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On generating the set of nondominated solutions of a linear programming problem with parameterized fuzzy numbers

Author

Listed:
  • Manuel Arana-Jiménez

    (University of Cádiz)

  • Carmen Sánchez-Gil

    (University of Cádiz)

Abstract

The paper presents a new method for solving fully fuzzy linear programming problems with inequality constraints and parameterized fuzzy numbers, by means of solving multiobjective linear programming problems. The equivalence is proven between the set of nondominated solutions of the fully fuzzy linear programming problem and the set of weakly efficient solutions of the considered and related multiobjective linear problem. The whole set of nondominated solutions for a fully fuzzy linear programming problem is explicitly obtained by means of a finite generator set.

Suggested Citation

  • Manuel Arana-Jiménez & Carmen Sánchez-Gil, 2020. "On generating the set of nondominated solutions of a linear programming problem with parameterized fuzzy numbers," Journal of Global Optimization, Springer, vol. 77(1), pages 27-52, May.
    • Handle: RePEc:spr:jglopt:v:77:y:2020:i:1:d:10.1007_s10898-019-00841-7
    DOI: 10.1007/s10898-019-00841-7
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    References listed on IDEAS

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    1. R. E. Bellman & L. A. Zadeh, 1970. "Decision-Making in a Fuzzy Environment," Management Science, INFORMS, vol. 17(4), pages 141-164, December.
    2. Izaz Ullah Khan & Tahir Ahmad & Normah Maan, 2013. "A Simplified Novel Technique for Solving Fully Fuzzy Linear Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 159(2), pages 536-546, November.
    3. A. Ebrahimnejad & S.H. Nasseri & F. Hosseinzadeh Lotfi & M. Soltanifar, 2010. "A primal-dual method for linear programming problems with fuzzy variables," European Journal of Industrial Engineering, Inderscience Enterprises Ltd, vol. 4(2), pages 189-209.
    4. Luciano Stefanini & Barnab?s Bede, 2012. "Generalized Fuzzy Differentiability with LU-parametric Representation," Working Papers 1210, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2012.
    5. Bindu Bhardwaj & Amit Kumar, 2014. "A Note on the Paper “A Simplified Novel Technique for Solving Fully Fuzzy Linear Programming Problems”," Journal of Optimization Theory and Applications, Springer, vol. 163(2), pages 685-696, November.
    6. Dipankar Chakraborty & Dipak Kumar Jana & Tapan Kumar Roy, 2016. "A new approach to solve fully fuzzy transportation problem using triangular fuzzy number," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 26(2), pages 153-179.
    7. K. Ganesan & P. Veeramani, 2006. "Fuzzy linear programs with trapezoidal fuzzy numbers," Annals of Operations Research, Springer, vol. 143(1), pages 305-315, March.
    8. Izaz Ullah Khan & Tahir Ahmad & Normah Maan, 2017. "A Reply to a Note on the Paper “A Simplified Novel Technique for Solving Fully Fuzzy Linear Programming Problems”," Journal of Optimization Theory and Applications, Springer, vol. 173(1), pages 353-356, April.
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