Abstract
This paper proposes new methods to reduce the uncertain information embedded in the secondary possibility distribution of a type-2 fuzzy variable. Based on possibility measure, we define the lower value-at-risk (VaR) and upper VaR of a regular fuzzy variable, and develop the VaR-based reduction methods for type-2 fuzzy variables. The proposed VaR-based reduction methods generalize some existing reduction methods by introducing possibility level parameter in distribution functions. For VaR reduced fuzzy variables, we employ Lebesgue–Stieltjes (L–S) integral to define three \(n\)th semideviations to gauge the risk resulted from asymmetric fuzzy uncertainty. Furthermore, we compute the mean values and semideviations of the VaR reduced fuzzy variables, and derive some useful analytical expressions. The theoretical results obtained in this paper have potential applications in practical risk management and engineering optimization problems.
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Acknowledgments
The authors wish to thank the Editor and anonymous reviewers, whose valuable comments led to an improved version of this paper. This work was supported by the National Natural Science Foundation of China (No.61374184), the Natural Science Foundation of Hebei Province (A2011201007), and the Training Foundation of Hebei Province Talent Engineering.
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Bai, X., Liu, Y. Semideviations of reduced fuzzy variables: a possibility approach. Fuzzy Optim Decis Making 13, 173–196 (2014). https://doi.org/10.1007/s10700-013-9175-8
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DOI: https://doi.org/10.1007/s10700-013-9175-8