Involving objective and subjective aspects in multistage decision making and control under fuzziness: Dynamic programming and neural networks

We extend the basic Bellman and Zadeh's [Manage. Sci., 17, 141–164 (1970)] model of multistage decision making (control) in a fuzzy environment to include both objective and subjective evaluations of how well fuzzy constraints on decisions (controls) applied and fuzzy goals on states (outputs) attained are satisfied. We discuss the solution by an extended fuzzy dynamic programming model. We present Francelin and Gomide's [Proc. of Second IEEE International Conference on Fuzzy Systems—FUZZ‐IEEE'93, San Francisco, CA, Vol. 1, 1993, pp. 655–660] [cf. also Francelin, Gomide, and Kacprzyk [Proc. of Sixth IFSA World Congress, Saõ Paolo, Brazil, Vol. II, 1995, pp. 221–224] and Kacprzyk, Romero, and Gomide [Neuro‐Fuzzy Techniques for Information Processing, Physica‐Verlag (Springer‐Verlag), Heidelberg–New York, forthcoming]] neural network implementing fuzzy dynamic programming, and then show its extension to cover both the objective and subjective evaluations involved in the proposed extension of the basic Bellman and Zadeh's [Manage. Sci., 17, 141–164 (1970)] model. We show its use for solving a socioeconomic regional planning problem proposed in Kacprzyk and Straszak [Applied Systems and Cybernetics, Pergamon, New York, 1982, Vol. 6, pp. 2997–3004; Recent Developments in Fuzzy Sets and Possibility Theory, Pergamon, New York, 1982, pp. 531–541; IEEE Trans. Syst. Man, Cybern., SMC‐14, 310–313 (1984)] [cf. Kacprzyk's [Multistage Fuzzy Control, Wiley, Chichester, 1997] book], extending Kacprzyk, Romero, and Gomide [Neuro‐Fuzzy Techniques for Information Processing, Physica‐Verlag (Springer‐Verlag), Heidelberg–New York, forthcoming]. ©1999 John Wiley & Sons, Inc.