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Fuzzy Dynamic Programming: A New Quality Through Fuzzy Sets

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Fuzzy Set Theory and Advanced Mathematical Applications

Part of the book series: International Series in Intelligent Technologies ((ISIT,volume 4))

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Abstract

We briefly show how fuzzy sets theory has provided dynamic programming, one of the most powerful tools of applied mathematics, with new qualities and prospects, by making it possible to more adequately formulate inherently “soft” real world problems.

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References

  • Baldwin J. F. and B. W. Pilsworth (1982) “Dynamic programming for fuzzy systems with fuzzy environment,” J. Math. Anal. and Appls. 85, 1–23.

    Article  MathSciNet  MATH  Google Scholar 

  • Bellman R. E. and L. A. Zadeh(1970) “Decision-making in a fuzzy environment,” Management Sct 17, B141–B164.

    MathSciNet  MATH  Google Scholar 

  • Chang S.S. L. (1969) “Fuzzy dynamic programming and the decision making process,” Proc. 3rd Princeton Conf. on Inf. Sci and Syst. (Princeton, USA), 200–203.

    Google Scholar 

  • Esogbue A. O. (1983a) “Dynamic programming, fuzzy sets, and the modeling of R&D management control systems,” IEEE Trans. on Syst., Man and Cybern. SMC-13,18–30.

    Article  MathSciNet  Google Scholar 

  • Esogbue A. O. (1983b) “Some novel applications of fuzzy dynamic programming,” Proc. IEEE, 501–505.

    Google Scholar 

  • Esogbue A. O. (1985) “A fuzzy dynamic programming model of intra-opera-tive anesthesia administration.” In J. Kacprzyk and R. R. Yager(Eds.), Management Decision—Support Systems Using Fuzzy Sets and Possibility Theory, Verlag TUV Rheinland, Cologne, 155–161.

    Google Scholar 

  • Esogbue A. O. (1986) “Optimal clustering of fuzzy data via fuzzy dynamic programming,” Fuzzy Sets and Systems 18, 283–298.

    Article  MathSciNet  MATH  Google Scholar 

  • Esogbue A. O. and R. E. Bellman(1981) “A fuzzy dynamic programming algorithm for clustering non-quantitative data arising in water pollution control planning,” Proc. 3rd International Conference on Mathematical Modeling (Los Angeles, USA).

    Google Scholar 

  • Esogbue A. O. and R. E. Bellman(1984) “Fuzzy dynamic programming and its extensions.” In H.-J. Zimmermann, L. A.Zadeh and B.R. Gaines (Eds.), Fuzzy Sets and Decision Analysis, Elsevier, Amsterdam, 147–167.

    Google Scholar 

  • Esogbue A. O., M. Fedrizzi and J. Kacprzyk (1988) “Fuzzy dynamic programming with stochastic systems.” In J. Kacprzyk and M. Fedrizzi (Eds.), Combining Fuzzy Imprecision with Probabilistic Uncertainty in Decision Making, Springer-Verlag, Berlin / New York / Tokyo, 266–287.

    Chapter  Google Scholar 

  • Esogbue A. O. and V. Ramesh (1970) “Dynamic programming and fuzzy allocation processes,” Memo No. 202, Dept. of Op. Res., Case Western Reserve University, Cleveland (USA).

    Google Scholar 

  • Esogbue A. O., M. Theologidu and K. Guo (1992) “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.

    Article  Google Scholar 

  • Fung L. W. and K. S. Fu(1977) “Characterization of a class of fuzzy optimal control problems.” In M. M. Gupta, G. N. Saridis and B. R. Games (Eds.), Fuzzy Automata and Decision Processes, North-Holland, Amsterdam, 205–220.

    Google Scholar 

  • Hojo T., T. Teranoand S. Masui (1993) “Design of quasi-optimal fuzzy controller by fuzzy dynamic programming,” Proc. of IEEE International Conference on Fuzzy Systems, vol. 2,1253–1258.

    Google Scholar 

  • Howard R. A. (1960) Dynamic Programming and Markov Processes, MIT Press, Cambridge (USA).

    Google Scholar 

  • Huang C. J., C. E. Linand C. L Huang (1992) “Fuzzy approach for generator maintenance scheduling,” Electric Power Systems Research, 31–38.

    Google Scholar 

  • Kacprzyk J. (1977) “Control of a nonfuzzy system in a fuzzy environment with fuzzy termination time,” Systems Sci 3, 325–341.

    MathSciNet  Google Scholar 

  • Kacprzyk J. (1878a) “A branch-and-bound algorithmfor the multistage control of a nonfuzzy system in a fuzzy environment,” Control and Cybern. 7, 51–64.

    Google Scholar 

  • Kacprzyk J. (1978b) “Control of a stochastic system in a fuzzy environment with fuzzy termination time,” Systems Sci 4, 291–300.

    MathSciNet  MATH  Google Scholar 

  • Kacprzyk J. (1978c) “Decision making in a fuzzy environment with fuzzy termination time,” Fuzzy Sets and Syst. 1,169–179.

    Article  MathSciNet  MATH  Google Scholar 

  • Kacprzyk J. (1979) “A branch-and-bound algorithm for the multistage control of a fuzzy system in a fuzzy environment,” Kybernetes 8,139–147.

    Google Scholar 

  • Kacprzyk J. (1983a) “A generalization of fuzzy multistage decision making and control via linguistic quantifiers,” Int. J. of Control 38,1249–1270.

    Article  MathSciNet  MATH  Google Scholar 

  • Kacprzyk J. (1983b) Multistage Decision-Making under Fuzziness, Verlag TUV Rheinland, Cologne.

