Approximate concepts acquisition based on formal contexts

Formal concepts are abstraction and formalization of the concepts in philosophy. Acquisition of formal concepts is the base of formal concept analysis. Besides the concrete concepts, uncertain but meaningful concepts sometimes are more appropriate for real life. The paper begins with this practical problem and obtains some interesting knowledge based on formal contexts. First, k-grade relation on the object set of a formal context is defined, and the different values of k in different cases are discussed in detail. Then the algorithms to acquire approximate concepts associated with each object are proposed and these approximate concepts are explained. Second, the relationships between approximate concepts associated with objects and concepts of concept lattice (property oriented concept lattice) are studied. Parallel to the above idea, k-grade relation on the attribute set is proposed dually, and approximate concepts associated with each attribute are obtained and interpreted. Meanwhile, the relationships between approximate concepts associated with attributes and concepts of concept lattice (object oriented concept lattice) are also discussed.