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Chance constrained programming with fuzzy parameters. (English) Zbl 0923.90141

Summary: This paper extends chance constrained programming from stochastic to fuzzy environments. Analogous to stochastic programming, some crisp equivalents of chance constraints in fuzzy environments are presented. We also propose a technique of fuzzy simulation for the chance constraints which are usually hard to be converted to their crisp equivalents. Finally, a fuzzy simulation based genetic algorithm is designed for solving this kind of problems and some numerical examples are discussed.

MSC:

90C70 Fuzzy and other nonstochastic uncertainty mathematical programming

Software:

Genocop
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References:

[1] Bellman, R. E.; Zadeh, L. A., Decision making in a fuzzy environment, Management Sci., 17, 141-164 (1970) · Zbl 0224.90032
[2] Charnes, A.; Cooper, W. W., Chance-constrained programming, Management Sci., 6, 73-79 (1959) · Zbl 0995.90600
[3] Dubois, D.; Prade, H., Possibility Theory (1988), Plenum: Plenum New York · Zbl 0645.68108
[4] Dubois, D.; Prade, H., Fuzzy numbers: an overview, (Bezdek, J. C., Analysis of Fuzzy Information, 2 (1988), CRC Press: CRC Press Boca Raton), 3-39
[5] Fogel, D. B., An introduction to simulated evolutionary optimization, IEEE Trans. Neural Networks, 5, 3-14 (1994)
[6] Goldberg, D. E., Genetic Algorithms in Search, Optimization and Machine Learning (1989), Addison-Wesley: Addison-Wesley Reading, MA · Zbl 0721.68056
[8] MareŇ°, M., Computation Over Fuzzy Quantities (1994), CRC Press: CRC Press Boca Raton · Zbl 0859.94035
[9] Michalewicz, Z., Genetic Algorithms + Data Structures = Evolution Programs (1994), Springer: Springer New York · Zbl 0818.68017
[10] Ostasiewicz, W., A new approach to fuzzy programming, Fuzzy Sets and Systems, 7, 139-152 (1982) · Zbl 0474.68007
[11] Rubinstein, R. Y., Simulation and the Monte Carlo Method (1981), Wiley: Wiley New York · Zbl 0529.68076
[12] Zadeh, L. A., Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets and Systems, 1, 3-28 (1978) · Zbl 0377.04002
[13] Zimmermann, H. J., Fuzzy Set Theory and its Applications (1985), Kluwer Nijhof: Kluwer Nijhof Boston · Zbl 0578.90095
[14] Zimmermann, H. J., Applications of fuzzy set theory to mathematical programming, Inform. Sci., 36, 29-58 (1985) · Zbl 0578.90095
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