Research Of Utility-based Three-way Decisions Model

By extending the two-way decisions to the three-way decisions,the three-way decisions theory provides three kinds of decision methods: acceptance,rejection and unpromise.Unpromise is the third way of decision making as lack of information to make deterministic deicision.It is more consistent with the human cognitive model.Meanwhile,it also provides a reasonable semantic explanation for the three regions of the rough sets.That is,the rules in the positive region correspond to acceptance decisions,the corresponding rules in the boundary region represent the unpromise decisions,and the corresponding rules in the negative region indicate rejection decisions.In recent years,the three-way decisions theory has developed rapidly,and has been widely used in machine learning,knowledge discovery,data mining and other research fields.The classical three-way decisions model mainly considers the influence of objective risk on decision making,but risk decisions are usually influenced by subjective factors and objective factors.In process of decision making,decisions are based on not only the objective risk but also the subjective activity by decision makers.Considering the subjective attitudes of decision makers in decision-making process,this paper focuses on the following research:(1)Since the classical three-way decisions model does not consider decision makers' subjective attitudes to the risk,we propose the model of Utility-based Three-Way Decisions(UTWD)by extending the risk function to utility function.The utility is used to measure the attitude of the decision makers to the risk.During the process of decision-making,combining the subjective and objective factors is more in line with the realistic decision.The monotonic relationships between the utility and probabilities of objects in three regions are investigated systematically.The computational methods for positive region utility,boundary region utility and negative region utility are also given respectively in the paper.Based on UTWD,the non-monotonicity of utility is proved by experiments.Using utility as the heuristic function,the backward greedy algorithm of maximal-utility attribute reduction and the forward greedy algorithm maximal-utility attribute reduction are proposed for the top-down and bottom-up heuristic strategies.The effectiveness of attribute reduction algorithms are verified by experiments.(2)In order to solve the problem that the definition of the strong indiscernibility relation is too strict and lacks an intolerance of errors in the UTWD,we propose the model of ?-cut Quantitative Utility-based Three-Way Decisions by combining weak indiscernibility relation and UTWD.The strong indiscernibility relation requires that two objects have the same value on all attributes.However,the weak indiscernibility relation only requires that two objects have the same value on at least one attribute.According to the different ? values,different degrees of indiscernibility relation can be obtained.The combination of weak indiscernibility relation can improve fault tolerance.Based on?-cut Quantitative Utility-based Three-Way Decisions,we give the formula of the totalutility and construct the heuristic maximal-utility attribute reduction algorithm,heuristic positive decision-monotocity attribute reductionc algorithm and heuristic non-negative decision-monotocity attribute reduction algorithm.The effectiveness of attribute reduction algorithms are verified by experiments.