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Multistage Fuzzy Control with a Soft Aggregation of Stage Scores

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Aggregation and Fusion of Imperfect Information

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 12))

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Abstract

We discuss multistage fuzzy control in Bellman and Zadeh’s (1970) setting. Instead of the traditional basic formulation which is to find an optimal sequence of controls best satisfying fuzzy constraints and fuzzy goals at all the control stages, we assune a softer requirement that the stage scores (degrees to which the fuzzy constraints and fuzzy goals at a particular control stage are fulfilled) be best satisfied at most, almost all, much more than a half, etc. control stages. Zadeh’s (1983) fuzzy-logic-based calculus of linguistically quantified statements is employed, and the resulting problem is solved by dynamic programming.

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Bibliography

  • Bellman R.E. and L.A. Zadeh (1970) Decision making in a fuzzy environment. Management Science 17: 141–164.

    Article  MathSciNet  Google Scholar 

  • Chang S.S.L. (1969a) Fuzzy dynamic programming and the decision making process. Proceedings of the Third Princeton Conference on Information Sciences ( Princeton, NJ, USA).

    Google Scholar 

  • Chang S.S.L. (1969b) Fuzzy dynamic programming and approximate optimization of partially known systems. Proceedings of the Second Hawaii International Conference on Systems Science ( Honolulu, HI, USA).

    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, pp. 266–285.

    Chapter  Google Scholar 

  • Kacprzyk J. (1977) Control of a nonfuzzy system in a fuzzy environment with a fuzzy termination time. Systems Science 3: 320–334.

    MathSciNet  Google Scholar 

  • Kacprzyk J. (1978) A branch-and-bound algorithm for the multistage control of a nonfuzzy system in a fuzzy environment. Control and Cybernetics 7: 51–64.

    MathSciNet  MATH  Google Scholar 

  • Kacprzyk J. (1978) Decision-making in a fuzzy environment with fuzzy termination time. Fuzzy Sets and Systems 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.

    Article  MATH  Google Scholar 

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

    MATH  Google Scholar 

  • Kacprzyk J. (1983b) A generalization of fuzzy multistage decision making and control via linguistic quantifiers. International Journal of Control 38: 1249–1270.

    Article  MathSciNet  MATH  Google Scholar 

  • Kacprzyk J. (1986) Towards ‘human-consistent’ multistage decision making and control models via fuzzy sets and fuzzy logic. Gellman Memorial Issue (A.O. Esogbue, Ed.), Fuzzy Sets and Systems 18: 299–314.

    Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  • Kacprzyk J. (1997) Multistage Fuzzy Control. Wiley, Chichester.

    MATH  Google Scholar 

  • Kacprzyk J. and A.O. Esogbue (1996) Fuzzy dynamic programming: main developments and applications. Fuzzy Sets and Systems 81: 31–46.

    Article  MathSciNet  MATH  Google Scholar 

  • Kacprzyk J. and C. Iwanski (1987) A generalization of discounted multistage decision making and control through fuzzy linguistic quantifiers: an attempt to introduce commonsense knowledge. International Journal of Control 45: 1909–1930.

    Article  MathSciNet  MATH  Google Scholar 

  • Kacprzyk J. and R.R. Yager (1984a) Linguistic quantifiers and belief qualification in fuzzy multicriteria and multistage decision making. Control and Cybernetics 13: 155–173.

    MathSciNet  MATH  Google Scholar 

  • Kacprzyk J. and R.R Yager (1984b) “Softer” optimization and control models via fuzzy linguistic quantifiers. Information Sciences 34: 157–178.

    Google Scholar 

  • Ralescu D.A. (1995) Cardinality, quantifiers, and the aggregation of fuzzy criteria. Fuzzy Sets and Systems 69: 355–365.

    Article  MathSciNet  MATH  Google Scholar 

  • Yager R.R. (1983) Quantifiers in the formulation of multiple objective decision functions. Information Sciences 31: 107–139.

    Article  MathSciNet  MATH  Google Scholar 

  • Yager R.R. (1988) On ordered weighted averaging aggregation operators in multi-criteria decision making. IEEE Transactions on Systems, Man and Cybernetics SMC-18: 183–190.

    Google Scholar 

  • Yager R.R. and J. Kacprzyk, Eds. (1997) The Ordered Weighted Averaging Operators. Kluwer, Boston.

    MATH  Google Scholar 

  • Zadeh L.A. (1983) A computational approach to fuzzy quantifiers in natural languages. Computers and Mathematics with Applications 9: 149–184.

    Article  MathSciNet  MATH  Google Scholar 

  • Zadeh L.A. and J. Kacprzyk, Eds. (1992) Fuzzy Logic for the Management of Uncertainty, Wiley, New York.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01-447, Warsaw, Poland

    Janusz Kacprzyk

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  1. Janusz Kacprzyk
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Editors and Affiliations

  1. Centre National de la Recherche Scientifique, LIP6 — Laboratoire d’Informatique de Paris 6, Université Pierre et Marie Curie, 4, Place Jussieu, Case 169, F-75252, Paris Cedex 05, France

    Bernadette Bouchon-Meunier

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© 1998 Springer-Verlag Berlin Heidelberg

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Kacprzyk, J. (1998). Multistage Fuzzy Control with a Soft Aggregation of Stage Scores. In: Bouchon-Meunier, B. (eds) Aggregation and Fusion of Imperfect Information. Studies in Fuzziness and Soft Computing, vol 12. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1889-5_8

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  • DOI: https://doi.org/10.1007/978-3-7908-1889-5_8

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-662-11073-7

  • Online ISBN: 978-3-7908-1889-5

  • eBook Packages: Springer Book Archive

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