Advertisement

Fuzzy Multiobjective Linear Programming: A Bipolar View

  • Dipti Dubey
  • Aparna Mehra
Part of the Communications in Computer and Information Science book series (CCIS, volume 300)

Abstract

The traditional frameworks for fuzzy linear optimization problems are inspired by the max-min model proposed by Zimmermann using the Bellman-Zadeh extension principle. This paper attempts to view fuzzy multiobjective linear programming problem (FMOLPP) from a perspective of preference modeling. The fuzzy constraints are viewed as negative preferences for rejecting what is unacceptable while the objective functions are viewed as positive preferences for depicting satisfaction to what is desired. This bipolar view enable us to handle fuzzy constraints and objectives separately and help to combine them in distinct ways. The optimal solution of FMOLPP is the one which maximizes the disjunctive combination of the weighted positive preferences provided it satisfy the negative preferences combined in conjunctive way.

Keywords

Fuzzy multiobjective linear program bipolarity OWA operator 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Atanassov, K.: Intuitionistic Fuzzy Sets. Physica-Verlag, Heidelberg (1999)zbMATHGoogle Scholar
  2. 2.
    Bellman, R.E., Zadeh, L.A.: Decision making in fuzzy environment. Management Sciences 17, B-141–B-164 (1970)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Benferhat, S., Dubois, D., Kaci, S., Prade, H.: Bipolar possibility theory in preference modeling: Representation, fusion and optimal solutions. Information Fusion 7, 135–150 (2006)CrossRefGoogle Scholar
  4. 4.
    Cadenes, J.M., Jimènez, F.: Interactive decision making in multiobjective fuzzy programming. Mathware and Soft Computing 3, 210–230 (1994)Google Scholar
  5. 5.
    Dubois, D., Prade, H.: Possibility theory, probability theory and multiple-valued logics: a clarification. Annals Math. and Artificial Intelligence 32, 35–66 (2001)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Dubois, D., Prade, H.: Bipolar Representations in Reasoning, Knowledge Extraction and Decision Processes. In: Greco, S., Hata, Y., Hirano, S., Inuiguchi, M., Miyamoto, S., Nguyen, H.S., Słowiński, R. (eds.) RSCTC 2006. LNCS (LNAI), vol. 4259, pp. 15–26. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  7. 7.
    Liu, X.-W., Chen, L.H.: The equivalence of maximal entropy OWA operator and geometric OWA operator. In: Proceeding of the Second International Conference of Machine Learning and Cybernetics, Xi’an, pp. 2673–2676 (2003)Google Scholar
  8. 8.
    O’Hagan, M.: Aggregating template or rule antecedents in real time expert systems with fuzzy set logic. In: Proceeding of 22nd Annual IEEE Asilomar Conf. Signals, Systems, Computers, Pacific Grove, pp. 681–689 (1988)Google Scholar
  9. 9.
    Sakawa, M., Inuiguchi, M.: A fuzzy satificing method for large- scale multiobjective linear programming problems with block angular structure. Fuzzy Sets and Systems 78, 279–288 (1996)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Sommer, G., Pollatschek, M.A.: A fuzzy programming approach to an air pollution regulation problem. Progress of Cybernetics and Systems Research III, 303–313 (1978)Google Scholar
  11. 11.
    Tsai, C.C., Chu, C.H., Barta, T.A.: Modelling and analysis of a manufacturing cell formation problem with fuzzy mixed integer programming. IIE Transactions 29, 533–547 (1997)Google Scholar
  12. 12.
    Tversky, A., Kahneman, D.: Advances in prospect theory: cumulative representation of uncertainty. Journal of Risk and Uncertainty 5, 297–323 (1992)zbMATHCrossRefGoogle Scholar
  13. 13.
    Werner, B.M.: Aggregation models in mathematical programming. In: Mitra, G. (ed.) Mathematical Models for Decision Support, pp. 295–305. Springer, Berlin (1988)Google Scholar
  14. 14.
    Yager, R.R.: On ordered weighted averaging aggregation operators in multicriteria decision making. IEEE Transaction on System, Man and Cybernetics 18, 183–190 (1988)MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    Yager, R.R.: Quantifier guided aggregation using OWA operators. Int. J. Intelligent Systems 11, 49–73 (1996)CrossRefGoogle Scholar
  16. 16.
    Yager, R.R.: Constrained OWA aggregation. Fuzzy Sets and Systems 81, 89–101 (1996)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Zimmerman, H.-J.: Fuzzy programming and linear programming with several objective functions. Fuzzy Sets and Systems 1, 45–55 (1978)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Zimmerman, H.-J., Zysno, P.: Latent connectives in human decision making. Fuzzy Sets and Systems 4, 37–51 (1980)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Dipti Dubey
    • 1
  • Aparna Mehra
    • 1
  1. 1.Department of MathematicsIndian Institute of TechnologyHauz KhasIndia

Personalised recommendations