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Duality in fuzzy quadratic programming with exponential membership functions

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Fuzzy Information and Engineering

Abstract

In this paper, we have presented fuzzy primal-dual quadratic programming problems and proved appropriate duality results taking exponential membership function.

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References

  1. Abdel-Malek L L, Areeractch N (2007) A quadratic programming approach to the multi-product newsvendor problem with side constraints. European Journal of Operational Research 176: 855–861

    Article  MathSciNet  Google Scholar 

  2. Ammar E, Khalifa H A (2003) Fuzzy portfolio optimization a quadratic programming approach. Chaos Solitons and Fractals 18: 10–54

    MathSciNet  Google Scholar 

  3. Zhang W G, Nie Z K (2005) On admissible efficient portfolio selection policy. Applied Mathematics and Computation 169: 608–623

    Article  MATH  MathSciNet  Google Scholar 

  4. Dwyer T, Koren Y, Marriott K (2006) Drawing directed graphs using quadratic programming. IEEE Transaction Visualization and Computer Graphics 12: 536–548

    Article  Google Scholar 

  5. Petersen J A M, Bodson M (2006) Constrained quadratic programming techniques for control allocation. IEEE Transaction on Control System Technology 14: 91–98

    Article  Google Scholar 

  6. Pavlovi L, Divni T (2007) A quadratic programming approach to the randi index. European Journal of Operational Research 176: 435–444

    Article  MathSciNet  Google Scholar 

  7. Schwarz H G (2006) Economic material-product chain models: current status, further development and an illustrative example. Ecological Economics 58: 373–392

    Article  Google Scholar 

  8. Ammar E (2000) Interactive stability of multiobjective NLP problems with fuzzy parameters in the objective functions and constraints. Fuzzy Sets and Systems 109: 83–90

    Article  MATH  MathSciNet  Google Scholar 

  9. Chen S P (2004) Parametric nonlinear programming for analyzing fuzzy queues with finite capacity. European Journal of Operational Research 157: 429–438

    Article  MATH  MathSciNet  Google Scholar 

  10. Liu S T (2004) Fuzzy geometric programming approach to a fuzzy machining economics model. International Journal Production Research 42: 3253–3269

    Article  MATH  Google Scholar 

  11. Nieto J J, Rodaiguez-Lopez R (2006) Bounded solutions for fuzzy differential and integral equations. Chaos, Solitons and Fractals 27: 1376–1386

    Article  MATH  MathSciNet  Google Scholar 

  12. Roman-Florse H, Chalco-Cano Y (2006) Some chaotic properties of Zaheh’s extensions. Chaos, Solitons and Fractals 35: 452–459

    Article  Google Scholar 

  13. Sakawa M (1993) Fuzzy sets and interactive multiobjective optimization. New York: Plenum Press

    MATH  Google Scholar 

  14. Soleimani-damaneh M (2006) Fuzzy upper bounds and their applications. Chaos, Solitons and Fractals 36: 217–225

    Article  MathSciNet  Google Scholar 

  15. Stefanini L, Sorini L, Guerra M L (2006) Solution of fuzzy dynamical systems using the LU-representation of fuzzy numbers. Chaos, Solitons and Fractals 29: 638–652

    Article  MATH  MathSciNet  Google Scholar 

  16. Bellman R E, Zadeh L A (1970) Decision Making in a Fuzzy Environment. Management Science 17: 141–164

    Article  MathSciNet  Google Scholar 

  17. Slowinski R (ed.) (1998) Fuzzy sets in decision analysis, Operations Research and Statistics. Boston: Kluwer Academic Publishers

    MATH  Google Scholar 

  18. Delgado M, Kacprzyk J, Verdegay J-L, Vila M A (ed.) (1994) Fuzzy optimization: Recent advances. New York, Physica-Verlag

    MATH  Google Scholar 

  19. Rodder W, Zimmermann H-J (1980) Duality in fuzzy linear programming. In: A.V. Fiacco, K.O. Kortanek (Eds.), Extremal Methods and System Analysis, Berlin, New York, pp. 415–429

  20. Hamacher H, Leberling H, Zimmermann H J (1978) Sensitivity analysis in fuzzy linear programming. Fuzzy Sets and Systems 1: 269–281

    Article  MATH  MathSciNet  Google Scholar 

  21. Bector C R, Chandra S (2002) On duality in linear programming under fuzzy environment. Fuzzy Sets and Systems 125(3): 317–325

    Article  MATH  MathSciNet  Google Scholar 

  22. Liu Y J, Shi Y, Liu Y H (1995) Duality of fuzzy MC2 linear programming: a constructive approach, Journal of Mathematical Analysis and Applications 194: 389–413

    Article  MATH  MathSciNet  Google Scholar 

  23. Bector C R, Chandra S (2005) Fuzzy mathematical programming and fuzzy matrix games. Springer, Berlin, Heidelberg

    MATH  Google Scholar 

  24. Bector C R, Chandra S, Vijay V (2004) Matrix games with fuzzy goals and fuzzy linear programming duality. Fuzzy Optimization and Decision Making 3(3): 255–269

    Article  MATH  MathSciNet  Google Scholar 

  25. Bector C R, Chandra S, Vijay V (2004) Duality in linear programming with fuzzy parameters and matrix games with fuzzy pay-offs. Fuzzy Sets and Systems 146(2): 253–269

    Article  MATH  MathSciNet  Google Scholar 

  26. Vijay V, Chandra S, Bector C R (2005) Matrix games with fuzzy goals and fuzzy pay offs. Omega 33(5): 425–429

    Article  Google Scholar 

  27. Gupta Pankaj, Mehlawat Mukesh Kumar (2009) Bector-Chandra type duality in fuzzy linear programming with exponential membership functions. Fuzzy Sets and Systems 160: 3290–3308

    Article  MATH  Google Scholar 

  28. Hersh H M, Caramazza A (1976) A fuzzy set approach to modifiers and vagueness in natural language. Journal of Experimental Psychology 105(3): 254–276

    Google Scholar 

  29. Mangasarian O L (1994) Nonlinear Programming, SIAM, Philadelphia, PA

    MATH  Google Scholar 

  30. Zimmermann H J (1978) Fuzzy programming and linear programming with several objective functions. Fuzzy Sets and Systems 1: 45–55

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Patna, Patna, 800 013, India

    S. K. Gupta & Debasis Dangar

Authors
  1. S. K. Gupta
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  2. Debasis Dangar
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Correspondence to S. K. Gupta.

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Gupta, S.K., Dangar, D. Duality in fuzzy quadratic programming with exponential membership functions. Fuzzy Inf. Eng. 2, 337–346 (2010). https://doi.org/10.1007/s12543-010-0054-5

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  • DOI: https://doi.org/10.1007/s12543-010-0054-5

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