International Journal of Business and Marketing Management
Volume 4 Issue 1 Page 1 - 4. December 2016

Copyright 2015 Discourse Journals

Application of fuzzy-Bayes decision rule to the optical illusion state discrimination problem

1Houju Hori Jr., and Yukio Matsumoto2

1Nara Community, Tsubakikishi Shine
2Institute of Mathematical Statistics



We perform multi-dimensionalization of the mathematical model for the fuzzy-Bayes decision rule constructed by Hori and Tsubaki, and investigate its application to the optical illusion state discrimination problem. We first consider two mutually exclusive states of nature as true and false states, incorporating the concept of 0-1 loss as a fuzzy mode of statistical discriminate analysis, and apply the principle of fuzzy expected utility maximization to perform optical illusion state discrimination. We then propose the addition of new functions for transformation of the true state and the false state to the subjective prior distribution and the membership function, compute the fuzzy event probabilities, and select the state exhibiting high probability. It is also noted that these functions, unlike utility functions and loss functions, are not inverse functions and can be applied even if both are zero (indicating a visual hallucination state)

Keywords: Fuzzy-Bayes decision, optical illusion state, visual hallucination state, true state, false state


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