Markov Decision Process in no-data Problem based on Probabilitic Differental Equation in Fuzzy Events

摘要

Tanaka et al formulated the fuzzy-Bayes decision making rule by integral transformation based on the expected utility maximization theory as an extension to Wald's subjective modification fuzzy event. Hoń et al formulated the fiizzy Bayes decision making rule which extended Wald's decision function to fuzzy OR combination and fuzzy AND combination with many subjective distribution. This decision-making law is based on the state of nature Is a decision-making rule after mapping and conversion to fuzzy events, and it is an OR type 2 fiizzy by mapping fuzzy functions such as subjective distribution and utility functions to fuzzy events. Furthermore, Hoń introduced the Markovian time concept to the state of nature, and derived the Markov process and Markov decision process in fuzzy events. This is a natural extension to the stochastic process theory of Wald's decision function, and the fuzzy event of appearance of the natural state becomes a Markov process having a fiizzy transition matrix, and as a result of the Monte Carlo simulation, the annihilation, reversal, resurrection Repeat the cycle. Finally, Hori et al proposed an illusion state identification method as an example of adaptation of these fuzzy / Bayes decision making rnles. In addition. Hori et al. Firstly used the max product method by mapping / transformation of membership functions of fuzzy events in a fiizzy event in which the subjective distribution and utility function in the no data problem transit like ergodic Markov We formulated these Markov decision processes. Note that this series of flows is a natural extension to the stochastic process of Wald's decision function. Next, we consider subjective distribution and utility function as fuzzy functions, subjectivity maps / converis natural state by subjective distribution, utility assumes that natural state is mapped / converted by utility function. The subjectivity and the utility also showed that it follows Markov process. Finally, the subjectivity and utility in fuzzy events were propagated by Markov processes in which each element of the transition matrix follows the Markov process, and proposed the Markov decision process by the Max product method