Construction of a Unified Model for Formal Contexts and Formal Decision Contexts

Abstract

This paper mainly constructs a unified model for formal contexts, consistent formal decision contexts and inconsistent formal decision contexts based on object oriented concept lattices, which is called a consistent approximate representation space. Congruence relations are first introduced into formal contexts and then relationships between congruence relations and the corresponding object oriented concept lattices are developed. Finally, consistent approximate representation space is defined for a formal context, which is a quadruple (U ,A ,R ,R'). It is verified that if we give R different meanings, then we obtain the corresponding formal context, consistent formal decision context and inconsistent formal decision context with respect to object oriented concept lattices. Therefore, the quadruple ( ,A ,R ,R') is a unified model for formal contexts and formal decision contexts.