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Linear Programming with Fuzzy Parameters: Non-simplex Based Approaches

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Fuzzy Sets-Based Methods and Techniques for Modern Analytics

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 364))

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Abstract

In this chapter, the non-simplex based approaches for solving several kinds of LPPs with fuzzy parameters are explored. In such approaches, the fuzzy constraints are first converted to crisp ones based on arithmetic operations on fuzzy numbers and then the standard methods are used for solving the crisp problems. Such approaches increase the number of functional constraints and thus directly affect the computational time of the simplex method.

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References

  1. Ramik, J., Rimanek, J.: Inequality relation between fuzzy numbers and its use in fuzzy optimization. Fuzzy Sets Syst. 16(2), 123–138 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  2. Tanaka, H., Ichihashi, H., Asai, K.: A formulation of fuzzy linear programming problems based on comparison of fuzzy numbers. Control Cybern. 13, 186–194 (1984)

    MathSciNet  MATH  Google Scholar 

  3. Dubois, D.: Linear programming with fuzzy data, in analysis of fuzzy information. Application in Engineering and Sciences, vol. III, pp. 241–263. CRC Press, Boca Raton (1987)

    Google Scholar 

  4. Li, H., Gong, Z.: Fuzzy linear programming with possibility and necessity relation. In: Fuzzy Information and Engineering. Advances in Intelligent and Soft Computing, pp. 305–311. Springer, Berlin (2010)

    Google Scholar 

  5. Lai, Y.J., Hwang, C.L.: A new approach to some possibilistic linear programming problem. Fuzzy Sets Syst. 49(2), 121–133 (1992)

    Article  MathSciNet  Google Scholar 

  6. Wan, S.P., Dong, J.Y.: Possibility linear programming with trapezoidal fuzzy numbers. Appl. Math. Model. 38, 1660–1672 (2014)

    Article  MathSciNet  Google Scholar 

  7. Rommelfanger, H., Hanuschech, R., Wolf, J.: Linear programming with fuzzy objective. Fuzzy Sets Syst. 29(1), 311–348 (1989)

    Article  MathSciNet  Google Scholar 

  8. Zimmerman, H.J.: Fuzzy programming and linear programming with several objective functions. Fuzzy Sets Syst. 1(1), 45–55 (1978)

    Article  MathSciNet  Google Scholar 

  9. Delgado, M., Verdegay, J.L., Vila, M.A.: Imprecise costs in mathematical programming problems. Control Cybern. 16(2), 113–121 (1987)

    MathSciNet  MATH  Google Scholar 

  10. Maeda, T.: Fuzzy linear programming problems as bi-criteria optimization problems. Appl. Math. Comput. 120(1–3), 109–121 (2001)

    MathSciNet  MATH  Google Scholar 

  11. Zhang, G., Wu, Y.H., Remias, M., Lu, J.: Formulation of fuzzy linear programming problems as four-objective constrained optimization problems. Appl. Math. Comput. 139(2–3), 383–399 (2003)

    MathSciNet  MATH  Google Scholar 

  12. Li, G., Guo, R.: Comments on “Formulation of fuzzy linear programming problems as four-objective constrained optimization problems”. Appl. Math. Comput. 186(1), 941–944 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  13. Cai, Q., Hao, Z., Pan, S.: The solution of linear programming with LR-fuzzy numbers in objective function. In: Fuzzy Information and Engineering (ICFIE), pp. 988–999. Springer, Berlin (2007)

    Google Scholar 

  14. Lai, Y.J., Hwang, C.L.: Fuzzy Mathematical Programming. Springer, Berlin (1992)

    Google Scholar 

  15. Buckley, J.J.: Possibilistic linear programming with triangular fuzzy numbers. Fuzzy Sets Syst. 26(1), 135–138 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  16. Buckley, J.J.: Solving possibilistic linear programming. Fuzzy Sets Syst. 31(3), 329–341 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  17. Negi, D.S., Lee, E.S.: Possibility programming by the comparison of fuzzy numbers. Comput. Math Appl. 25(9), 43–50 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  18. Fullér, R.: On stability in fuzzy linear programming problems. Fuzzy Sets Syst. 30(3), 339–344 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  19. Hatami-Marbini, A., Agrell, P.J., Tavana, M., Emrouznejad, A.: A stepwise fuzzy linear programming model with possibility and necessity relations. J. Intell. Fuzzy Syst. 25(1), 81–93 (2013)

    MathSciNet  MATH  Google Scholar 

  20. Buckley, J.J., Feuring, T.: Evolutionary algorithm solution to fuzzy problems: fuzzy linear programming. Fuzzy Sets Syst. 109(1), 35–53 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  21. Saati, S., Tavana, M., Hatami-Marbini, A., Hajiakhondi, E.: A fuzzy linear programming model with fuzzy parameters and decision variables. Int. J. Inf. Decis. Sci. 7(4), 312–333 (2015)

    Google Scholar 

  22. Kumar, A., Kaur, J.: A new method for solving fuzzy linear programs with trapezoidal fuzzy numbers. J. Fuzzy Set Valued Anal. Art. ID 00102, 12 (2011)

    Google Scholar 

  23. Hashemi, S.M., Modarres, M., Nasrabadi, E., Nasrabadi, M.M.: Fully fuzzified linear programming, solution and duality. Intell. Fuzzy Syst. 17(1), 253–261 (2006)

