Fuzzy programming with recourse. (English) Zbl 1114.90487
Summary: In this study, we deal with the optimization methodology in fuzzy decision-making systems. The issue of convergence for sequences of integrable fuzzy variables is discussed. Based on credibility theory, a new class of fuzzy programming – two-stage fuzzy programming or fuzzy programming with recourse problem is introduced, and a discussion about basic properties of the recourse problems is included. To solve the two-stage fuzzy programming problems, a heuristic solution method, which combines fuzzy simulations, genetic algorithm and neural network, is proposed, and the convergence of approximating a recourse function is proved. We provide three numerical examples to illustrate the feasibility and effectiveness of the designed algorithm.
MSC:
| 90C70 | Fuzzy and other nonstochastic uncertainty mathematical programming |
| 92B20 | Neural networks for/in biological studies, artificial life and related topics |
References:
| [1] | DOI: 10.1007/978-1-4684-5287-7 · doi:10.1007/978-1-4684-5287-7 |
| [2] | DOI: 10.1016/S0165-0114(97)00371-0 · Zbl 0984.94045 · doi:10.1016/S0165-0114(97)00371-0 |
| [3] | DOI: 10.1016/0165-0114(78)90029-5 · Zbl 0377.04002 · doi:10.1016/0165-0114(78)90029-5 |
| [4] | DOI: 10.1016/S0165-0114(96)00236-9 · Zbl 0923.90141 · doi:10.1016/S0165-0114(96)00236-9 |
| [5] | DOI: 10.1016/S0898-1221(99)00126-1 · Zbl 0931.90069 · doi:10.1016/S0898-1221(99)00126-1 |
| [6] | DOI: 10.1016/0020-0255(93)90086-2 · Zbl 0770.90078 · doi:10.1016/0020-0255(93)90086-2 |
| [7] | DOI: 10.1016/S0165-0114(98)00449-7 · Zbl 0938.90074 · doi:10.1016/S0165-0114(98)00449-7 |
| [8] | DOI: 10.1007/978-3-642-48753-8 · doi:10.1007/978-3-642-48753-8 |
| [9] | Lee E. S., Appl. Math. Comput. 120 pp 79– |
| [10] | DOI: 10.1007/978-3-7908-1781-2 · doi:10.1007/978-3-7908-1781-2 |
| [11] | DOI: 10.1016/0165-0114(89)90019-5 · Zbl 0677.90088 · doi:10.1016/0165-0114(89)90019-5 |
| [12] | DOI: 10.1007/978-1-4899-1633-4 · doi:10.1007/978-1-4899-1633-4 |
| [13] | DOI: 10.1016/S0165-0114(98)00463-1 · Zbl 0961.90136 · doi:10.1016/S0165-0114(98)00463-1 |
| [14] | Liu B., IEEE Trans. Fuzzy Syst. 10 pp 445– |
| [15] | DOI: 10.1007/978-3-540-39987-2 · doi:10.1007/978-3-540-39987-2 |
| [16] | DOI: 10.1016/0165-0114(78)90011-8 · Zbl 0383.03038 · doi:10.1016/0165-0114(78)90011-8 |
| [17] | DOI: 10.1023/A:1013771608623 · Zbl 1068.90618 · doi:10.1023/A:1013771608623 |
| [18] | Birge J. R., Introduction to Stochastic Programming (1997) · Zbl 0892.90142 |
| [19] | Kall P., Stochastic Programming (1994) |
| [20] | DOI: 10.1137/0115113 · Zbl 0203.21806 · doi:10.1137/0115113 |
| [21] | DOI: 10.1287/mnsc.27.6.698 · doi:10.1287/mnsc.27.6.698 |
| [22] | DOI: 10.1016/0165-0114(82)90032-X · Zbl 0493.28001 · doi:10.1016/0165-0114(82)90032-X |
| [23] | DOI: 10.1142/S0218488503002016 · Zbl 1074.90056 · doi:10.1142/S0218488503002016 |
| [24] | Gen M., Genetic Algorithms & Engineering Design (1997) |
| [25] | Gen M., Genetic Algorithms & Engineering Optimization (2000) |
| [26] | Goldberg D. E., Genetic Algorithms in Search, Optimization and Machine Learning (1989) · Zbl 0721.68056 |
| [27] | DOI: 10.1007/978-3-662-03315-9 · doi:10.1007/978-3-662-03315-9 |
| [28] | Jan van T., Convex Analysis: An Introduction Text (1984) |
| [29] | DOI: 10.1016/S0893-6080(97)00097-X · doi:10.1016/S0893-6080(97)00097-X |
| [30] | Karayiannis N. B., IEEE Transactions on Circuits and Systems–II: Analog and Digital Signal Processing 39 pp 453– · Zbl 0759.68074 · doi:10.1109/82.160170 |
| [31] | DOI: 10.1109/72.572092 · doi:10.1109/72.572092 |
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
