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Abstract:
In Fuzzy Bayes decision making rule, we consider two distributions of subjectivity distribution which expresses human subjectivity and membership function which converts and maps state of nature into fuzzy event by membership function. The membership function is a kind of filter function that is set by each decision maker and transforms and maps the natural state into fuzzy events with membership functions. As this filter function is set by the subjectivity of each decision maker, consequently giving a certain degree of freedom to fuzzy events. With Zadeh, a fuzzy set was proposed, and Tanaka et al extended it to a decision-making problem. This extension is called fuzzy Bayes decision making rule, but it was shown by Hori that it is included in the subjective modification of the Wald function. This indicates that fuzzy . Bayes decision making rule is included in subjective Bayes theory. However, Hori has mentioned that Type 2 fuzzy is unique in fuzzy-Bayes decision making law. In addition, Markov decision process in the fuzzy event after the mapped and transformed the state of nature by the decision-making membership function, subjectivity after mapping the state of nature by subjective distribution and utility function Markov decision process in utility was derived. In this paper, the subjective view is a subjective distribution of the state of nature, after conversion and mapping, and utility regards the state of nature as a utility function after conversion and mapping, and map technique in the expansion principle of The mapping We formulates the stochastic differential equations based on. Furthermore, as a mapping of the mapping, fuzzy theory formalizes the stochastic differential equations based on the subjective distribution and the utility function in the fuzzy event as type 3 fuzzy. Here, it is considered that solutions of these stochastic differential equations follow Ito's integral. As a future subject, I would like to study the effectiveness and validity of fuzzy theory by actually guiding the difference in optimal behavior when not introducing fuzzy logic theory from Ito integral and Max product law. In particular, by this formulation, when the membership function is an identity function, the probability differential equations are equal when introducing fuzzy logic and not introducing it. This proves that fuzzy logic is one type of subjective Bayes theory when the decision maker is a dangerous neutral person
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