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A fuzzy control system with application to production planning problems. (English) Zbl 1208.93051
Summary: A considerable part of the literature on fuzzy sets is devoted to the field of fuzzy control system. In this paper, an alternative control system is introduced to describe a dynamic system with fuzzy white noise. In order to find optimal ways to control such a system, fuzzy optimal control theory is further developed. Specifically, a linear quadratic model is formulated and solved as a fuzzy optimal control problem. The formulation and solution of this model provide an economic interpretation of a production planning model both in the finite horizon and in the infinite horizon.

MSC:
93C42 Fuzzy control/observation systems
90B30 Production models
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[1] Bensoussan, A.; Sethi, S.P.; Vickson, R.; Derzko, N., Stochastic production planning with production constraints, SIAM journal on control and optimization, 22, 920-935, (1984) · Zbl 0561.90044
[2] Boukas, E.K.; Zhang, Q.; YinRobust, G., Robust production and maintenance planning in stochastic manufacturing systems, IEEE transactions on automatic control, 40, 6, 1098-1102, (1995) · Zbl 0837.90054
[3] Chen, C.S., Dynamic structure adaptive neural fuzzy control for MIMO uncertain nonlinear systems, Information sciences, 179, 15, 2676-2688, (2009) · Zbl 1165.93322
[4] Chen, C.Y.; Li, T.H.; Yeh, Y.C., EP-based kinematic control and adaptive fuzzy sliding-mode dynamic control for wheeled mobile robots, Information sciences, 179, 1-2, 180-195, (2009) · Zbl 1158.93356
[5] Fleming, W.H.; Sethi, S.P.; Soner, H.M., An optimal stochastic production planning problem with randomly fluctuating demand, SIAM journal on control and optimization, 25, 6, 1494-1502, (1987) · Zbl 0635.93077
[6] Li, X.; Liu, B., A sufficient and necessary condition for credibility measures, International journal of uncertainty, fuzziness and knowledge-based systems, 14, 5, 527-535, (2006) · Zbl 1113.28014
[7] Liu, B., Fuzzy process, hybrid process and uncertain process, Journal of uncertain systems, 2, 1, 3-16, (2008)
[8] Liu, B., Uncertainty theory, (2007), Springer-Verlag Berlin
[9] Liu, B.; Liu, Y.K., Expected value of fuzzy variable and fuzzy expected value models, IEEE transactions on fuzzy systems, 10, 4, 445-450, (2002)
[10] Mamdani, E.H., Applications of fuzzy algorithms for control of simple dynamic plant, Proceedings IEE, 121, 1585-1588, (1974)
[11] Z. Qin, X. Li, Fuzzy calculus for finance. Available from: <http://orsc.edu.cn/process/fc.pdf>.
[12] Qin, Z.; Gao, X., Fractional Liu process with application to finance, Mathematical and computer modelling, 50, 9-10, 1538-1543, (2009) · Zbl 1185.60039
[13] Sethi, S.P.; Suo, W.; Taksar, M.I.; Zhang, Q., Optimal production planning in a stochastic manufacturing system with long-run average cost, Journal of optimization theory and applications, 92, 1, 161-188, (1997) · Zbl 0886.90084
[14] Sousa, J.M.; Kaymak, U., Fuzzy decision making in modeling and control, (2002), World Scientific Singapore · Zbl 1015.91019
[15] Takagi, T.; Sugeno, M., Fuzzy identification of systems and its applications to modelling and control, IEEE transactions on systems, man and cybernetics, 15, 1, 116-132, (1985) · Zbl 0576.93021
[16] van der Laan, E.A.; Salomon, M., Production planning and inventory control with remanufacturing and disposal, European journal of operational research, 102, 264-278, (1997) · Zbl 0955.90018
[17] Zadeh, L.A., Fuzzy sets, Information and control, 8, 338-353, (1965) · Zbl 0139.24606
[18] Zadeh, L.A., Outline of a new approach to the analysis of complex systems and decision processes, IEEE transactions on systems, man and cybernetics, 3, 28-44, (1973) · Zbl 0273.93002
[19] Zadeh, L.A., Toward a generalized theory of uncertainty (GTU) - an outline, Information sciences, 172, 1-40, (2005) · Zbl 1074.94021
[20] Zadeh, L.A., Is there a need for fuzzy logic?, Information sciences, 178, 2751-2779, (2008) · Zbl 1148.68047
[21] Zhu, Y., A fuzzy optimal control model, Journal of uncertain systems, 3, 4, 270-279, (2009)
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