The Research On Probabilistic Dominance Relation And The Related Problems Based On Ordered Information Systems

Rough set theory is an effective mathematical tool in solving uncertain, inaccurate and inconsistent data, which provides a new theoretical foundation to deal with uncertainty problems. As an extension of equivalent relation in rough set theory, dominance relation can deal with comparing, sorting problems better, so it attracts more attrition and widely application in uncertain area.In this paper, the new probabilistic dominance relations are proposed based on com-plete ordered information systems as well as incomplete ordered information systems, fol-lowing with the rough set models and the related properties, then the methods of objects sorting and attributes reduction are discussed. The main contents are as follows:1. A new definition of structure diversity on dominance classes is proposed under traditional dominance relation, then a novel method of the measurement upon attributes importance is put forward. Besides, an algorithm of attribute reduction based on the structure of attribute diversity on dominance classes is studied. The examples verify the feasibility and effectiveness, which lay a foundation for the following attribute reduction based on probabilistic dominance relation.2. In the view of the excessively strict demands upon previous definition based on complete ordered information systems, a new probabilistic dominance relation is proposed firstly, and the related properties are discussed; secondly, the concept of probabilistic attribute diversity on dominance classes is introduced, following with several properties and conclusions; lastly, rough set model, objects sorting and attributes reduction are studied based on the new relation, which provides a new method and a train of thought for ordered information systems.3. For the defects of previous compatible and limited dominance relation in incomplete ordered information systems, a new a-prior probabilistic dominance relation is proposed. The research approach is the same as the complete one:Firstly, the related characters of the new relation are discussed; secondly, the concept of prior probabilistic attribute diver- sity on dominance classes is introduced, including several characters and the corresponding conclusions; lastly, rough set model, objects sorting and attributes reduction are studied based on a-prior probabilistic relation. Compared with the traditional study of incom-plete ordered information systems, the proposed dominance relation has more reliability and interpretability, which makes up for the deficiency of the prior study. Simultaneously, the research on the characters of rough set model, objects sorting and attribute reduction provide new theory for incomplete ordered information.