The Minimal Description of Formal Concept Analysis

Abstract

In rough sets, there were some of results of minimal description formed by covering, this paper gives some remarks about them.Using the idea of minimal description in formal concept analysis, discusses the corresponding relation between the covering of objects set and the attributes set.Keywords: Rough set, Formal concept analysis, Minimal description, Covering, PartitionIn 1982, R.Wille (1999) proposed a new model to represent the formal concepts associated to a context (G, M, I), named formal concept analysis based on the formal context, which is a pair consisting of a set of objects (the extension) and a set of attributes (the intension) such that the intension consists of exactly those attributes that the objects in the extension have in common, and the extension contains exactly those objects that share all attributes in the intension. The extension and the intension of a concept uniquely determine each other. The main goal is to reveal the hierarchical structure of formal concepts and to investigate the dependencies among attributes. It provides a theoretical framework for the discovery and design of concept hierarchies from relational information systems. It serves as a basis for conceptual data analysis and knowledge processing. The family of all formal concepts is a complete lattices, 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 (F.M. Baltasar, 1998;J.S. Deogun, 2004;So Kuznetsov, 2002;R.Godin, 1995) etc, one of the important challenges in data handling is generating or navigating the concept lattice of binary relation.The theory of rough sets as a tool for processing uncertain and incomplete information, proposed by Z. Pawlak (1991) in 1982, in which the lower approximation and upper approximation of an arbitrary subset of universe U are the basic operators.The concepts of the lower and upper approximations in rough sets theory are fundamental to the examination of granularity in knowledge, and are an effective way of studying imprecision, vagueness, and uncertainty, and rough set has been successed using all kinds of artificial intelligence fields, such as: data mining , machine learning. There are many authors studying rough sets and formal concept analysis, the readers can see (Zhang wenxiu, 2006; A