zbMATH — the first resource for mathematics

Uncertain random programming with applications. (English) Zbl 1428.90194
Summary: Uncertain random variable is a tool to deal with a mixture of uncertainty and randomness. This paper presents an operational law of uncertain random variables, and shows an expected value formula by using probability and uncertainty distributions. This paper also provides a framework of uncertain random programming that is a type of mathematical programming involving uncertain random variables. Finally, some applications of uncertain random programming are discussed.

90C70 Fuzzy and other nonstochastic uncertainty mathematical programming
90C15 Stochastic programming
90B25 Reliability, availability, maintenance, inspection in operations research
Full Text: DOI
[1] Kolmogorov A. N. (1933) Grundbegriffe der Wahrscheinlichkeitsrechnung. Julius Springer, Berlin · Zbl 0007.21601
[2] Kruse R., Meyer K. D. (1987) Statistics with vague data. D. Reidel Publishing Company, Dordrecht · Zbl 0663.62010
[3] Kwakernaak, H., Fuzzy random variables—I: definitions and theorems, Information Sciences, 15, 1-29, (1987) · Zbl 0438.60004
[4] Kwakernaak, H., Fuzzy random variables—II: algorithms and examples for the discrete case, Information Sciences, 17, 253-278, (1979) · Zbl 0438.60005
[5] Liu, B., Fuzzy random chance-constrained programming, IEEE Transactions on Fuzzy Systems, 9, 713-720, (2001)
[6] Liu, B., Fuzzy random dependent-chance programming, IEEE Transactions on Fuzzy Systems, 9, 721-726, (2001)
[7] Liu, B., Random fuzzy dependent-chance programming and its hybrid intelligent algorithm, Information Sciences, 141, 259-271, (2002) · Zbl 1175.90439
[8] Liu, B.; Liu, Y. K., Expected value of fuzzy variable and fuzzy expected value models, IEEE Transactions on Fuzzy Systems, 10, 445-450, (2002)
[9] Liu B. (2007) Uncertainty theory. Springer, Berlin · Zbl 1141.28001
[10] Liu, B., Some research problems in uncertainty theory, Journal of Uncertain Systems, 3, 3-10, (2009)
[11] Liu B. (2009b) Theory and practice of uncertain programming. Springer, Berlin · Zbl 1158.90010
[12] Liu B. (2011) Uncertainty theory: A branch of mathematics for modeling human uncertainty. Springer, Berlin
[13] Liu, B., Why is there a need for uncertainty theory?, Journal of Uncertain Systems, 6, 3-10, (2012)
[14] Liu, Y. H. (2012b). Uncertain random variables: A mixture of uncertainty and randomness. Soft Computing (to be published).
[15] Liu, Y. H.; Ha, M. H., Expected value of function of uncertain variables, Journal of Uncertain Systems, 4, 181-186, (2010)
[16] Liu, Y. K.; Liu, B., Fuzzy random variables: A scalar expected value operator, Fuzzy Optimization and Decision Making, 2, 143-160, (2003)
[17] Liu, Y. K.; Liu, B., Fuzzy random programming with equilibrium chance constraints, Information Sciences, 170, 363-395, (2005) · Zbl 1140.90520
[18] Peng, Z. X.; Iwamura, K., A sufficient and necessary condition of uncertainty distribution, Journal of Interdisciplinary Mathematics, 13, 277-285, (2010) · Zbl 1229.28029
[19] Puri, M. L.; Ralescu, D. A., Fuzzy random variables, Journal of Mathematical Analysis and Applications, 114, 409-422, (1986) · Zbl 0592.60004
[20] Zadeh, L. A., Fuzzy sets, Information and Control, 8, 338-353, (1965) · Zbl 0139.24606
[21] Zadeh, L. A., Fuzzy sets as a basis for a theory of possibility, Fuzzy sets and Systems, 1, 3-28, (1978) · Zbl 0377.04002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.