Attribute Reduction Approach To Concept Lattice In Interval-valued Information System

The theory of rough set, proposed by Pawlak in1982, is a mathematical theory for datatheory. And the theory concept lattice, proposed by German mathematician Will R. in thesame year, is a kind of data anlaysis method for discovery ordering, etc. As an efficient tool ofknowledge, they have attracted much attention of scholars in artifical intelligence andincreasly become a hot research in the international academic. At present, the theories ofrough set and concept lattice have been appied to many fields such as machine learning,pattern recognition and data minng.In this paper, combining the theory of rough set with the theory of concept lattice, conceptlattice is introduced to interval-valued information system. Applying the properties andstructure of concept lattice, attribute reductions and attribute characteristics of interval-valuedinformation system are discussed. The interval-valued information system is first transferredinto a classical0-1formal context by using the dominance relation. Based on a pair ofoperators, the concept lattice in the interval-valued information system is proposed. Propertiesof concept lattice are studied. Judgement theorems of consistenties are also present. By usingof indiscinbility attribute matrix, algrothrim of attribute reduction and attribute characteries ofthe concept lattice in the interval-valued information system are the investigated. Furthermore,algorithms of generating concept lattice and attribute reductions in interval-valuedinformation system are shown according to the algorithms for generating concept lattice andattribute reductions in classical formal context. Finally, by example, we show theeffectiveness of the proposed algorithm.