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Three-way Bayesian Confirmation in Classifications

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Abstract

Bayesian confirmation provides a practical approach to reasoning about the truth of hypotheses based on the observation of evidence. It has been applied in many topics closely related to cognitive computing, such as decision makings and problem solving, especially those involving learning and reasoning based on the descriptions of objects. This paper investigates the application of Bayesian confirmation into classification which is a basis in many cognitive computing topics. Bayesian confirmation measures are adopted to evaluate the degree to which a description of objects (i.e., a piece of evidence) confirms the belongingness of the objects to a given class (i.e., a hypothesis). Accordingly, a description space is divided into three regions of confirmatory, disconfirmatory, and neutral descriptions, formulating a three-way Bayesian confirmation model. Based on a sequence of description spaces induced by either attributes or attribute–value pairs, the neutral regions can be further refined, which leads to a sequential model. Furthermore, with a discussion on constructing meaningful trisections of attributes or attribute–value pairs according to their utility, we present a three-level three-way Bayesian confirmation framework where each level focuses on one set in a trisection. Due to their different utility levels, the three sets in a trisection are used in different appropriate ways in constructing the three levels. Bayesian confirmation provides a meaningful perspective of evaluating descriptions in the context of classifications. This work may bring new insights into research on related topics such as decision makings, three-level analysis, rough set theory, and concept analysis.

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Acknowledgements

The author thanks the reviewers and the editor for their valuable comments and constructive suggestions.

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  1. Department of Computer Science, University of Regina, Regina, Saskatchewan, S4S 0A2, Canada

    Mengjun Hu

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Hu, M. Three-way Bayesian Confirmation in Classifications. Cogn Comput 14, 2020–2039 (2022). https://doi.org/10.1007/s12559-021-09924-8

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