Research On Three-way Decision Based On Measure Theory

This dissertation comes from the key scientific and technological project of Education Department of Henan Province, China(No.14A520082) “Research on Constructing of the Intuitionistic Fuzzy Rough Implicators and it’s Application for Stable Control System”, Foundation and Advanced Technology Research Program of Henan Province, China(No.132300410174) “Research on Interval-valued Fuzzy Implicators and it’s Algebraic Structure”, and the key scientific and technological project of Xinxiang City, China(No.ZG14020) “Research on Constructing of the Intuitionistic Fuzzy Rough Implicators and it’s Application for Decision and Control”.Since rough set was first put forward by Pawlak in 1982, it has been an important mathematic tool to deal with uncertainty. And its theory and applications were both developed rapidly. With the aid of the Bayesian decision procedure, decision-theoretic rough sets(DTRS) were proposed by Yao in 1990 s. Based on DTRS, the concept of three-way decision was put forward by Yao. As the extension of the traditional two decision theory, the purpose of three-way decision theory was given a reasonable interpretation about the positive, the negative and the boundary regions. The positive rules make decisions of acceptance. The negative rules make decisions of rejection, and the boundary rules make decisions of non-commitment(deferment). The three-way decision theory could reflect people’s thinking mode, which had been received the extensive attention of international and domestic academics. There were two main categories about the promotion of the decision rough set model. The first category changed the equivalence relation into the arbitrary binary relation, such as similarity relations, the general relationship, covering, fuzzy relation, etc. The second category replaced the probability measure with other measures. But there were few researches about the three-way decision, which took into the above two categories account. According the above analyses, the Sugeno measure decision rough set model, the covering Sugeno measure rough set model and the decision rough set model based on the evidence theory were proposed, the important properties and theorems were proved. By combining with the three-way decision theory, we could have a reasonable semantic interpretation about the new models. Finally, seval comprehensive illustrations are presented to verify the models’ effectiveness and feasibility. The innovation points of the research are as follows:(1) Combining the Sugeno measure rough set model with Bayesian decision, Sugeno measure decision rough sets model was proposed. Then the new decision rules were proposed by combining with the three-way decision theory. Finally, the feasibility of the model was verified by the illustration.(2) The covering Sugeno measure rough set model was first proposed, which based on the Sugeno measure rough set model and the covering rough set. The upper and lower approximate operators were defined and the properties underlying the union, intersection and complement of the operators were provided, at the same time two definition of the roughness and approximation accuracy were given. Secondly, covering Sugeno measure decision rough set model was proposed, which combined with Bayesian decision. Finally, the three-way decision rules based on the model were proposed and a comprehensive illustration was presented to verify the model’s effectiveness and feasibility.(3) A new model of the three-way decision was proposed based on the belief function. The probability function was replaced with belief function in the classical three-way decision model. These decision rules were proposed in this model, and properties were discussed. Finally, comprehensive illustrative was presented to verify the effectiveness and feasibility of this model.Based on the research for the above three kinds of three-way decision models, the theory has been enriched, and the application range of the three-way decision had been expanded.