Paper:

# Toward a Generalization of Rough Sets Based on Active and Passive Relations

## Masashi Emoto^{*}, Rolly Intan^{**}, and Masao Mukaidono^{*}

^{*}Meiji University, 1-1-1 Higashi-mita, Tama-ku, Kawasaki, Japan

^{**}Department of Informatics Engineering, Petra Christian University, Jl. Siwalankerto 121-131, Surabaya 60236, Indonesia

In the generalization of rough sets, many concepts use a relation weaker than the equivalence relation usually used in classical rough sets, e.g., induced by a conditional probability relation. The conditional probability relation is binary and assumes that the relationship between two data (elements or objects) resembles a relationship between two events in conditional probability. We use the asymmetric property of the conditional probability relation to propose active and passive relations, then discuss a generalization and properties of rough sets based on active and passive relations.

*J. Adv. Comput. Intell. Intell. Inform.*, Vol.10, No.6, pp. 939-945, 2006.

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