Algebras from Semiconcepts in Rough Set Theory

Abstract

In this article, we propose a notion of a semiconcept in the framework of Yao’s object oriented concepts. A study of the algebra of such ‘object oriented semiconcepts’ is carried out, in the line of the study by Wille for the algebra of semiconcepts in formal concept analysis. Two further unary operators, ‘semi-topological’ in nature, are introduced on these structures. On abstraction, the properties of these operators lead to the definition of a ‘semi-topological double Boolean algebra’, of which the algebra of object oriented semiconcepts becomes an instance.