Research On The Granular Computing Model Based On Formal Concept Analysis

Formal concept analysis (FCA), proposed by Prof. Wille in1982, is founded on the reconstruction of Lattice Theory. With concept lattice as its core data structure, this model starts with a binary relation of objects and attributes and depicts the relationship of generalization and instantiation of formal concepts, visually represented by Hasse diagram. FCA has a rigorous mathematical background and provides a better theoretical methods and tools for the field of artificial intelligence, so it is widely studied by the majority of the scholars in the field of Artificial Intelligence. Over the past years, FCA has become a powerful tool for machine learning, export system, software engineering, knowledge discovery and acquisition and information retrieval. In addition to being a technique for classifying and defining concepts from data, FCA can also be exploited to discover implications among the objects and the attributes.In this thesis, we shall make a systematic and in-depth investigation on FCA. The main results and originalities are summarized as follows:1. Discuss the fusion of FCA and Granular Computing Theory (GrC). From the similarity between FCA and GrC, we shall derive the so-called Conceptual Granular Model, a granular computing model based on FCA, which brings some important notions, such as granular-concept, and some related properties. In addtition, we also consider how to give proper operators on granular-concepts.2. Propose a granular computing model based on inclusion degree theory. In this part, we shall consider how to apply inclusion degree theory to Conceptual Granular Model. In particular, a new inclusion degree on conceptual granules will be defined and verified, and some interesting results concerning conceptual granules thus follow. In fact, in a general sense, the approach is not only a tool to study this model from a quantitative point of view, but also an effective measure of the degree of the knowledge acquisition. 3. Application of FCA on polysemy analysis. We generate a decision context based on relations between word meanings and the corresponding parts of speech. And then we construct a formal context based on the decision context, extract the decision rules from the context by using the rule-extracting algorithms from FCA, and give their explanations from the point view of natural language. An illustrative example verifies the validity of this method in the word sense disambiguation.4. Application of FCA on semantic analysis. We propose a method for sememe analysis based on FCA. The method first forms a formal context based on relations between linguistic objects and their semantic features, and then analyzes the formal context under the framework of FCA. Experiments show that we can not only classify the linguistic objects easily, but view relations between different word classifications intuitively, and also suggest that formal concept analysis is an efficient tool for semantic analysis.