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An approach based on reliability-based possibility degree of interval for solving general interval bilevel linear programming problem

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Abstract

This paper presents a new method based on reliability-based possibility degree of interval to handle the general interval bilevel linear programming problem involving interval coefficients in both objective functions and constraints. Considering reliability of the uncertain constraints, the interval inequality constraints are first converted into their deterministic equivalent forms by virtue of the reliability-based possibility degree of interval, and then the original problem is transformed into a bilevel linear programming with interval coefficients in the upper and lower level objective functions only. Then, the notion of the optimal solution of the problem is given by means of a type of the interval order relation. Based on this concept, the transformed problem is reduced into a deterministic bilevel programming with the aid of linear combination method. Furthermore, the proposed method is extended to deal with the fuzzy bilevel linear programming problem through the nearest interval approximation. Finally, three numerical examples are given to illustrate the effectiveness of the proposed approach.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 61602010) and Natural Science Basic Research Plan in Shaanxi Province of China (Grant No. 2017JQ6046).

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Authors and Affiliations

  1. Department of Mathematics, Baoji University of Arts and Sciences, Baoji, 721013, Shaanxi, China

    Aihong Ren

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

    Yuping Wang

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  1. Aihong Ren
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  2. Yuping Wang
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Correspondence to Aihong Ren.

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Communicated by V. Loia.

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Ren, A., Wang, Y. An approach based on reliability-based possibility degree of interval for solving general interval bilevel linear programming problem. Soft Comput 23, 997–1006 (2019). https://doi.org/10.1007/s00500-017-2811-4

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  • DOI: https://doi.org/10.1007/s00500-017-2811-4

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