Relation granulation and algebraic structure based on concept lattice in complex information systems

Normally, there may exist some kind of relationship among different attribute values such as order relationship, similarity relationship or other more complicated relationship hidden in complex information systems. In the case, the binary relation on the universe is probably a kind of more general binary relation rather than equivalence relation, tolerance relation, order relation, etc. For the case, the paper tries to take concept lattice as theoretical foundation, which is appropriate very well for analyzing and processing binary relations, and finally proposes a new rough set model from the perspective of sub-relations. In the model, one general binary relation can be decomposed into several sub-relations, which can be viewed as granules to study algebraic structure and offer solutions to problems such as reduction, core. The algebraic structure mentioned above can organized all of relation granulation results in the form of lattice structure. In addition, the computing process based on concept lattice is often accompanied by high time complexity, aiming at the problem, the paper attempts to overcome it by introducing granular computing, and further converts complex information systems into relatively simple ones. In general, the paper is a new attempt and exploring to the fusion of rough set and concept lattice, and also offers a new idea for the expansion of rough set from the perspective of relation granulation.