The Generalization And Uncertainty Of The Model In Tolerance Approximation Space

There are many ways to handle the uncertainty of knowledge and using rough set to dealwith uncertain datas is an effective method in recent years. The theory was developed byPolish mathematician Z. Pawlak in1982about data analysis. It has been appliedsuccessfully in the decision-making and data analysis, pattern recognition, machinelearning and knowledge discovery, etc. The classical rough set theory is based onequivalence relations, but for many practical problems, the relations between datas aretolerance relations, so it is necessary to weaken the equivalence relations to tolerance ones.That is to establish generalized rough set models and to discuss the uncertainty ofknowledge in tolerance approximation space.Based on the above starting point, this paper promotes several rough set models andstudies the uncertainty of knowledge in these models from the view point of granularcomputing, using the tolerance approximation space as the research object. The main ideasof this paper are listed as follows:1. The evidence theory in tolerance approximation space is constructed, and the conceptsof belief consistent set and plausibility consistent set are introduced, then the issues ofattributes reduction are solved and the uncertainty of knowledge is analyzed.2. From the perspective of granular computing, the single equivalence relation (i.e., asingle granulation) in classical rough set theory is weakened to multiple tolerance relations(i.e., multiple granulations), and the multi-granulation rough set models in toleranceapproximation space are proposed to satisfy the requirement of a more rigorous or moreaccurate characterization of knowledge. The propositions provide the practical problemswith more guidance.3. Taking into account certain practical problems, the knowledge itself is fuzzy. On thebasis of the multi-granulation fuzzy rough set on multiple equivalence relations, themulti-granulation fuzzy rough set models in tolerance approximation space are established,and the properties of approximation operators and the uncertainty of knowledge areanalyzed. Besides, the differences and relationships among single-granulation rough setand multi-granultion rough sets are discussed. Moreover, the multi-granulation fuzzy roughset models in tolerance fuzzy approximation space and the corresponding approximationoperators are studied further.4. The concepts of upper and lower approximation reduction are proposed in inconsistentlattice target information system which takes the broadest range of value, and the judgment theorems based on discernibility matrix are obtained. Moreover, the detailed approachesare provided in order to get the upper and lower approximation reduction. An example isshowed to demonstrate the validity of the approaches.