Expansion Of The Concept Lattice Reduction And Object-oriented (attributes) Concept Lattice Structure

R. Wille proposed a mathematical theory called formal concept analysis which was also called concept lattice at first in 1982. It presented a method for data analysis used in finding, displaying and ordering of concepts. At the same year, Z. Pawlak proposed rough sets theory which was a mathematical tool used in knowledge discovery and data analysis. Concept lattice theory and rough sets theory provide two different methods for mining and analyzing potential knowledge from data. I. Duntsh, G. Gediga and Y. Y. Yao introduced approximation operators of rough sets into concept lattice, which integrated the two different mathematical theories, and obtained property oriented concept lattices and object oriented concept lattices.The construction of concept lattices is the basis of theoretical study and practical application in concept lattice theory. The size of the formal context always plays an important role in the construction of concept lattices. Methods of concept lattice expansion and recovery based on reduced formal context and the construction of property oriented concept lattices and object oriented concept lattices are studied in this thesis.Specifically, the main innovations and results are presented as follow.1 Formal context reduction is proposed based on inclusion-reduction. The reduced concept lattice is expanded with selecting objects and attributes dynamically, and the concept lattice of original formal context is converted eventually. The concept lattices of original formal context and reduced formal context are monomorphic. Moreover, typical examples of UCI database are analyzed.2 Based on elementary concepts we define, the construction methods of property oriented concept lattices and object oriented concept lattices are given.