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Initial Basic Solution for the Fuzzy Primal Simplex Algorithm Using a Two-Phase Method

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Fuzzy Engineering and Operations Research

Part of the book series: Advances in Intelligent and Soft Computing ((AINSC,volume 147))

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Abstract

Fuzzy primal and dual simplex algorithms have been recently proposed to solve the linear programming with fuzzy variables (FVLP) problems. The fuzzy primal simplex method has been developed with the assumption that an initial basic feasible solution is at hand. In many cases, such a solution is not readily available, and some work may be needed to get the fuzzy primal method started. Furthermore, there exists a shortcoming in the fuzzy dual simplex algorithm when the dual feasibility or equivalently the primal optimality is not at hand and in this case we can not use the fuzzy dual simplex method for solving FVLP problem. In this paper, we propose a fuzzy two-phase method involving fuzzy artificial variables, to obtain an initial fuzzy basic feasible solution to a slightly modified set of constraints. Then the fuzzy primal simplex method is used to eliminate the fuzzy artificial variables and to solve the original problem.

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References

  1. Ebrahimnejad, A., Nasseri, S.H.: Using complementary slackness property to solve linear programming with fuzzy parameters. Fuzzy Information and Engineering 3, 233–245

    Google Scholar 

  2. Ebrahimnejad, A., Nasseri, S.H., Hosseinzadeh Lotfi, F., Soltanifar, M.: A primal- dual method for linear programming problems with fuzzy variables. European Journal of Industrial Engineering 4(2), 189–209 (2010)

    Article  Google Scholar 

  3. Ebrahimnejad, A., Nasseri, S.H., Hosseinzadeh Lotfi, F.: Bounded linear programs with trapezoidal fuzzy numbers. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 18(3), 269–286 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  4. Ebrahimnejad, A., Nasseri, S.H.: A dual simplex method for bounded linear programmes with fuzzy numbers. International Journal of Mathematics in Operational Research 2(6), 762–779 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  5. Ebrahimnejad, A., Nasseri, S.H., Mansourzadeh, S.M.: Bounded primal simplex algorithm for bounded linear programming with fuzzy cost coefficients. International Journal of Operations Research and Information Systems 2(1), 96–120 (2011)

    Google Scholar 

  6. Fortemps, P., Roubens, M.: Ranking and defuzzification methods based on area compensation. Fuzzy Sets and Systems 82, 319–330 (1986)

    Article  MathSciNet  Google Scholar 

  7. Inuiguchi, M.: Necessity measure optimization in linear programming problems with fuzzy polytopes. Fuzzy Sets and Systems 158, 1882–1891 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  8. Inuiguchi, M., Ramik, J.: Possibilistic linear programming: a brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem. Fuzzy Sets and Systems 111(1), 3–8 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  9. Jimenez, M., Bilbao, A.: Pareto-optimalsolutionsinfuzzymulti-objectivelinear programming. Fuzzy Sets and Systems 160, 2714–2721 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  10. Klir, G.J., Yuan, B.: Fuzzy Sets and Fuzzy Logic: Theory and Applications. Prentice-Hall, PTR, New Jersey (1985)

    Google Scholar 

  11. Lai, Y.J., Hwang, C.L.: Fuzzy Mathematical Programming Methods and Applications. Springer, Berlin (1992)

    Book  MATH  Google Scholar 

  12. Mahdavi-Amiri, N., Nasseri, S.H.: Duality in fuzzy number linear programming by use of a certain linear ranking function. Applied Mathematics and Computation 180, 206–216 (2006)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  14. Mahdavi-Amiri, N., Nasseri, S.H., Yazdani, A.: Fuzzy primal simplex algorithms for solving fuzzy linear programming problems. Iranian Journal of Operational Research 1(2), 68–74 (2009)

    Google Scholar 

  15. Maleki, H.R., Tata, M., Mashinchi, M.: Linear programming with fuzzy variables. Fuzzy Sets and Systems 109, 21–33 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  16. Mehra, S.A., Chandra, C.R.: Bector: Acceptable optimality in linear fractional programming with fuzzy coefficient. Fuzzy Optimization and Decision Making 6, 5–16 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  17. Nasseri, S.H., Ebrahimnejad, A.: A fuzzy dual simplex method for fuzzy number linear programming problem. Advances in Fuzzy Sets and Systems 5(2), 81–95 (2009)

    MathSciNet  Google Scholar 

  18. Okada, S., Soper, T.: A shortest path problem on a network with fuzzy arc lengths. Fuzzy Sets and Systems 109, 129–140 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  19. Rommelfanger, H.: Fuzzy linear programming and applications. European Journal of Oprational Research 92(3), 512–527 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  20. Rommelfanger, H.: The advantages of fuzzy optimization models in practical use. Fuzzy Optimization and Decision Making 3(4), 295–309 (2004)

    Article  MATH  Google Scholar 

  21. Rommelfanger, H.: A general concept for solving linear multicriteria programming problems with crisp, fuzzy or stochastic values. Fuzzy Sets and Systems 158, 1892–1904 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  22. Safi, Z.M.R., Maleki, H.R., Zaeimazad, E.: A geometric approach for solving fuzzy linear programming problems. Fuzzy Optimization and Decision Making 6, 315–336 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  23. Tanaka, H., Okuda, T., Asai, K.: On fuzzy mathematical programming. The Journal of Cybernetics 3, 37–46 (1974)

    Article  MathSciNet  Google Scholar 

  24. Vijay, V., Mehra, A., Chandra, S., Bector, C.R.: Fuzzy matrix games via a fuzzy relation approach. Fuzzy Optimization and Decision Making 6, 299–314 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  25. Yager, R.R.: A procedure for ordering fuzzy subsets of the unit interval. Information Sciences 24, 143–161 (1981)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Mazandaran, Babolsar, Iran

    S. H. Nasseri & Z. Alizadeh

  2. Department of Mathematics, Islamic Azad University, Jouybar Branch, Jouybar, Iran

    B. Khabiri

Authors
  1. S. H. Nasseri
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  2. Z. Alizadeh
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  3. B. Khabiri
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Corresponding author

Correspondence to S. H. Nasseri .

Editor information

Editors and Affiliations

  1. School of Mathematics and, Information Science, Guangzhou University, Wai Huan Xi Road, Guangdong, 510006, China, People's Republic

    Bing-Yuan Cao

  2. , School of Science, Southwest Petroleum University, Xindu Avenue 8#, Chengdu, 610500, China, People's Republic

    Xiang-Jun Xie

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© 2012 Springer-Verlag Berlin Heidelberg

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Nasseri, S.H., Alizadeh, Z., Khabiri, B. (2012). Initial Basic Solution for the Fuzzy Primal Simplex Algorithm Using a Two-Phase Method. In: Cao, BY., Xie, XJ. (eds) Fuzzy Engineering and Operations Research. Advances in Intelligent and Soft Computing, vol 147. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28592-9_1

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  • DOI: https://doi.org/10.1007/978-3-642-28592-9_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-28591-2

  • Online ISBN: 978-3-642-28592-9

  • eBook Packages: EngineeringEngineering (R0)

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