Applying Rough Sets to Information Tables Containing Probabilistic Values

Authors:
Michinori Nakata;Hiroshi Sakai
Affiliations:
Faculty of Management and Information Science, Josai International University, 1 Gumyo, Togane, Chiba, 283-8555, Japan;Department of Mathematics and Computer Aided Sciences, Faculty of Engineering, Kyushu Institute of Technology, Tobata, Kitakyushu, 804-8550, Japan
Venue:
MDAI '07 Proceedings of the 4th international conference on Modeling Decisions for Artificial Intelligence
Year:
2007

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Abstract

Rough sets are applied to information tables containing imprecise values that are expressed in a probability distribution. A family of weighted equivalence classes is obtained where each equivalence class is accompanied by the probability to which it is an actual one. By using the family of weighted equivalence classes, we derive lower and upper approximations. The lower and upper approximations coincide with ones obtained from methods of possible worlds. Therefore, the method of weighted equivalence classes is justified. In addition, this method is applied to missing values interpreted probabilistically. Using weighted equivalence classes correctly derives a lower approximation, even in the case where the method of Kryszkiewicz does not derive any lower approximation.