Paper:

# Mutually Dependent Markov Decision Processes

## Toshiharu Fujita^{*} and Akifumi Kira^{**}

^{*}Graduate School of Engineering, Kyushu Institute of Technology, 1-1 Sensui-cho, Tobata, Kitakyushu 804-8550, Japan

^{**}Graduate School of Economics and Management, Tohoku University, 27-1 Kawauchi, Aoba-ku, Sendai 980-8576, Japan

*J. Adv. Comput. Intell. Intell. Inform.*, Vol.18 No.6, pp. 992-998, 2014.

- [1] R.E. Bellman, “Dynamic Programming,” Princeton Univ. Press, NJ, 1957.
- [2] R. A. Howard, “Dynamic Programming and Markov Processes,” MITPress, Cambridge, Mass., 1960.
- [3] G. L. Nemhauser, “Introduction to Dynamic Programming,” Wiley, NY, 1966.
- [4] D.P. Bertsekas, “Dynamic Programming and Stochastic Control,” Academic Press, NY, 1976.
- [5] D.J. White, “Dynamic Programming,” Holden-Day, San Francisco, Calif., 1969.
- [6] M. L. Puterman, “Markov Decision Processes : discrete stochastic dynamic programming,” Wiley & Sons, NY, 1994.
- [7] M. Sniedovich, “Dynamic Programming,” Marcel Dekker, Inc. NY, 1992.
- [8] S. Iwamoto and T. Fujita, “Stochastic decision-making in a fuzzy environment,” J. of Operations Research Society of Japan, Vol.38, pp. 467-482, 1995.
- [9] S. Iwamoto, T. Ueno and T. Fujita, “Controlled Markov Chains with Utility Functions,” Eds. H. Zhenting, J. A. Filar and A. Chen, Markov Processes and Controlled Markov Chains, Chap.8, pp. 135-148, Kluwer, 2002.
- [10] T. Fujita, “An optimal path problem with fuzzy expectation,” Proc. of the 8th Bellman Continuum, pp. 191-195, 2000.
- [11] T. Fujita, “An optimal path problem with threshold probability,” Frontiers in Artificial Intelligence and Applications, Vol.69, pp. 792-796, 2001.
- [12] T. Fujita, “On nondeterministic dynamic programming,” Mathematical Analysis in Economics (Kyoto, 2005), RIMS
*Kôkyûroku*No.1488, pp. 15-24, 2006. - [13] T. Fujita, “Infinite stage nondeterministic stopped decision processes and maximum linear equation,” Bulletin of the Kyushu Institute of Technology, Vol.55, pp. 15-24, 2008.
- [14] T. Fujita, “Deterministic decision process under range constraint through all stages,” Proc. of Modeling Decisions for Artificial Intelligence 2008 (CD-ROM), pp. 60-70, 2008.
- [15] T. Fujita, and K. Tsurusaki, “Stochastic optimization of multiplicative functions with negative value,” J. of Operations Research Society of Japan, Vol.41, No.3, pp. 351-373, 1998.
- [16] A. Kira, T. Ueno and T. Fujita “Threshold probability of nonterminal type in finite horizon Markov decision processes,” J. of Mathematical Analysis and Applications, Vol.386, pp. 461-472, 2012.
- [17] T. Fujita, “Re-examination of Markov policies for additive decision process,” Bulletin of Informatics Cybernetics, Vol.29, No.1, pp. 51-65, 1997.
- [18] T. Fujita, “On policy classes in dynamic programming theory,” Proc. of the 9th Bellman Continuum Int. Workshop on Uncertain System and Soft Computing, Series of Information & Management Sciences Vol.2, pp. 39-43, 2002.
- [19] U. Bertelé and F. Brioschi, “Nonserial Dynamic Programming,” Academic Press, NY, 1972.

This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.