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Fuzzy Optimization and Decision Making

Erschienen in:

01.06.2014

Semideviations of reduced fuzzy variables: a possibility approach

Erschienen in: Fuzzy Optimization and Decision Making | Ausgabe 2/2014

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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.

Vorheriger Artikel Pessimistic, optimistic, and minimax regret approaches for linear programs under uncertainty

Nächster Artikel Blackwell’s theorem for fuzzy variables

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Titel: Semideviations of reduced fuzzy variables: a possibility approach
Publikationsdatum: 01.06.2014
Erschienen in: Fuzzy Optimization and Decision Making / Ausgabe 2/2014
Print ISSN: 1568-4539
Elektronische ISSN: 1573-2908
DOI: https://doi.org/10.1007/s10700-013-9175-8

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