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Studying interconnections between two classes of two-stage fuzzy optimization problems

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Abstract

In this paper, we study two types of risk aversion two-stage fuzzy optimization problems. The first type is called two-stage fuzzy minimum risk problem (FMRP), while the second type is referred to as two-stage fuzzy value-at-risk problem (FVRP). In order to facilitate the solution of the two optimization problems, it is required to study the properties of FMRP and FVRP as well as their relationships. For this purpose, we first discuss the semicontinuity about the recourse function of two-stage FMRP. After that, we discuss the interconnections between optimal objective value of FMRP and that of FVRP, and the relationships between optimal solution of FMRP and that of FVRP. Using the obtained results, it would be possible to solve one two-stage optimization problem indirectly by solving its counterpart.

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Acknowledgments

This work was supported by the Natural Science Foundation of Hebei Province (A2011201007), and National Natural Science Foundation of China (no.60974134).

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Authors and Affiliations

  1. College of Mathematics and Computer Science, Hebei University, Baoding, 071002, Hebei, China

    Yankui Liu

  2. College of Management, Hebei University, Baoding, 071002, Hebei, China

    Xuejie Bai

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  1. Yankui Liu
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  2. Xuejie Bai
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Correspondence to Yankui Liu.

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Liu, Y., Bai, X. Studying interconnections between two classes of two-stage fuzzy optimization problems. Soft Comput 17, 569–578 (2013). https://doi.org/10.1007/s00500-012-0925-2

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