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Combining Rough Sets and Bayes' Rule
Author(s) -
Pawlak Zdzisław
Publication year - 2001
Publication title -
computational intelligence
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.353
H-Index - 52
eISSN - 1467-8640
pISSN - 0824-7935
DOI - 10.1111/0824-7935.00153
Subject(s) - rough set , bayes' theorem , bayes' rule , decision rule , mathematics , admissible decision rule , inference , bayes factor , inductive reasoning , rule of inference , conditional probability , bayesian inference , set (abstract data type) , bayesian probability , chain rule (probability) , artificial intelligence , computer science , posterior probability , influence diagram , statistics , law of total probability , decision tree , weighted sum model , programming language
In rough set theory with every decision rule two conditional probabilities, called certainty and coverage factors, are associated. These two factors are closely related with the lower and the upper approximation of a set, basic notions of rough set theory. It is shown that these two factors satisfy the Bayes' rule. The Bayes' rule in our case simply shows some relationship in the data, without referring to prior and posterior probabilities intrinsically associated with Bayesian inference. This relationship can be used to “invert” decision rules, i.e., to find reasons (explanation) for decisions thus providing inductive as well as deductive inference in our scheme.