    MATH  Google Scholar 

  24. Hosseinzadeh Lotfi, F., Allahviranloo, T., Alimardani Jondabeh, M., Alizadeh, L.: Solving a full fuzzy linear programming using lexicography method and fuzzy approximate solution. Appl. Math. Model. 33(7), 3151–3156 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  25. Kumar, A., Kuar, A.: Optimal solution of fuzzy transportation problems based on fuzzy linear programming formulation. J. Adv. Res. Appl. Math. 2(4), 70–84 (2010)

    Article  MathSciNet  Google Scholar 

  26. Kumar, A., Kaur, J., Singh, P.: A new method for solving fully fuzzy linear programming problems. Appl. Math. Modell. 35, 817–823 (2011)

    Google Scholar 

  27. Ezzati, R., Khorram, E., Enayati, R.: A new algorithm to solve fully fuzzy linear programming problems using the MOLP problem. Appl. Math. Model. 39, 3183–3193 (2015)

    Article  MathSciNet  Google Scholar 

  28. Das, S.K., Mandal, T., Edalatpanah, S.A.: A mathematical model for solving fully fuzzy linear programming problem with trapezoidal fuzzy numbers. Appl. Intell. 46(3), 509–519 (2017)

    Article  Google Scholar 

  29. Cheng, H., Huang, W., Cai, J.: Solving a fully fuzzy linear programming problem through compromise programming. J. Appl. Math. Art. ID 726296, 10 (2013)

    Google Scholar 

  30. Hosseinzadeh, A., Edalatpanah, S.A.: A new approach for solving fully fuzzy linear programming by using the lexicography method. Adv. Fuzzy Syst. Art. ID 1538496, 6 (2016)

    Google Scholar 

  31. Ishibuchi, H., Tanaka, H.: Multiobjective programming in optimization of the interval objective function. Eur. J. Oper. Res. 48, 219–225 (1990)

    Article  MATH  Google Scholar 

  32. Chanas, S.: The use of parametric programming in fuzzy linear programming problems. Fuzzy Sets Syst. 11, 243–251 (1983)

    Article  MATH  Google Scholar 

  33. Dubois, D., Prade, H.: Fuzzy Sets and Systems: Theory and Applications. Academic, New York (1980)

    MATH  Google Scholar 

  34. Mahdavi-Amiri, N., Nasseri, S.H.: Duality results and a dual simplex method for linear programming problems with trapezoidal fuzzy variables. Fuzzy Sets Syst. 158(17), 1961–1978 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  35. Ganesan, K., Veeramani, P.: Fuzzy linear programming with trapezoidal fuzzy numbers. Ann. Oper. Res. 143(1), 305–315 (2006)

    Article  MATH  Google Scholar 

  36. Ebrahimnejad, A., Tavana, M.: A novel method for solving linear programming problems with symmetric trapezoidal fuzzy numbers. Appl. Math. Model. 38(17–18), 4388–4395 (2014)

    Article  MathSciNet  Google Scholar 

  37. Nasrabadi, M.M., Nasrabadi, E.: A mathematical programming approach to fuzzy linear regression analysis. Appl. Math. Comput. 155, 873–881 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  38. Ebrahimnejad, A., Nasseri, S.H., Hosseinzadeh Lotfi, F.: Bounded linear programs with trapezoidal fuzzy numbers. Int. J. Uncertainty Fuzziness Knowl. Based Syst. 18(3), 269–286 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  39. Ebrahimnejad, A., Nasseri, S.H., HosseinzadehLotfi, F., Soltanifar, M.: A primal-dual method for linear programming problems with fuzzy variables. Eur. J. Ind. Eng. 4(2), 189–209 (2010)

    Article  Google Scholar 

  40. Mahdavi-Amiri, N., Nasseri, S.H.: Duality in fuzzy number linear programming by use of a certain linear ranking function. Appl. Math. Comput. 180(1), 206–216 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  41. Maleki, H.R., Tata, M., Mashinchi, M.: Linear programming with fuzzy variables. Fuzzy Sets Syst. 109(1), 21–33 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  42. Kumar, A., Kaur, J.: Fuzzy optimal solution of fully fuzzy linear programming problems using ranking function. J. Intell. Fuzzy Syst. 26, 337–344 (2014)

    MathSciNet  MATH  Google Scholar 

  43. Bhardwaj, B., Kumar, A.: A note on the paper “A new algorithm to solve fully fuzzy linear programming problems using the MOLP problem”. J Appl. Math. Model. 39(19), 5982–5985 (2015)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Qaemshahr Branch Islamic Azad University, Qaemshahr, Iran

    Ali Ebrahimnejad

  2. Department of Computer Science and Artificial Intelligence, University of Granada, Granada, Spain

    José Luis Verdegay

Authors
  1. Ali Ebrahimnejad
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  2. José Luis Verdegay
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Correspondence to Ali Ebrahimnejad .

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Ebrahimnejad, A., Verdegay, J.L. (2018). Linear Programming with Fuzzy Parameters: Non-simplex Based Approaches. In: Fuzzy Sets-Based Methods and Techniques for Modern Analytics. Studies in Fuzziness and Soft Computing, vol 364. Springer, Cham. https://doi.org/10.1007/978-3-319-73903-8_4

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  • DOI: https://doi.org/10.1007/978-3-319-73903-8_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-73902-1

  • Online ISBN: 978-3-319-73903-8

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