Affiliations: Department of Economics & Business, University of Catania, Italy and Portsmouth Business School, Operations & Systems Management, University of Portsmouth, United Kingdom. salgreco@unict.it | Institute of Computing Science, Poznan University of Technology, Poland and Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland. Roman.Slowinski@cs.put.poznan.pl | Institute of Computing Science, Poznan University of Technology, Poland. Izabela.Szczech@cs.put.poznan.pl
Note: [] Address for correspondence: Roman.Slowinski@cs.put.poznan.pl, Institute of Computing Science, Poznan University of Technology, Piotrowo 2, 60-965 Poznan, Poland
Note: [] The research has been supported by the Polish Ministry of Science and Higher Education (grant no. NN519441939).
Abstract: The paper focuses on Bayesian confirmation measures used for evaluation of rules induced from data. To distinguish between many confirmation measures, their properties are analyzed. The article considers a group of symmetry properties. We demonstrate that the symmetry properties proposed in the literature focus on extreme cases corresponding to entailment or refutation of the rule's conclusion by its premise, forgetting intermediate cases. We conduct a thorough analysis of the symmetries regarding that the confirmation should express how much more probable the rule's hypothesis is when the premise is present rather than when the negation of the premise is present. As a result we point out which symmetries are desired for Bayesian confirmation measures. Next, we analyze a set of popular confirmation measures with respect to the symmetry properties and other valuable properties, being monotonicity M, Ex1 and weak Ex1, logicality L and weak L. Our work points out two measures to be the most meaningful ones regarding the considered properties.
