Incomplete Formal Context And Knowledge Acquisition On Many-valued Context

Formal Concept Analysis (FCA) is an order-theoretic method for the mathematical analysis of scientific data, pioneered by German scholar R.Wille in mid 80's. The main idea of FCA originates from philosophy and in philosophy a concept is composed of two parts, namely the intent and the extent. In FCA the extent of a concept is the set of all objects that belong to the concept and the intent of concept is the set of all attributes that all these objects have. The core data structure of FCA is called concept lattice which essentially describes the relation between the objects and the attributes .And concept lattice can be visualized by Hasse graph that vividly shows the relations of concepts. Over the past twenty years, FCA has been widely studied and become a powerful tool for machine learning, software engineering and information retrieval.Generally speaking, formal context discussed in the classic FCA is complete and the relationship between any object and attribute is determinate. Under many actual circumstances, however, the knowledge acquisition becomes more difficult because of the error of data measurement and transmission or the difference of data understanding. This kind of context with imperfect data is called incomplete context. In this thesis we presented a completion approach called attribute extension for incomplete formal contexts which makes extracting rules from incomplete contexts possible.Currently, what FCA was mainly studied focuses on the one-valued contexts whereas the work on many-valued contexts is little. The most familiar method to deal with many-value contexts in classic FCA is scaling which transforms a many-value context into a derived one-valued one by endowing each attribute with a unique context called scale. However, the process of scaling could generate a huge one-valued context. In order to make up this shortage we introduced formal description as a replaceable method of scaling. By the method of formal description we can construct the concept on many-valued context and then carry on knowledge acquisition using the classic method of FCA.In this thesis, the main results and originalities are summarized as follows:1. A completion approach for incomplete formal contexts called attribute extension is presented. The advantage of using attribute extension is that the completion doesn't lose any information of original context but the number of attributes increases.2. We introduce formal description as a replaceable method for scaling on the view of mapping, and define the so-called standard description that has no restriction on any attribute except for one attribute. Using the standard description we can construct the concept in many-valued context. One advantage of using descriptions is that we can avoid generating a huge one-valued context and reduce the numbers of redundant rules in the process of knowledge acquisition.