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Fuzzy dynamic programming: Main developments and applications. (English) Zbl 0879.90185

Summary: We survey major developments and applications of fuzzy dynamic programming which is here advocated as a promising attempt at making dynamic programming models more realistic by a relaxation of often artificial assumptions of precision as to the constraints, goals, states and their transitions, termination time, etc. Issues related to numerical efficiency are considered. Applications in R&D planning, health care and medicine, socioeconomic regional development, energy systems, water and environmental systems, chemical engineering, etc. are surveyed.

MSC:

90C70 Fuzzy and other nonstochastic uncertainty mathematical programming
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[1] Baldwin, J. F.; Pilsworth, B. W., Dynamic programming for fuzzy systems with fuzzy environment, J. Math. Anal. and Appls., 85, 1-23 (1982) · Zbl 0491.90090
[2] Bellman, R. E.; Zadeh, L. A., Decision-making in a fuzzy environment, Management Sci., 17, B141-B164 (1970) · Zbl 0224.90032
[3] Bertsekas, D. P., Dynamic Programming and Stochastic Control (1976), Academic Press: Academic Press New York · Zbl 0549.93064
[4] Chang, S. S.L., Fuzzy dynamic programming and approximate optimization of partially known systems, (Proc. 2nd Hawaii Int. Conf on Syst. Sci.. Proc. 2nd Hawaii Int. Conf on Syst. Sci., Honolulu, USA (1969)) · Zbl 0366.90031
[5] Chang, S. S.L., Fuzzy dynamic programming and the decision making process, (Proc. 3rd Princeton Conf. on Inf. Sci. and Syst.. Proc. 3rd Princeton Conf. on Inf. Sci. and Syst., Princeton, USA (1969)), 200-203 · Zbl 0366.90031
[6] Esogbue, A. O., On the application of fuzzy allocation theory to the modelling of cancer research appropriation process, (Rose, J.; Bilciu, C., Modern Trends in Cybernetics and Systems (1977), Springer: Springer Berlin), 183-193 · Zbl 0433.90042
[7] Esogbue, A. O., Dynamic programming, fuzzy sets, and the modeling of R&D management control systems, IEEE Trans. Systems Man and Cybern., SMC13, 18-30 (1983) · Zbl 0501.90054
[8] Esogbue, A. O., Some novel applications of fuzzy dynamic programming, (Proc. IEEE (1983)), 501-505
[9] Esogbue, A. O., Some novel applications of fuzzy dynamic programming, (Proc. IEEE Systems, Man, Cybernetics Conference. Proc. IEEE Systems, Man, Cybernetics Conference, Bombay, India (1984)) · Zbl 0931.90065
[10] Esogbue, A. O., A fuzzy dynamic programming model of intra-operative anesthesia administration, (Kacprzyk, J.; Yager, R. R., Management Decision. Support Systems Using Fuzzy Sets and Possibility Theory (1985), Verlag TÜV Rheinland: Verlag TÜV Rheinland Cologne), 155-161
[11] Esogbue, A. O., Optimal clustering of fuzzy data via fuzzy dynamic programming, Fuzzy Sets and Systems, 18, 283-298 (1986) · Zbl 0616.62088
[12] Esogbue, A. O., Computational and data acquisition issues in fuzzy dynamic programming, (Proc. ORSA/TIMS Conf.. Proc. ORSA/TIMS Conf., Anaheim, USA (1991)) · Zbl 0960.92015
[13] Esogbue, A. O., Computational aspects and applications of a branch and bound algorithm for fuzzy multistage decision processes, Comput. Math. Appl., 21, 117-127 (1991) · Zbl 0743.90113
[14] Esogbue, A. O.; Bellman, R., A fuzzy dynamic programming algorithm for clustering non-quantitative data arising in water pollution control planning, (Proc. 3rd Internat. Conf on Mathematical Modeling. Proc. 3rd Internat. Conf on Mathematical Modeling, Los Angeles, USA (1981))
