A variable precision rough set model based on the granularity of tolerance relation

As one of core problems in rough set theory, normally, classification analysis requires that “all” rather than “most”elements in one class are similar to each other. Nevertheless, the situation is just opposite to that in many actual applications. This means users actually just require “most” rather than “all”elements in a class are similar to each other. In the case, to further enhance the robustness and generalization ability of rough set based on tolerance relation, this paper, with concept lattice as theoretical foundation, presents a variable precision rough set model based on the granularity of tolerance relation, in which users can flexibly adjust parameters so as to meet the actual needs. The so-called relation granularity means that the tolerance relation can be decomposed into several strongly connected sub-relations and several weakly connected sub-relations. In essence, classes defined by people usually correspond to strongly connected sub-relations, but classes defined in the paper always correspond to weakly connected sub-relations. In the paper, an algebraic structure can be inferred from an information system, which can organize all hidden covers or partitions in the form of lattice structure. In addition, solutions to the problems are studied, such as reduction, core and dependency. In short, the paper offers a new idea for the expansion of classical rough set models from the perspective of concept lattice.