Research On Some Issues Of Concept Lattice Generation And Knowledge Acquiring Based On Uncertainty Theory

The concept lattice is also called the Galois lattice, and its basic idea is based on a binary relation of concept hierarchy. As a core data structure of formal concept analysis theory, concept lattice becomes the currently effective tool for data analysis and knowledge discovery, in many areas it made more extensive and successful applications, and gradually the tendency of many subjects crossing and integration.The formation of concept lattice is one of the most important problems in the concept lattice theory. When the amount of data is increasing, the concept lattice hierarchy will become more complicated and difficult to deal with. In order to simplify lattice structure and effectively reduce the generation of formal concept, many studies on formation of concept lattice and knowledge discovery based on uncertainty theory were to be considered.Knowledge reduction under the view of lattice, Galois lattice based on the similarity,multi-scaled concept lattice based on neighborhood system, the propositional reasoning in formal decision context and knowledge acquisition of incomplete formal decision context are respectively proposed in this dissertation. The original work obtained includes the following aspects:1. We propose some new concepts such as knowledge reduction and consistent set based on rough set theory under the view of lattice. By means of defining lower approximate and upper approximate operators, we give two specific reductions. Then, we present the judgment theorems for consistent sets and proved. These representations are the deeper reveals the essence of knowledge, and some relevant results of knowledge reduction are obtained.2. By using similarity degree, we introduced two new Galois connections and discussed their properties, on the basis we studied the basic properties of concept lattice induced by the specific Galois connection. Moreover, we gave the definition of a specific reduction, and proposed two judgment theorems for consistent sets and proved. Some relevant results of concept lattice have been done to promote.3. Based on a kind of Galois connection via a concept of inclusion degree using a special neighborhood system, we propose a multi-scaled concept lattice. We show that theconcept lattice produced by the original context is equal to the concept lattice produced by the induced context. An example shows that the structure of concept lattice is controlled by choosing appropriate parameters, and the purpose of reducing the number of concepts is achieved in practical application.4. On the basis of a formal context, by weakening the composition condition of concept form, we give the basic unit of cognition, i.e. proposition. Based on some basic concepts such as necessarily proposition and sufficient proposition, some related properties of the proposition and the relationship between various propositions are given, and the effective ways to obtain a new proposition is proposed. Using the determine degree of proposition, we discuss the propositional reasoning in formal decision context, and provide a new framework in a formal context for uncertain reasoning.5. The results of the research on the generation of approximate concepts, rules extraction and attribute reduction in incomplete formal decision context are presented. It provides a new way of thinking for knowledge acquisition in incomplete formal decision context.