.
    Lai, Y.J., Hwang, C.: Fuzzy Mathematical Programming. Springer (1992)Google Scholar
  7. 7.
    Kacprzyk, J., Orlovski, S.A.: Optimization Models Using Fuzzy Sets and Possibility Theory. Kluwer Academic Press (1987)Google Scholar
  8. 8.
    Pandiant, M.V.: Application of Fuzzy Linear Programming in Production Planning. Fuzzy Optimization and Decision Making 2(3), 229 (2003)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Zimmermann, H.J.: Fuzzy programming and Linear Programming with Several Objective Functions. Fuzzy Sets and Systems 1(1), 45–55 (1978)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    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 2012

Authors and Affiliations

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

Personalised recommendations