The Object - Oriented (attribute) Concept Lattice Is Based On The Preservative (cross) Reduction Of The Visual Graph

Rough sets theory, put forward by Polish mathematician Pawlak in 1982, is a theory to deal with the incompleteness and the uncertainty of the data. In the same year, Germany mathematician Wille proposed formal concept analysis, an effective tool to aquire and display the concepts. Since these two theories are all based on the classification, many sholars studied them together and then proposed property-oriented concept lattices and object-oriented concept lattices. Thus a new method to knowledge discovery is born.Due to the importance of the join(meet) irreducible element, this paper mainly studies MIE(meet irreducible element)-preserving reduction and JIE(join irreducible element)-preserving reduction of property-oriented and object-oriented concept lattices. The main results are summarized as follows:1. Study JIE-preserving reduction theory of object(property)-oriented concept lattices. Firstly, JIE-preserving consistent set and JIE-preserving reduction of object-oriented concept lattices are defined. Based on object pictorial diagram, the JIE-preserving reduction of object-oriented lattices and judgment theorem of unnecessary attributes are gianed. Then, JIE-preserving consistent set and JIE-preserving reduction of property-oriented concept lattices are defined. According to the property pictorial diagram, the theory and method of finding JEE-preserving reduction and core attributes of JIE-preserving reduction of property-oriented concept lattices are given.2. Study MIE-preserving reduction theory of object(property)-oriented concept lattices. Firstly, the MIE-preserving consistent set and MIE-preserving reduction of property-oriented concept lattices and object-oriented concept lattices are defined. Then theorems are presented to elaborate the equivalence of MIE(JIE)-preserving reduction of property-oriented concept lattices and JIE(MIE)-preserving reduction of object-oriented concept lattice. Lastly, the methods to acquiring MIE-preserving reduction of object (property)-oriented concept lattices are gained. Besides, we also study the relationship between JIE-preserving reduction and MIE-preserving reduction of object-oriented concept lattice and property-oriented concept lattice, respectively.