International Journal of Business and Marketing Management
Volume 5 Issue 2 Page 5 - 8. May 2017

Copyright 2017 Discourse Journals


Markov decision process in fuzzy events based on the mapping extension principle

Houju Hori Jr1., Kazuhisa Takemura2 and Yukio Matsumoto3

1 Chief in Nara Community, Tsubakikishi Shrine
2 Department of Psychology, Waseda University

3 Visiting Research Fellow, The Institute of Mathematical Statistics


Abstract

It has been shown by Hori and Matsumoto that if a state of nature constitutes an ergodic Markov process, then the fuzzy events manifested by that state of nature also follow a Markov process. Here, we first perform mapping and transformation in accordance with their membership function of the subjective distribution and the utility function that occur in the no-data problem in fuzzy events with Markov transition in order to formulate their Markov decision processes using the max-product method. We note that this series flow is a natural extension of the Wald decision function to a stochastic process. Next, taking the subjective distribution and the utility function as fuzzy functions and assuming that the state of nature is mapped and transformed to subjectivity by the subjective distribution and to utility by the utility function, we show that the subjectivity and the utility also follow Markov processes. We conclude by proposing a Markov decision process in which the subjectivity and the utility in fuzzy events transition according to Markov processes and are elements that constitute the transition matrices that define the Markov processes, and the max-product method is applied.

Keywords: fuzzy events, subjective distribution, utility function, extension principle, Markov process, Markov decision process

 

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