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An interval programming approach for the bilevel linear programming problem under fuzzy random environments

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Abstract

In this paper, we address a class of bilevel linear programming problems with fuzzy random variable coefficients in objective functions. To deal with such problems, we apply an interval programming approach based on the \(\alpha \)-level set to construct a pair of bilevel mathematical programming models called the best and worst optimal models. Through expectation optimization model, the best and worst optimal problems are transformed into the deterministic problems. By means of the Kth best algorithm, we obtain the best and worst optimal solutions as well as the corresponding range of the objective function values. In this way, more information can be provided to the decision makers under fuzzy random circumstances. Finally, experiments on two examples are carried out, and the comparisons with two existing approaches are made. The results indicate the proposed approaches can get not only the best optimal solution (ideal solution) but also the worst optimal solution, and is more reasonable than the existing approaches which can only get a single solution (ideal solution).

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Acknowledgments

This work was supported by National Natural Science Foundation of China (No.61272119), National Natural Science Foundation of China (No.61203372) and Fundamental Research Funds for the Central Universities (No. K5051303009).

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Authors and Affiliations

  1. School of Computer Science and Technology, Xidian University, Xi’an, 710071, China

    Aihong Ren, Yuping Wang & Xingsi Xue

Authors
  1. Aihong Ren
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  2. Yuping Wang
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  3. Xingsi Xue
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Corresponding author

Correspondence to Yuping Wang.

Additional information

Communicated by G. Acampora.

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Ren, A., Wang, Y. & Xue, X. An interval programming approach for the bilevel linear programming problem under fuzzy random environments. Soft Comput 18, 995–1009 (2014). https://doi.org/10.1007/s00500-013-1120-9

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