Abstract
We formulate a fuzzy perceptive model for Markov decision processes with discounted payoff in which the perception for transition probabilities is described by fuzzy sets. Our aim is to evaluate the optimal expected reward, which is called a fuzzy perceptive value, based on the perceptive analysis. It is characterized and calculated by a certain fuzzy relation. A machine maintenance problem is discussed as a numerical example.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Blackwell, D.: Discrete dynamic programming. Ann. Math. Statist. 33, 719–726 (1962)
Derman, C.: Finite State Markovian Decision Processes. Academic Press, New York (1970)
Dubois, D., Prade, H.: Fuzzy Sets and Systems: Theory and Applications. Academic Press, London (1980)
Howard, R.: Dynamic Programming and Markov Process. MIT Press, Cambrige (1960)
Kurano, M., Song, J., Hosaka, M., Huang, Y.: Controlled Markov set-chains with discounting. J. Appl. Prob. 35, 293–302 (1998)
Kurano, M., Yasuda, M., Nakagami, J., Yoshida, Y.: Ordering of fuzzy sets – A brief survey and new results. J. Operations Research Society of Japan 43, 138–148 (2000)
Kurano, M., Yasuda, M., Nakagami, J., Yoshida, Y.: A fuzzy treatment of uncertain Markov decision process. RIMS Koukyuroku 1132, 221–229 (2000)
Kurano, M., Yasuda, M., Nakagami, J., Yoshida, Y.: A fuzzy stopping problem with the concept of perception. Fuzzy Optimization and Decision Making 3, 367–374 (2004)
Mine, H., Osaki, S.: Markov Decision Process. Elsevier, Amsterdam (1970)
Puterman, M.L.: Markov Decision Process: Discrete Stochastic Dynamic Programming. John Wiley & Sons, Chichester (1994)
Solan, E.: Continuity of the value of competitive Markov decision processes. J. Theoretical Probability 16, 831–845 (2004)
Yoshida, Y., Kerre, E.E.: A fuzzy ordering on multi-dimensional fuzzy sets induced from convex cones. Fuzzy Sets and Systems 130, 343–355 (2002)
Zadeh, L.A.: Fuzzy sets. Inform. and Control 8, 338–353 (1965)
Zadeh, L.A.: Toward a perception-based theory of probabilistic reasoning with imprecise probabilities. J. of Statistical Planning and Inference 105, 233–264 (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kurano, M., Yasuda, M., Nakagami, Ji., Yoshida, Y. (2005). Perceptive Evaluation for the Optimal Discounted Reward in Markov Decision Processes. In: Torra, V., Narukawa, Y., Miyamoto, S. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2005. Lecture Notes in Computer Science(), vol 3558. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11526018_28
Download citation
DOI: https://doi.org/10.1007/11526018_28
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-27871-9
Online ISBN: 978-3-540-31883-5
eBook Packages: Computer ScienceComputer Science (R0)