[15] Esogbue, A. O.; Bellman, R. E., Contributions to fuzzy dynamic programming, (Proc. 2nd Conf. on Maths. in the Service of Man. Proc. 2nd Conf. on Maths. in the Service of Man, Las Palmas, Spain (1982)), 275-285
[16] Esogbue, A. O.; Bellman, R. E., Fuzzy dynamic. programming and its extensions, (Zimmerman, H.-J.; Zadeh, L. A.; Gaines, B. R., Fuzzy Sets and Decision Analysis. Fuzzy Sets and Decision Analysis, TIMS Studies in Management Science, Vol. 20 (1984), Elsevier: Elsevier Amsterdam), 147-167
[17] Esogbue, A. O.; Bellman, R. E., Dynamic programming in health care, (Proc. 4th Internat. Conf. on Mathematical Modeling. Proc. 4th Internat. Conf. on Mathematical Modeling, Los Angeles, USA (1985))
[18] Esogbue, A. O.; Bellman, R. E., A fuzzy dynamic programming algorithm for clustering non-quantitative data arising in water pollution and planning, (Proc. 4th Internat. Conf. on Mathematical Modeling. Proc. 4th Internat. Conf. on Mathematical Modeling, Los Angeles, USA (1985))
[19] Esogbue, A. O.; Fedrizzi, M.; Kacprzyk, J., Fuzzy dynamic programming with stochastic systems, (Kacprzyk, J.; Fedrizzi, M., Combining Fuzzy Im precision with Probabilistic Uncertainty in Decision Making (1988), Springer: Springer Berlin), 266-287
[20] Esogbue, A. O.; Ramesh, V., Dynamic programming and fuzzy allocation processes, (Memo. No. 202 (1970), Dept. of Op. Res., Case Western Reserve University: Dept. of Op. Res., Case Western Reserve University Cleveland, USA)
[21] Esogbue, A. O.; Singh, A. J., Reduction of dimensionality in dynamic programming revisited: a comparative study and analysis of three algorithms, OPSEARCH, 12, 59-79 (1975)
[22] Esogbue, A. O.; Theologidu, M.; Guo, K., On the application of fuzzy sets theory to the optimal flood control problem arising in water resources systems, Fuzzy Sets and Systems, 48, 155-172 (1992)
[23] Fung, L. W.; Fu, K. S., Characterization of a class of fuzzy optimal control problems, (Gupta, M. M.; Saridis, G. N.; Gaines, B. R., Fuzzy Automata and Decision Processes (1977), North-Holland: North-Holland Amsterdam), 205-220
[24] Gluss, B., Fuzzy multistage decision-making, fuzzy state and terminal regulators and their relationship to nonfuzzy quadratic state and terminal regulators, Int. J. Control, 17, 177-192 (1973) · Zbl 0268.90004
[25] Hojo, T.; Terano, T.; Masui, S., Design of quasi-optimal fuzzy controller by fuzzy dynamic programming, (Proc. IEEE Internat. Conf. on Fuzzy Systems, Vol. 2 (1993)), 1253-1258
[26] Howard, R. A., Dynamic Programming and Markov Processes (1960), MIT Press: MIT Press Cambridge · Zbl 0091.16001
[27] Huang, C. J.; Lin, C. E.; Huang, C. L., Fuzzy approach for generator maintenance scheduling, Electric Power Systems Res., 31-38 (1992)
[28] Hussein, M. L.; Abo-Sinna, M. A., Decomposition of multiobjective programming problems by hybrid fuzzy dynamic programming, Fuzzy Sets and Systems, 60, 25-32 (1993) · Zbl 0791.90070
[29] Kacprzyk, J., Control of a nonfuzzy system in a fuzzy environment with fuzzy termination time, Systems Sci., 3, 325-341 (1977)
[30] Kacprzyk, J., A branch-and-bound algorithm for the multistage control of a nonfuzzy system in a fuzzy environment, Control Cybern., 7, 51-64 (1878) · Zbl 0376.90095
[31] Kacprzyk, J., Control of a stochastic system in a fuzzy environment with fuzzy termination time, Systems Sci., 4, 291-300 (1978) · Zbl 0421.93084
[32] Kacprzyk, J., Decision making in a fuzzy environment with fuzzy termination time, Fuzzy Sets and Systems, 1, 169-179 (1978) · Zbl 0403.93004
