Study On Analysis Methods Of Decision Making In Decision System With Incomplete Information Based On Rough Sets Theory

Rough sets theory for decision analysis in decision system with incomplete information is studied in this dissertation. To incomplete decision systems with different characteristics, rough set theory for incomplete information system are improved and extended; several corresponding rough analysis methods of decision making are proposed. Main contents of the dissertation are as follows:Rough set methods for discovering decision rules from incomplete decision system are studied. Extended rough set models for incomplete information system are reviewed. An improved algorithm of valued tolerance relation is proposed. A rough analysis method of multi-attribute decision making based on improved valued tolerance relation is presented in detail. New method proves better than original one in some extent by an example. Thus it expands the application range of rough set theory.To incomplete decision system with noise, a rough analysis method of decision making based on tolerance relation is discussed. Based on substitution of the indiscernible relation with tolerance relation and a threshold value of consistency degree, Rough approximations of knowledge are defined and some basic properties of rough approximations are proved. Results demonstrate that it can discover compact probabilistic decision rules.In order to discover decision rules from incomplete decision system with preference information, two methods based on rough sets are proposed. One is rough analysis method of decision making based on limited extended dominance relation. Since extended dominance relation existed has its limitations, the concept of limited extended dominance relation is presented; the rough approximations of knowledge are obtained by replacing dominance relation with limited extended dominance relation and preference decision rules of classification are acquired. Another is rough analysis method of decision making based on generalized extended dominance relation. The concept of generalized extended dominance relation is put forward. By contrast analysis, both extended dominance relation and limited extended dominance relation prove to be special case of generalized extended dominance relation. As including a confidential threshold value, the method has better adaptability and flexibility. Examples are given to demonstrate the feasibility and effectiveness of above methods respectively.For incomplete decision system with both preference information and noise, rough analysis method of decision making based on dominance relation is discussed. The concept of consistency degree based on extended dominance relation is put forward. Upper approximation, lower approximation and boundary domain of knowledge based on consistency degree are defined formally. Basic properties of rough approximations are proved and the probabilistic sorting decision rules are given. An example shows that new method could deal with inconsistency caused by preference information and acquire some valuable decision knowledge.Finally, to decision problems with dynamic set of decision factors, thoughts of fuzzy decision analysis and two-direction S-rough sets theory are discussed. Rough decision model based on assistant set is proposed. Judgment theorem and cognition theorem of rough decision making are presented. Then an algorithm of rough decision making is developed.