    MATH  Google Scholar 

  • Kacprzyk J. (1991) “Fuzzy linguistic quantifiers in decision making and control,” Proc. of International Fuzzy Engineering Symposium—IFES’ 91 (Yokohama, Japan), vol. 2, 800–811.

    Google Scholar 

  • Kacprzyk J. (1992a) “Fuzzy optimal control revisited: toward a new generation of fuzzy control?” Proc. of Second Int. Conference on Fuzzy Logic and Neural Networks IIZUKA’ 92 (Iizuka, Japan), vol. 1, 429–432.

    Google Scholar 

  • Kacprzyk J. (1992b) “Fuzzy logic with linguistic quantifiers in decision making and control,” Archives of Control Sciences 1 (XXXVII), 127–141.

    Google Scholar 

  • Kacprzyk J. (1993a) “Fuzzy control with an explicit performance function using dynamic programming and interpolative reasoning,” Proceedings of Eupit First European Congress on Fuzzy and Intelligent Technologies (Aachen, Germany), vol. 3,1459–1463.

    Google Scholar 

  • Kacprzyk J. (1993b) “In search for a new generation of fuzzy control: can a prescriptive approach based on interpolative reasoning and neural networks help?” Proc. of ANZIIS’ 93—Australian and New Zealand Conference on Intelligent Information Systems (Perth, Australia), 402–406.

    Google Scholar 

  • Kacprzyk J. (1993c) “Interpolative reasoning for computationally efficient optimal fuzzy control,” Proc. of Fifth Int. IFSA World Congress (Seoul, Korea), vol. II, 1270–1273.

    Google Scholar 

  • Kacprzyk J. (1993d) “A prescriptive approach to fuzzy control: a step toward a ‘more mature’ fuzzy control?,” Proc. of First Asian Fuzzy Systems Symposium (Singapore), 360–365.

    Google Scholar 

  • Kacprzyk J. (1994) “Fuzzy dynamic programming-basic issues.” In M. Del-gado, J. Kacprzyk, J.-L. Verdegay and M. A. Vila(Eds.), Fuzzy Optimization: Recent Advances, Physica-Verlag, Heidelberg (A Springer-Verlag Company), 321–331.

    Google Scholar 

  • Kacprzyk J. and C. Iwaéski(1987) “A generalization of discounted multistage decision making and control via fuzzy linguistic quantifiers,” Int. J. of Control 45,1909–1930.

    Article  MATH  Google Scholar 

  • Kacprzyk J., K. Safteruk and P. Staniewski (1981) “On the control of stochastic systems in a fuzzy environment over infinite horizon,” Systems Sci 7, 121–131.

    Google Scholar 

  • Kacprzyk J. and P. Staniewski(1980) “A new approach to the control of stochastic systems in a fuzzy environment,” Archiwum Automatyki i Tele-mechaniki XXV, 443–444.

    Google Scholar 

  • Kacprzyk J. and P. Staniewski (1982) “Long-term inventory policy making through fuzzy decision-making models,” Fuzzy Sets and Syst. 8,117–132.

    Article  MATH  Google Scholar 

  • Kacprzyk J. and P. Staniewski (1983) “Control of a deterministic system in a fuzzy environment over infinite horizon,” Fuzzy Sets and Syst. 10, 291–298.

    Article  MathSciNet  MATH  Google Scholar 

  • Kacprzyk J. and A. Straszak (1980) “Optimal policies for’ stable’ integrated regional development through fuzzy decision making models.” In P. P. Wang and S. K. Chang (Eds.), Fuzzy Set Theory and Applications. Plenum, New York, 321–328.

    Google Scholar 

  • Kacprzyk J. and A. Straszak (1984) “Determination of’ stable’ integrated regional development strategies via fuzzy decision-making models,” IEEE Trans. on Syst, Man and Cybern. SMC-14, 310–313.

    Article  Google Scholar 

  • Komolov S. V., S. P. Makeev, G. P. Serovand J. F. Shakhnov (1979) “On the problem of optimal control of a finite automaton with fuzzy constraints and goals (in Russian),” Kybernetika (Kiev) 6, 30–34.

    Google Scholar 

  • Kraslawski A., A. Gorak and A. Vogelpohl (1989) “Fuzzy dynamic programming in the synthesis of distillation column systems,” Computers and Chemical Engineering 13, 611–618.

    Article  Google Scholar 

  • Stein W. E. (1980) “Optimal stopping in a fuzzy environment,” Fuzzy Sets and Syst. 3, 252–259.

    Article  Google Scholar 

  • Su C. C. and Y. Y. Hsu(1991) “Fuzzy dynamic programming: An application to unit commitment,” IEEE Transactions on Power Systems PS-6,1231–1237.

    Google Scholar 

  • Yuan Y. and Z. Wu(1991) “Algorithm of fuzzy dynamic programming in AGV scheduling,” Proceedings of International Conference on Computer Integrated Manufacturing ICCIM 91, 405–408.

    Google Scholar 

  • Zadeh L A. (1968) “Probability measures of fuzzy events,” J. Math. Anal, and Appl. 23,421–427.

    Google Scholar 

  • Zadeh L. A. (1983) “A computational approach to fuzzy quantifiers in natural languages,” Computers and Math. with Appl. 9, 149–184.

    Article  MathSciNet  MATH  Google Scholar 

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Kacprzyk, J. (1995). Fuzzy Dynamic Programming: A New Quality Through Fuzzy Sets. In: Ruan, D. (eds) Fuzzy Set Theory and Advanced Mathematical Applications. International Series in Intelligent Technologies, vol 4. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-2357-4_5

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  • DOI: https://doi.org/10.1007/978-1-4615-2357-4_5

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-6000-1

  • Online ISBN: 978-1-4615-2357-4

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