[33] Kacprzyk, J., A branch-and-bound algorithm for the multistage control of a fuzzy system in a fuzzy environment, Kybernetes, 8, 139-147 (1979) · Zbl 0401.49026
[34] Kacprzyk, J., Multistage decision-making problems in a fuzzy environment: a survey, (Gupta, M. M.; Sanchez, E., Fuzzy Information and Decision Processes (1982), North-Holland: North-Holland Amsterdam), 251-254
[35] Kacprzyk, J., A generalization of fuzzy multistage decision making and control via linguistic quantifiers, Int. J. Control, 38, 1249-1270 (1983) · Zbl 0544.93004
[36] Kacprzyk, J., Multistage Decision-Making under Fuzziness (1983), Verlag TÜV Rheinland: Verlag TÜV Rheinland Cologne · Zbl 0507.90023
[37] Kacprzyk, J., Yager’s probability of a fuzzy event in stochastic control under fuzziness, (Sanchez, E.; Gupta, M. M., Proc. IFAC Symp. on Fuzzy Inf. Proc., Knowledge Represent. and Dec. Anal.. Proc. IFAC Symp. on Fuzzy Inf. Proc., Knowledge Represent. and Dec. Anal., Marseille, France (1983), Pergamon Press: Pergamon Press Oxford), 379-384 · Zbl 0562.93082
[38] Kacprzyk, J., Fuzzy linguistic quantifiers in decision making and control, (Proc. Internat. Fuzzy Engineering Symp. IFES’91, Yokohama, Japan, Vol. 2 (1991)), 800-811
[39] Kacprzyk, J., Fuzzy optimal control revisited: toward a new generation of fuzzy control?, (Proc. Second Int. Conf. on Fuzzy Logic and Neural Networks IIZUKA’92, Iizuka, Japan, Vol. 1 (1992)), 429-432
[40] Kacprzyk, J., Fuzzy logic with linguistic quantifiers in decision making and control, Archives of Control Sciences, 1, XXXVII, 127-141 (1992) · Zbl 0760.03006
[41] Kacprzyk, J., Fuzzy control with an explicit performance function using dynamic programming and interpolative reasoning, (Proc. of EUFIT ’93 — First European Congress on Fuzzy and Intelligent Technologies, Aachen, Germany, Vol. 3 (1993)), 1459-1463
[42] Kacprzyk, J., A prescriptive approach to fuzzy control: a step toward a ‘more mature’ fuzzy control?, (Proc. 1st Asian Fuzzy Systems Symposium. Proc. 1st Asian Fuzzy Systems Symposium, Singapore (1993)), 360-365
[43] Kacprzyk, J., In search for a new generation of fuzzy control: can a prescriptive approach based on interpolative reasoning and neural networks help?, (Proc. ANZIIS ’93 — Australian and New Zealand Conf. on Intelligent Information Systems. Proc. ANZIIS ’93 — Australian and New Zealand Conf. on Intelligent Information Systems, Perth, Australia (1993)), 402-406
[44] Kacprzyk, J., Interpolative reasoning for computationally efficient optimal fuzzy control, (Proc. 5th Internat. IFSA World Congress, Seoul, Korea, Vol. II (1993)), 1270-1273
[45] Kacprzyk, J., Fuzzy dynamic programming — basic issues, (Delgado, M.; Kacprzyk, J.; Verdegay, J.-L.; Vila, M. A., Fuzzy Optimization: Recent Advances (1994), Physica: Physica Heidelberg), 321-331 · Zbl 0826.90127
[46] Kacprzyk, J.; Iwanski, C., A generalization of discounted multistage decision making and control via fuzzy linguistic quantifiers, Int. J. Control, 45, 1909-1930 (1987) · Zbl 0628.90039
[47] Kacprzyk, J.; Safteruk, K.; Staniewski, P., On the control of stochastic systems in a fuzzy environment over infinite horizon, Systems Sci., 7, 121-131 (1981)
[48] Kacprzyk, J.; Staniewski, P., A new approach to the control of stochastic systems in a fuzzy environment, Archiwum Automatyki i Telemechaniki, XXV, 443-444 (1980) · Zbl 0468.93061
[49] Kacprzyk, J.; Staniewski, P., Long-term inventory policy-making through fuzzy decision-making models, Fuzzy Sets and Systems, 8, 117-132 (1982) · Zbl 0491.90030
