Research On Methods Of Clustering Reduction On Fuzzy Concept Lattices

Concept lattices are the core data structures in the theory of formal concept analysis. It is put into wide use in information retrieval, knowledge discovery, and so on. Concept lattice reduction makes it easy to find the implied knowledge in the formal background and simple to represent the implied knowledge. Thus, concept lattice reduction further extends the concept lattice theory, and makes difference to the research and application of it.In formal concept analysis methods, fuzzy concept lattices may be built. At present, the fuzzy formal background can be reduced through the method of threshold value, but there is less research to put clustering into the use of concept lattice reduction, which exists limitations. Thus, new methods, which combine the clustering approaches and the lattice and Boolean algebra theory, to reduce the size of fuzzy concept lattices is researched. The major work completed as follows.(1) One of the limitations of the existing methods of clustering reduction of fuzzy concept lattices is analyzed and proved that the set of clustered concepts doesn’t have a lattice structure.(2) A new definition of the incremental algorithm operation to insert a new concept into the existing lattice is brought forward. Then a conclusion is made and proved. It is that a fuzzy concept lattice constructed by the method presented in the specified references is the sub-lattice of that built by the new method given in this paper.(3) A method of clustering reduction on fuzzy concept lattices is built. It is a new method to reduce the size of fuzzy concept lattices by clustering fuzzy concepts. The main idea is that when there are similar concepts in a concept lattice, a new concept is formed by clustering the set of concepts which includes the supremum, the infimum of the similar concepts and all the other concepts between the supremum and the infimum. A theorem that the set of concepts gained by the method of clustering reduction has a lattice structure is proposed. And then a detailed process of proof is given to prove it.(4) A method of clustering reduction on fuzzy concept Boolean lattices is put forward for the special case of fuzzy concept lattices. This approach has the use of the base theory of Boolean algebra. It is still a Boolean algebra after the fuzzy concept Boolean lattices being reduced by using the approach. As a result, the lattices before and after being clustered are homomorphic.(5) A new method of properties division on a concept lattice is put forward.Through the research on the method of clustering reduction on fuzzy concept lattices, the fuzzy concept lattices’algebraic properties is kept while its scale is reduced, which makes the set of clustered concepts still have a lattice structure. The research plays a potential role in promoting the application of lattice based on its structure in each field at the theoretical level.