Lower and upper approximations in data tables containing possibilistic information

Authors:
Michinori Nakata;Hiroshi Sakai
Affiliations:
Faculty of Management and Information Science, Josai International University, Togane, Chiba, Japan;Department of Mathematics and Computer Aided Sciences, Faculty of Engineering, Kyushu Institute of Technology, Tobata, Kitakyushu, Japan
Venue:
Transactions on rough sets VII
Year:
2007

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Abstract

An extended method of rough sets, called a method of weighted equivalence classes, is applied to a data table containing imprecise values expressed in a possibility distribution. An indiscerniblity degree between objects is calculated. A family of weighted equivalence classes is obtained via indiscernible classes from a binary relation for indiscernibility between objects. Each equivalence class in the family is accompanied by a possibilistic degree to which it is an actual one. By using the family of weighted equivalence classes we derive a lower approximation and an upper approximation. These approximations coincide with those obtained from methods of possible worlds. Therefore, the method of weighted equivalence classes is justified.