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Exact fuzzy optimal solution of fully fuzzy linear programming problems with unrestricted fuzzy variables

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Abstract

Kumar et al. (Appl. Math. Model. 35:817–823, 2011) pointed out that there is no method in literature to find the exact fuzzy optimal solution of fully fuzzy linear programming (FFLP) problems and proposed a new method to find the fuzzy optimal solution of FFLP problems with equality constraints having non-negative fuzzy variables and unrestricted fuzzy coefficients. There may exist several FFLP problems with equality constraints in which no restriction can be applied on all or some of the fuzzy variables but due to the limitation of the existing method these types of problems can not be solved by using the existing method. In this paper a new method is proposed to find the exact fuzzy optimal solution of FFLP problems with equality constraints having non-negative fuzzy coefficients and unrestricted fuzzy variables. The proposed method can also be used to solve the FFLP problems with equality constraints having non-negative fuzzy variables and unrestricted fuzzy coefficients. To show the advantage of the proposed method over existing method the results of some FFLP problems with equality constraints, obtained by using the existing and proposed method, are compared. Also, to show the application of proposed method a real life problem is solved by using the proposed method.

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References

  1. Bellman RE, Zadeh LA (1970) Decision making in a fuzzy environment. Manag Sci 17:141–164

    Article  MathSciNet  Google Scholar 

  2. Tanaka H, Okuda T, Asai K (1973) On fuzzy mathematical programming. J. Cybern Syst 3:37–46

    Article  MathSciNet  MATH  Google Scholar 

  3. Zimmerman HJ (1978) Fuzzy programming and linear programming with several objective functions. Fuzzy Sets Syst 1:45–55

    Article  Google Scholar 

  4. Campos L, Verdegay JL (1989) Linear programming problems and ranking of fuzzy numbers. Fuzzy Sets Syst 32:1–11

    Article  MathSciNet  MATH  Google Scholar 

  5. Maleki HR, Tata M, Mashinchi M (2000) Linear programming with fuzzy variables. Fuzzy Sets Syst 109:21–33

    Article  MathSciNet  MATH  Google Scholar 

  6. Maleki HR (2002) Ranking functions and their applications to fuzzy linear programming. Far East J Math Sci 4:283–301

    MathSciNet  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  8. Ebrahimnejad A, Nasseri SH, Lotfi FH, Soltanifar M (2010) A primal-dual method for linear programming problems with fuzzy variables. Eur J Ind Eng 4:189–209

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  10. Hashemi SM, Modarres M, Nasrabadi E, Nasrabadi MM (2006) Fully fuzzified linear programming solution and duality. J Intell Fuzzy Syst 17:253–261

    MATH  Google Scholar 

  11. Allahviranloo T, Lotfi FH, Kiasary MK, Kiani NA, Alizadeh L (2008) Solving full fuzzy linear programming problem by the ranking function. Appl Math Sci 2:19–32

    MATH  Google Scholar 

  12. Dehghan M, Hashemi B, Ghatee M (2006) Computational methods for solving fully fuzzy linear systems. Appl Math Comput 179:328–343

    Article  MathSciNet  MATH  Google Scholar 

  13. Lotfi FH, Allahviranloo T, Jondabeha MA, Alizadeh L (2009) Solving a fully fuzzy linear programming using lexicography method and fuzzy approximate solution. Appl Math Model 33:3151–3156

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  15. Kaufmann A, Gupta MM (1985) Introduction to fuzzy arithmetic theory and applications. Van Nostrand Reinhold, New York

    MATH  Google Scholar 

  16. Liou TS, Wang MJ (1992) Ranking fuzzy numbers with integral value. Fuzzy Sets Syst 50:247–255

    Article  MathSciNet  MATH  Google Scholar 

  17. Kaur A, Kumar A (2011) A new method for solving fuzzy transportation problems using ranking function. Appl Math Model 35:5652–5661

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. School of Mathematics and Computer Applications, Thapar University, Patiala, 147 004, India

    Jagdeep Kaur & Amit Kumar

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  1. Jagdeep Kaur
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  2. Amit Kumar
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Correspondence to Jagdeep Kaur.

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Kaur, J., Kumar, A. Exact fuzzy optimal solution of fully fuzzy linear programming problems with unrestricted fuzzy variables. Appl Intell 37, 145–154 (2012). https://doi.org/10.1007/s10489-011-0318-8

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  • DOI: https://doi.org/10.1007/s10489-011-0318-8

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