Random fuzzy dependent-chance programming and its hybrid intelligent algorithm.

*(English)*Zbl 1175.90439Summary: A fuzzy random variable is a measurable function from a probability space to a collection of fuzzy sets, while a random fuzzy variable is a function from a collection of random variables to \([0,1]\). This paper provides a spectrum of random fuzzy dependent-chance programming in which the underlying philosophy is based on selecting the decision with maximal chance to meet the event. In order to speed up the solution process, we train a neural network to approximate chance functions based on the training data generated by the random fuzzy simulation. Finally, we integrate random fuzzy simulation, neural network and genetic algorithm to produce a more powerful and effective hybrid intelligent algorithm for solving random fuzzy dependent-chance programming models, and illustrate its effectiveness by some numerical examples.

##### MSC:

90C70 | Fuzzy and other nonstochastic uncertainty mathematical programming |

90C15 | Stochastic programming |

Full Text:
DOI

##### References:

[1] | Bouchon-Meunier, B.; Kreinovich, V.; Lokshin, A.; Nguyen, H.T., On the formulation of optimization under elastic constraints (with control in mind), Fuzzy sets and systems, 81, 5-29, (1996) · Zbl 0883.93038 |

[2] | Buckley, J.J.; Hayashi, Y., Fuzzy genetic algorithm and applications, Fuzzy sets and systems, 61, 129-136, (1994) |

[3] | Charnes, A.; Cooper, W.W., Chance-constrained programming, Management science, 6, 1, 73-79, (1959) · Zbl 0995.90600 |

[4] | Klement, E.P.; Puri, M.L.; Ralescu, D.A., Limit theorems for fuzzy random variables, Proceedings of the royal society of London, 407, 171-182, (1986) · Zbl 0605.60038 |

[5] | Kruse, R.; Meyer, K.D., Statistics with vague data, (1987), Reidel Dordrecht · Zbl 0663.62010 |

[6] | Kwakernaak, H., Fuzzy random variables I, Information sciences, 15, 1-29, (1978) · Zbl 0438.60004 |

[7] | Kwakernaak, H., Fuzzy random variables II, Information sciences, 17, 253-278, (1979) · Zbl 0438.60005 |

[8] | Liu, B., Dependent-chance programming: A class of stochastic optimization, Computers and mathematics with applications, 34, 12, 89-104, (1997) · Zbl 0905.90127 |

[9] | Liu, B.; Iwamura, K., Chance constrained programming with fuzzy parameters, Fuzzy sets and systems, 94, 2, 227-237, (1998) · Zbl 0923.90141 |

[10] | Liu, B.; Iwamura, K., A note on chance constrained programming with fuzzy coefficients, Fuzzy sets and systems, 100, 1-3, 229-233, (1998) · Zbl 0948.90156 |

[11] | Liu, B., Minimax chance constrained programming models for fuzzy decision systems, Information sciences, 112, 1-4, 25-38, (1998) · Zbl 0965.90058 |

[12] | Liu, B., Dependent-chance programming with fuzzy decisions, IEEE transactions on fuzzy systems, 7, 3, 354-360, (1999) |

[13] | Liu, B., Uncertain programming, (1999), Wiley New York |

[14] | Liu, B., Dependent-chance programming in fuzzy environments, Fuzzy sets and systems, 109, 1, 97-106, (2000) · Zbl 0955.90153 |

[15] | Liu, B.; Iwamura, K., Fuzzy programming with fuzzy decisions and fuzzy simulation-based genetic algorithm, Fuzzy sets and systems, 122, 2, 253-262, (2001) · Zbl 1020.90048 |

[16] | Liu, B., Fuzzy random chance-constrained programming, IEEE transactions on fuzzy systems, 9, 5, 713-720, (2001) |

[17] | Liu, B., Fuzzy random dependent-chance programming, IEEE transactions on fuzzy systems, 9, 5, 721-726, (2001) |

[18] | B. Liu, Random fuzzy variables and random fuzzy programming, Technical Report 2001-66, Department of Mathematical Sciences, Tsinghua University |

[19] | B. Liu, Y.-K. Liu, Expected value of fuzzy variable and fuzzy expected value models, IEEE Transactions on Fuzzy Systems (to be published) · Zbl 1074.90056 |

[20] | Luhandjula, M.K., Linear programming under randomness and fuzziness, Fuzzy sets and systems, 10, 45-55, (1983) · Zbl 0514.90067 |

[21] | Luhandjula, M.K., On possibilistic linear programming, Fuzzy sets and systems, 18, 15-30, (1986) · Zbl 0616.90038 |

[22] | Luhandjula, M.K., Fuzziness and randomness in an optimization framework, Fuzzy sets and systems, 77, 291-297, (1996) · Zbl 0869.90081 |

[23] | Luhandjula, M.K.; Gupta, M.M., On fuzzy stochastic optimization, Fuzzy sets and systems, 81, 47-55, (1996) · Zbl 0879.90187 |

[24] | Medsker, L.R., Hybrid intelligent systems, (1995), Kluwer Academic Publishers Boston · Zbl 0831.68104 |

[25] | Negoita, C.V.; Ralescu, D., Simulation, knowledge-based computing, and fuzzy statistics, (1987), Van Nostrand Reinhold New York · Zbl 0683.68097 |

[26] | Puri, M.L.; Ralescu, D.A., Fuzzy random variables, Journal of mathematical analysis and applications, 114, 409-422, (1986) · Zbl 0592.60004 |

[27] | Wang, G.; Qiao, Z., Linear programming with fuzzy random variable coefficients, Fuzzy sets and systems, 57, 295-311, (1993) · Zbl 0791.90072 |

[28] | Yazenin, A.V., Fuzzy and stochastic programming, Fuzzy sets and systems, 22, 171-180, (1987) · Zbl 0623.90058 |

[29] | Yazenin, A.V., On the problem of possibilistic optimization, Fuzzy sets and systems, 81, 133-140, (1996) · Zbl 0877.90087 |

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.