Concept Lattice Based on the Rough Sets

In 1982, R.Wille proposed a new model to represent the formal concepts associated to a context (G,M, I), named formal concept analysis based on formal context, which is a binary relation between a set of objects and a set of attributes. The main goal is to reveal the hierarchical structure of formal concepts and to investigate the dependencies among attributes. The family of all formal concepts is a complete lattice, which is an effective method for several real-world applications in data analysis, such as object-oriented databases, inheritance lattices, mining for association rules, generating frequent sets etc. One of the important challenges in data handing is generating or navigating the concept lattice of binary relation. The theory of rough sets, proposed by Z.Pawlak, is an extension of set theory for the study of intelligent systems characterized by insufficient and incomplete information. The knowledge about a considered universe is the starting point. Using two operations, a lower approximation and an upper approximation, we can describe every subset of the universe. The concepts of the lower and upper approximations in rough set theory are fundamental to the examination of granularity in knowledge. These concepts is an effective way of studying imprecision, vagueness, and uncertainty. In this paper, we discuss the rough properties of concept lattice in rough set. The rest of the paper is organized as following, in section 2, we define rough