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Expected value operator of random fuzzy variable and random fuzzy expected value models. (English) Zbl 1074.90056

Summary: A random fuzzy variable is a mapping from a possibility space to a collection of random variables. This paper first presents a new definition of the expected value operator of a random fuzzy variable, and proves the linearity of the operator. Then, a random fuzzy simulation approach, which combines fuzzy simulation and random simulation, is designed to estimate the expected value of a random fuzzy variable. Based on the new expected value operator, three types of random fuzzy expected value models are presented to model decision systems where fuzziness and randomness appear simultaneously. In addition, random fuzzy simulation, neural networks and genetic algorithm are integrated to produce a hybrid intelligent algorithm for solving those random fuzzy expected valued models. Finally, three numerical examples are provided to illustrate the feasibility and the effectiveness of the proposed algorithm.

MSC:

90C70 Fuzzy and other nonstochastic uncertainty mathematical programming
60A05 Axioms; other general questions in probability
68T37 Reasoning under uncertainty in the context of artificial intelligence
90B50 Management decision making, including multiple objectives
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[1] DOI: 10.1109/3477.650062 · doi:10.1109/3477.650062
[2] DOI: 10.1007/978-1-4684-5287-7 · doi:10.1007/978-1-4684-5287-7
[3] DOI: 10.1016/S0165-0114(98)00449-7 · Zbl 0938.90074 · doi:10.1016/S0165-0114(98)00449-7
[4] DOI: 10.1016/0165-0114(92)90277-B · Zbl 0786.90090 · doi:10.1016/0165-0114(92)90277-B
[5] DOI: 10.1016/0020-0255(93)90086-2 · Zbl 0770.90078 · doi:10.1016/0020-0255(93)90086-2
[6] DOI: 10.1016/S0165-0114(97)00371-0 · Zbl 0984.94045 · doi:10.1016/S0165-0114(97)00371-0
[7] Liu B., Fuzzy Sets Syst. 100 pp 229–
[8] Liu B., IEEE Trans. Fuzzy Syst. 7 pp 354–
[9] Liu B., Uncertain Programming (1999)
[10] DOI: 10.1016/S0165-0114(97)00384-9 · Zbl 0955.90153 · doi:10.1016/S0165-0114(97)00384-9
[11] Liu B., IEEE Trans. Fuzzy Syst. 9 pp 713–
[12] Liu B., IEEE Trans. Fuzzy Syst. 9 pp 721–
[13] DOI: 10.1007/978-3-7908-1781-2 · doi:10.1007/978-3-7908-1781-2
[14] DOI: 10.1016/S0020-0255(02)00176-7 · Zbl 1175.90439 · doi:10.1016/S0020-0255(02)00176-7
[15] DOI: 10.1023/A:1013771608623 · Zbl 1068.90618 · doi:10.1023/A:1013771608623
[16] Liu B., IEEE Trans. Fuzzy Syst. 10 pp 445–
[17] DOI: 10.1016/0165-0114(95)00043-7 · Zbl 0869.90081 · doi:10.1016/0165-0114(95)00043-7
[18] DOI: 10.1016/0165-0114(95)00240-5 · Zbl 0879.90187 · doi:10.1016/0165-0114(95)00240-5
[19] DOI: 10.1016/0165-0114(78)90011-8 · Zbl 0383.03038 · doi:10.1016/0165-0114(78)90011-8
[20] DOI: 10.1016/0165-0114(95)00241-3 · Zbl 0877.90085 · doi:10.1016/0165-0114(95)00241-3
[21] DOI: 10.1007/978-1-4899-1633-4 · doi:10.1007/978-1-4899-1633-4
[22] DOI: 10.1016/S0165-0114(98)00241-3 · Zbl 0978.90111 · doi:10.1016/S0165-0114(98)00241-3
[23] DOI: 10.1016/S0165-0114(98)00463-1 · Zbl 0961.90136 · doi:10.1016/S0165-0114(98)00463-1
[24] Qiao Z., Fuzzy Sets Syst. 58 pp 155–
[25] DOI: 10.1007/978-1-4757-5303-5 · doi:10.1007/978-1-4757-5303-5
[26] DOI: 10.1016/0165-0114(87)90014-5 · Zbl 0623.90058 · doi:10.1016/0165-0114(87)90014-5
[27] DOI: 10.1016/0165-0114(78)90029-5 · Zbl 0377.04002 · doi:10.1016/0165-0114(78)90029-5
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