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Interior Point Method for Solving Fuzzy Number Linear Programming Problems Using Linear Ranking Function

Author

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  • Yi-hua Zhong
  • Yan-lin Jia
  • Dandan Chen
  • Yan Yang

Abstract

Recently, various methods have been developed for solving linear programming problems with fuzzy number, such as simplex method and dual simplex method. But their computational complexities are exponential, which is not satisfactory for solving large‐scale fuzzy linear programming problems, especially in the engineering field. A new method which can solve large‐scale fuzzy number linear programming problems is presented in this paper, which is named a revised interior point method. Its idea is similar to that of interior point method used for solving linear programming problems in crisp environment before, but its feasible direction and step size are chosen by using trapezoidal fuzzy numbers, linear ranking function, fuzzy vector, and their operations, and its end condition is involved in linear ranking function. Their correctness and rationality are proved. Moreover, choice of the initial interior point and some factors influencing the results of this method are also discussed and analyzed. The result of algorithm analysis and example study that shows proper safety factor parameter, accuracy parameter, and initial interior point of this method may reduce iterations and they can be selected easily according to the actual needs. Finally, the method proposed in this paper is an alternative method for solving fuzzy number linear programming problems.

Suggested Citation

  • Yi-hua Zhong & Yan-lin Jia & Dandan Chen & Yan Yang, 2013. "Interior Point Method for Solving Fuzzy Number Linear Programming Problems Using Linear Ranking Function," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:795098
    DOI: 10.1155/2013/795098
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    References listed on IDEAS

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    1. Rommelfanger, Heinrich, 1996. "Fuzzy linear programming and applications," European Journal of Operational Research, Elsevier, vol. 92(3), pages 512-527, August.
    2. A. Ebrahimnejad & S. H. Nasseri, 2009. "Using complementary slackness property to solve linear programming with fuzzy parameters," Fuzzy Information and Engineering, Springer, vol. 1(3), pages 233-245, September.
    3. A Ebrahimnejad & S.H Nasseri, 2009. "Using Complementary Slackness Property to Solve Linear Programming with Fuzzy Parameters," Fuzzy Information and Engineering, Taylor & Francis Journals, vol. 1(3), pages 233-245, September.
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    Cited by:

    1. A. Srinivasan & G. Geetharamani, 2016. "Linear Programming Problem with Interval Type 2 Fuzzy Coefficients and an Interpretation for Its Constraints," Journal of Applied Mathematics, John Wiley & Sons, vol. 2016(1).

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