Generalisation of rough set for rule induction in incomplete system

Rough set models based on the tolerance and similarity relations, have been widely used to deal with incomplete information systems. However, tolerance and similarity relations have their own limitations because the former is too loose while the latter is too strict in classification analysis. To make a reasonable and flexible classification in incomplete information system, a new binary relation is proposed in this paper 1 . Such binary relation is only reflexive and it is a generalisation of tolerance and similarity relations. Furthermore, rough set models based on the above three different binary relations are compared. Finally, the direct approach to rules induction is investigated by using the proposed rough set, some illustrative examples are analysed to substantiate the conceptual arguments.