Abstract
In many cases, fuzziness and randomness simultaneously appear in a system. In order to describe this phenomena, a fuzzy random variable was introduced by Kwakernaak [142] as a random element taking “fuzzy variable” values. By fuzzy random programming we mean the optimization theory in fuzzy random environments. Liu and Liu [198] presented a spectrum of fuzzy random expected value model (EVM), Liu [179] initialized a general framework of fuzzy random chance-constrained programming (CCP), and Liu [180] introduced the concepts of uncertain environment and chance function for fuzzy random decision problems, and constructed a theoretical framework of fuzzy random dependent-chance programming (DCP).
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© 2009 Springer-Verlag Berlin Heidelberg
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Liu, B. (2009). Hybrid Programming. In: Theory and Practice of Uncertain Programming. Studies in Fuzziness and Soft Computing, vol 239. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89484-1_6
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DOI: https://doi.org/10.1007/978-3-540-89484-1_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-89483-4
Online ISBN: 978-3-540-89484-1
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