A possibilistic analogue to Bayes estimation with fuzzy data and its application in machine learning

Abstract

A Bayesian approach in a possibilistic context, when the available data for the underlying statistical model are fuzzy, is developed. The problem of point estimation with fuzzy data is studied in the possibilistic Bayesian approach introduced. For calculating the point estimation, we introduce a method without considering a loss function, and one considering a loss function. For the point estimation with a loss function, we first define a risk function based on a possibilistic posterior distribution, and then the unknown parameter is estimated based on such a risk function. Briefly, the present work extended the previous works in two directions: First the underlying model is assumed to be probabilistic rather than possibilistic, and second is that the problem of Bayes estimation is developed based on two cases of without and with considering loss function. Then, the applicability of the proposed approach to concept learning is investigated. Particularly, a naive possibility Bayes classifier is introduced and applied to some real-world concept learning problems.