Rough ontology: Extension of ontologies by rough sets

Ontology is widely used in the areas of knowledge engineering, web based data mining, etc. In rough set theory, accuracy of approximation of set and a concept of granularity are introduced. Rough set theory is very useful to define dependency among attributes and extract decision rules from the set. One of our main aims of this paper is to propose a concept of rough ontology. A concept of rough ontology is extended concept of rough set, and it enables us to use flexible information system in the form of ontology. And rough ontology is useful to introduce concepts rough set theory in to ontology. In this paper we formulate a concept of rough ontology, which is extended concept of rough set theory. We define upper and lower approximation, accuracy of approximation of preference, concept of granularity of preference. And we also show the property of rough ontology.