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Solution of Multi-Objective Linear Programming Problems in Intuitionistic Fuzzy Environment

Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 236)

Abstract

In the paper, we give a new method for solution of multi-objective linear programming problem in intuitionistic fuzzy environment. The method uses computation of the upper bound of a non-membership function in such way that the upper bound of the non-membership function is always less than the upper bound of the membership function of intuitionistic fuzzy number. Further, we also construct membership and non-membership function to maximize membership function and minimize non-membership function so that we can get a more efficient solution of a probabilistic problem by intuitionistic fuzzy approach. The developed method has been illustrated on a problem, and the result has been compared with existing solutions to show its superiority.

Keywords

Multi-objective programming Positive ideal solution Intuitionistic fuzzy sets Intuitionistic fuzzy optimization 

Notes

Acknowledgments

Authors are thankful to University Grants Commission (UGC), Government of India, for financial support to carry out this research work.

References

  1. 1.
    Atanassov, K.T.: Intuitionistic fuzzy sets. Fuzzy Sets and Systems. 20, 87–96 (1986)CrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    Atanassov, K.T., Gargov, G.: interval valued intuitionistic fuzzy sets. Fuzzy Sets and Systems. 31, 343–349 (1989)CrossRefMATHMathSciNetGoogle Scholar
  3. 3.
    Angelov, P.: P Optimization in an intuitionistic fuzzy environment. Fuzzy Sets and Systems. 86, 299–306 (1997)CrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    De, S.K., Biswas, R.A.: Ray R. Some operations on intuitionistic fuzzy sets, Fuzzy Sets and Systems. 114, 474–487 (2000)Google Scholar
  5. 5.
    Dipti, Dubey, Mehra, Aparna: Linear programming with Triangular Intuitionistic Fuzzy Number, EUSFLAT-LFA 2011. Advances in Intelligent Systems Research 1(1), 563–569 (2011). Atlantis PressGoogle Scholar
  6. 6.
    Dipti, Dubey, Suresh, Chandra, Aparna, Mehra: Fuzzy linear programming under interval uncertainty based on IFS representation. Fuzzy Sets and Systems. 188(1), 68–87 (2012)CrossRefMATHMathSciNetGoogle Scholar
  7. 7.
    Garg, A., Singh, S.R.: Optimization under uncertainty in agricultural production planning. iconcept pocket journal: Computational Intelligence for Financial Engineers 1(1), 1–12 (2010)Google Scholar
  8. 8.
    Itoh, T., Ishii, H., Nanseki, T.: Fuzzy crop planning problem under uncertainty in agriculture management. Int. J. Production Economics. 81–82, 555–558 (2003)CrossRefGoogle Scholar
  9. 9.
    Jana, B., Roy, T.K.: Multiobjective intuitionistic fuzzy linear programming and its application in transportation model NIFS–13–1–34–51, 1–18 (2007)Google Scholar
  10. 10.
    Li, D.F.: Linear programming method for MADM with interval valued intuitionistic fuzzy sets. Expert Systems and Applications. 37, 5939–5945 (2010)CrossRefGoogle Scholar
  11. 11.
    Mohamed, R.H.: The relationship between goal programming and fuzzy programming. Fuzzy Sets and Systems 89, 215–222 (1997)CrossRefMathSciNetGoogle Scholar
  12. 12.
    Mondal, T.K., Samanta, S.K.: Generalized intuitionistic fuzzy set. Journal of Fuzzy Math 10, 839–861 (2002)MATHMathSciNetGoogle Scholar
  13. 13.
    Mahaparta, G.S., Mitra, M., Roy, T.K.: Intuitionistic fuzzy multiobjective mathematical programming on reliability optimization model. International Journal of Fuzzy Systems. 12(3), 259–266 (2010)MathSciNetGoogle Scholar
  14. 14.
    Nachamani, A.L., Thangaraj, P.: Solving Intuitionistic fuzzy linear programming problems by using similarity measures. European Journal of Scientific Research 72(2), 204–210 (2012)Google Scholar
  15. 15.
    Nagoorgani, A., Ponnalagu, K.: A new approach on solving intuitionistic fuzzy linear programming problem. Applied Mathematical Sciences 6(70), 3467–3474 (2012)MATHMathSciNetGoogle Scholar
  16. 16.
    Shahrokhi M, Bernard A, Shidpour H, An integrated method using intuitionistic fuzzy set and linear programming for supplier selection problem, 18\(^{th}\) IFAC World congress Milano(Italy)Aug18-Sept2, 2011, 6391–6395.Google Scholar
  17. 17.
    Zadeh, L.: A Fuzzy Sets. Information and Control 8, 338–353 (1965)CrossRefMATHMathSciNetGoogle Scholar
  18. 18.
    Zimmermann, H.: J. Fuzzy programming and linear programming with several objective functions. Fuzzy Sets and Systems 1, 45–55 (1978)CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer India 2014

Authors and Affiliations

  1. 1.Department of MathematicsBanaras Hindu UniversityVaranasiIndia

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