To make conventional Bayesian optimal classifier possess the abilities of disposing fuzzy information and realizing the automation of reasoning process, a new Bayesian optimal classifier is proposed with fuzzy information embedded. It can not only dispose fuzzy information effectively, but also retain learning properties of Bayesian optimal classifier. In addition, according to the evolution of fuzzy set theory, vague set is also imbedded into it to generate vague Bayesian optimal classifier. It can simultaneously simulate the twofold characteristics of fuzzy information from the positive and reverse directions. Further, a set pair Bayesian optimal classifier is also proposed considering the threefold characteristics of fuzzy information from the positive, reverse, and indeterminate sides. In the end, a knowledge-based artificial neural network (KBANN) is presented to realize automatic reasoning of Bayesian optimal classifier. It not only reduces the computational cost of Bayesian optimal classifier but also improves its classification learning quality.
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