Knowledge Representation And Knowledge Acquisiton On Formal Concept Analysis

Formal Concept Analysis (FCA) is an order-theoretic method for the mathematical analysis of scientific data, pioneered by R.Wille in mid 80's. Over the past twenty years, FCA has been widely studied and become a powerful tool for machine learning, software engineering 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 make a systematic and in-depth investigation on FCA. The main results and originalities are summarized as follows:1. Serve to introduce partially ordered set (poset) and inclusion degree theory to FCA. For this, we establish three posets, namely, G poset, M poset as well as GM poset and based on the three posets, we define three inclusion degrees on them. Then we show the relationship between the posets and concept lattice, and prove that the basic concepts such as intents, extents and implications can be reconstructed either by the partial orders or by the inclusion degrees of the posets. These results will be very helpful for peopleto understand the essence of concepts and the structure of concept lattice in FCA, and can be regarded as the main foundation of quantitative measures, which are defined for FCA.2. Serve to introduce decision context and decision rule to FCA. Since extracting decision rules directly from decision context takes time, we present an inference rule to minimize the number of decision rules. Moreover, based on the inference rule we introduce the concept of a maximal decision rule and prove that the set of all a maximal decision rules is complete and non-redundant. At last, we propose a method to generate the set.3. Aim to establish the relationship between FCA and rough set theory. The following results are obtained: (1) a derivative formal context of an information system can be induced by the notion of nominal scale and the technique of plain scaling in formal concept analysis;(2) some core notions in rough set theory such as partition, upper and lower approximations, independence, dependence and reduct can be reinterpreted in derivative formal contexts. In addition, the limitation of rough set theory to data processing is analyzed. The results presented in this paper provide a basis to the synthesis of formal concept analysis and rough set theory.