Research On Rough Sets Methodology Of L_A Maximal Compatible Class Model And Interactive Tolerance Relation Model

Rough sets Theory, which was introduced by Professor Z.Pawlak, is an ef-fective and new type of theory as the tool dealing with the fuzzy and uncertain knowledge. Without any prior information and probability, it can recognize relations among data, discover and excavate implicit knowledge, and then ex-plain and extract potential regulations by directly analyzing information the data supplies. During three decades research and development, rough sets theory has experienced constantly improvement and innovation, and has been successfully used in wide fields such as machine learning, pattern recognition, process control, knowledge discovery in database, expert system etc.Incomplete information system is a special but important information sys-tem. Due to the error of measurements or the restriction of human cognition, some data is unknown, that is to say, some is missing or some is interval-valued. There are lots of incomplete information systems in the real world, and as a result, researches on these systems has become a hot issue in re-cent years. Aiming at incomplete information system and based on rough sets theory, this paper does some research on incomplete information system with unknown data and interval-valued decision table, and propose models and methods dealing with incomplete information.Firstly incomplete information system with unknown data is discussed. At present the widely used methods to process information system with unknown data are tolerance relation rough sets model and its improved forms, such as limited tolerance relation. With the concept of maximal compatible class, a new definition of compatible class is proposed, which is called LA maximal compatible class, and a new model named LA maximal compatible class rough sets model is established. Through the contrast between these models it finds that the new model overcomes the phenomenon that contradictive objects are classified in the same class, with the reducing of the error rate of classification and improving of the approximation rate. At the same time, the definition of reduction of LA maximal compatible class rough sets model is presented, which is the supplement of this new method.Secondly interactive tolerance relation model in interval-valued decision table is proposed and attribute reduction is discussed. The existing methods to process interval-valued decision table take no focus on the interactive relation between intervals, resulting in the neglect of potential knowledge. This paper firstly proposes the thought of considering interval relationship when compare with intervals, using the concept of interactive similarity degree defined by this paper. And then it establishes a interactive tolerance relation model in interval-valued decision table, which makes the classification more scientific and accurate. At last the attribute reduction of interval-valued decision table is discussed and reduction methods by discernibility matrix are proposed. As a scientific, effective, accurate and flexible method dealing with interval-valued decision table, interactive tolerance relation model provides a new thinking to process interval-valued information system.