Research On Extension Models Of Rough Set For Uncertain Information System

Rough set theory was first proposed by Poland researcher Pawlak, which is a new data analysis tool and has been successfully applied in data mining, pattern recognition and decision analysis, etc. The classical rough set theory is constructed on the basis of equivalence relation, and it can be used to solve uncertainty problems caused by the limited discernibility of knowledge. However, when it comes to the uncertainty description of data itself, the classical rough set theory can hardly provide a corresponding processing mechanism. Therefore, when facing the uncertainty of massive amounts of data, it is very important to research on expanding the rough set model to obtain knowledge for the development of rough set theory and its applications.In this dissertation, the extension models of rough set and its applications under incomplete and fuzzy information are systematically studied for knowledge reduction and decision rule acquisition. This dissertation is laid out as follows:1) As for the shortcomings of characteristic dominance relation in classification, we proposed an improved characteristic dominance relation, and rough decision analysis model is also presented in incomplete ordered information system. Compared with original rough decision analysis model, the improved one is proved to be better in accuracy and quality about approximation classification. Meanwhile, discernibility matrix based knowledge reduction is proposed to simplify the decision rule under the improved characteristic dominance relation.2) A 8-dominance relation is defined in set-valued ordered information system to classify the objects, and uncertainty measure of set-valued ordered information system is presented. Based on δ-dominance relation, we introduce an extension model of rough set into the set-valued ordered information system for knowledge reduction and decision rule acquisition. In addition, according to the different advantage degree between objects, a fuzzy dominance relation which doesn’t depend on any unknown parameters is defined in set-valued ordered information system. Meanwhile, fuzzy dominance relation based fuzzy discernibility matrix is constructed in set-valued ordered information system to reduce knowledge.3) Rough decision problem of set-valued ordered fuzzy decision system in which decision attribute value is fuzzy concept is studied on the basis of set-valued ordered information system. As for the extension of rough set in fuzzy sense, dominance relation based rough fuzzy set model is firstly proposed. Then, the notions of lower and upper approximation reductions are given, and judgment theorems of lower and upper approximation consistent sets are further investigated. Combined with judgement theorems, the lower and upper approximation reductions based on discernibility matrix are proposed, and the simplified fuzzy decision rules are also extracted.4) Dominance relation is introduced into intuitionistic fuzzy information system, and then the intuitionistic fuzzy multiple attribute decision making method based on dominance relation is proposed. Dominance relation based intuitionistic fuzzy rough set model is extended to the classical rough set model, and its uncertainty measure is discussed. Distribution reduction and assignment reduction based on discernibility matrices are put forward in intuitionistic fuzzy decision system in which intuitionistic fuzzy decision value is more than one. In addition, we generalize the notions of the relative positive domain and the significance of attributes in classical rough set theory to intuitionistic fuzzy decision system, and then investigate the monotone property of the relative positive domain. According to the different characteristics of attributes and judgment theorem for positive domain reduction, the positive domain reduction algorithm using attribute significance as heuristic information is presented, and the complexity analysis of the algorithm is also given. The effectiveness of the proposed algorithm is further illustrated by experimental data.