Discrete-Time Hybrid Decision Processes: The Discounted Case

Abstract

This paper is a sequel to Kageyama et al. [1], in which a Markov-type hybrid process has been constructed and the corresponding discounted total reward has been characterized by the recursive equation. The objective of this paper is to formulate a hybrid decision process and to give the existence and characterization of optimal policies.

Share and Cite:

Yang, B. , Hou, P. and Kageyama, M. (2013) Discrete-Time Hybrid Decision Processes: The Discounted Case. Applied Mathematics, 4, 1490-1494. doi: 10.4236/am.2013.411201.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] M. Kageyama, B. Yang and P. Hou, “Discrete-Time Hybrid Processes and Discounted Total Expected Values,” Fuzzy Optimization Decision Making, Vol. 10, No. 4, 2011, pp. 341-355.
http://dx.doi.org/10.1007/s10700-011-9109-2
[2] B. Liu, “Uncertain Theory,” 2nd Edition, Springer-Verlag, Berlin, 2007.
[3] X. Li and B. Liu, “Chance Measure for Hybrid Events with Fuzziness and Randomness,” Soft Computing, Vol. 13, No. 2, 2009, pp. 105-115.
http://dx.doi.org/10.1007/s00500-008-0308-x
[4] O. Hernandez-Lerma and J. B. Lasserre, “Discrete-Time Markov Control Processes, Basic Optimality Criteria,” Springer, New York, 1996.
http://dx.doi.org/10.1007/978-1-4612-0729-0
[5] M. Puterman, “Markov Decision Processes,” John Wiley and Sons, Inc., 1994.
http://dx.doi.org/10.1002/9780470316887
[6] B. Liu, “Uncertain Theory,” 3rd Edition, UTLAB, 2009.
[7] M. Kageyama and K. Iwamura, “Discrete Time Credibilistic Processes: Construction and Convergences,” Information Sciences, Vol. 179, No. 24, 2009, pp. 42774283.
[8] J. L. Doob, “Stochastic Processes,” John Wiley, New York, 1953.
[9] R. E. Bellman, “Dynamic Programming,” Princeton University Press, Princeton, 1957.

Copyright © 2024 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.