[50] Kacprzyk, J.; Staniewski, P., Control of a deterministic system in a fuzzy environment over infinite horizon, Fuzzy Sets and Systems, 10, 291-298 (1983) · Zbl 0527.90100
[51] Kacprzyk, J.; Straszak, A., Optimal policies for ‘stable’ integrated regional development through fuzzy decision making models, (Wang, P. P.; Chang, S. K., Fuzzy Set Theory and Applications (1980), Plenum: Plenum New York), 321-328
[52] Kacprzyk, J.; Straszak, A., A fuzzy approach to the ‘stability’ of integrated regional development, (Lasker, G. E., Applied Systems and Cybernetics, Vol. 5 (1982), Pergamon Press: Pergamon Press New York), 2997-3004
[53] Kacprzyk, J.; Straszak, A., Determination of ‘stable’ regional development trajectories via fuzzy decision-making models, (Yager, R. R., Recent Advances in Fuzzy Sets and Possibility Theory (1982), Pergamon Press: Pergamon Press New York), 333-344
[54] Kaeprzyk, J.; Straszak, A., Determination of “stable” integrated regional development strategies via fuzzy decision making models, IEEE Trans. Systems Man and Cybern., SMC-14, 310-313 (1984)
[55] Klein, C. M., Fuzzy shortest paths, Fuzzy Sets and Systems, 39, 27-41 (1991) · Zbl 0728.90090
[56] Klein, C. M., A model for the transportation of hazardous waste, Dec. Sci., 22, 1091-1108 (1991)
[57] Komolov, S. V.; Makeev, S. P.; Serov, G. P.; Shakhnov, J. F., On the problem of optimal control of a finite automaton with fuzzy constraints and goals, Kybernetika, 6, 30-34 (1979), (Kiev) · Zbl 0466.68049
[58] Kraslawski, A.; Gorak, A.; Vogelpohl, A., Fuzzy dynamic programming in the synthesis of distillation column systems, Comput. Chem. Eng., 13, 611-618 (1989)
[59] Lew, A., Richard Bellman’s contributions to computer science, J. Math. Anal. Appls., 119, 90-96 (1986) · Zbl 0602.01014
[60] Morin, T. L., Computational advances in dynamic programming, (Puterman, M. L., Dynamic Programming and Its Applications (1978), Academic Press: Academic Press New York), 53-90
[61] Morin, T. L.; Esogbue, A. O., Some efficient dynamic programming algorithms for the optimal sequencing and scheduling of water supply projects, (Water Resources Res., 7 (1971)), 479-484
[62] Morin, T. L.; Esogbue, A. O., Imbedded state approach to reduction of dimensionality in dynamic programming, J. Math. Anal. Appl., 48, 801-810 (1974) · Zbl 0321.49023
[63] Narshima Sastry, V.; Tiwari, R. N.; Sastry, K. S., Dynamic programming approach to multiple objective control problems having deterministic or fuzzy goals, Fuzzy Sets and Systems, 2, 195-202 (1993) · Zbl 0809.90132
[64] Robinson, T., A fuzzy dynamic programming algorithm for incremental network design, (Proc. ORSA/TIMS Conf.. Proc. ORSA/TIMS Conf., Anaheim, USA (1991))
[65] Stein, W. E., Optimal stopping in a fuzzy environment, Fuzzy Sets and Systems, 3, 252-259 (1980) · Zbl 0435.90105
[66] Su, C. C.; Hsu, Y. Y., Fuzzy dynamic programming: an application to unit commitment, IEEE Trans. Power Systems, 6, 1231-1237 (1991)
[67] Yager, R. R., A note on probabilities of fuzzy events, Inf. Science, 34, 143-161 (1979) · Zbl 0438.60006
[68] Yuan, Y.; Wu, Z., Algorithm of fuzzy dynamic programming in AGV scheduling, (Proc. Internat. Conf. on Computer Integrated Manufacturing, ICCIM ’91 (1991)), 405-408
[69] Zadeh, L. A., Probability measures of fuzzy events, J. Math. Anal. Appls., 23, 421-427 (1968) · Zbl 0174.49002
[70] Zadeh, L. A., A computational approach to fuzzy quantifiers in natural languages, Comput. Math. Appl., 9, 149-184 (1983) · Zbl 0517.94028
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