Research On Isomorphism Generating Method Of Concept Lattices And Implementation Of IsoFCA System

Our researches aim at construction method of concept lattices in Formal Concept Analysis (FCA), and the presentation model of knowledge similarity based on formal context kernels. FCA is a field of applied mathematics based on the mathematization of concept and conceptual hierarchy. Thereby it activates mathematical thinking for conceptual data analysis and knowledge processing. The major content in FCA is to extract formal concepts and connections between them from data in form of formal context so as to form a lattice structure of formal concepts. Concept lattices have been regarded as perfect abstraction of knowledge system. There are two significant aspects. First, the results of data analysis are conepts instead of data themselves. Differing to traditional data analysis methods based on statistics, FCA obtains knowledge view which is higher level of representation of data. Second, concept lattices provide better foundation for knowledge processing, such as association rule discovery, intelligent search engine, semantic Web and natural language processing.One of important issues in FCA is construction of concept lattices. So far, there are two kinds of algorithms for concept lattices constructing, batch algorithms and incremental algorithms. However, most of the researches dedicated to build concept lattices directly from contexts. Rare research papers were published in addition to [5] which give out some brief descriptions on exploiting the relations bewteen contexts to generate concept lattices.In this dissertation, five emphases are placed on the development of the methods including,1. A novel method of isomorphic generating of concept lattices based on nth-order context kernels, of which the central idea is that an arbitrary context K can be split onto subcontexts in smaller size of order, then, for every subcontext Ki, there exists a isomorphic context Hj in the kernel with the same order as Ki, and concept lattice B(Ki) can be yielded in terms of B(Hj), and finally, the result B(K) can be reconstructed from B(Ki).2. Equivalent class algorithm, a rapid algorithm for context isomorphism detecting, which is to determine whether a context can be transformed into another one by exchanging rows or columns, and focuses on finding out rapid algorithm of context transform.