Research On Three-Way Decisions Model For Incomplete Neighborhood Data And Attribute Reducts Algorithm

Incomplete,imprecise and fuzzy data widely exists in real life and practical applications.Classic rough sets and probabilistic rough sets are effective mathematical tools of granular calculation for dealing with such uncertain data.With the continuous improvement of granular calculation,three-way decisions as a new information calculation paradigm is proposed.The three-way decisions inherits the classification ability and fills in a gap of the granular calculation theories.The core idea of three-way decisions is“trisecting-and-acting”,A pair of thresholds calculated based on Bayesian decision risk minimization divides the universe of discourse into three disjoint regions(positive region,boundary region,and negative region)and one can make corresponding decisions(acceptance,deferred acceptance,and rejection)for objects in the three regions.The idea of “divide and rule” of three-way decisions improves the efficiency of people in data analysis and management decisions.Compared with the two-way decisions that only accept and reject,the non-commitment decision corresponding to the boundary region reduces the probability of wrong acceptance and false rejection in decision-making problems and the cost of decision-making to a certain extent.In practice,there are wide ranges of incomplete continuous data and incomplete composite data,etc.However,the research of three-way decisions on these decision systems that contain such data is relatively rare.To further expand the three-way decision models and its application field,this paper studies three-way decision models for incomplete neighborhood data and attribute reduction algorithms,and specificly builds the three-way decisions models for neighborhood systems,incomplete neighborhood systems,and incomplete hybrid decision systems.Since the existing algorithms of three-way attribute reduction are mostly oriented to all decision classes,and less research on class-specific,two algorithms of three-way attribute probabilistic attributes reducts for class-specific are proposed in this paper.(1)In the three-way decisions model for the neighborhood system,the concept of neighborhood is introduced into the classical three-way decisions model for processing continuous data.In this model,only the conditional probability that an object belongs to the object set,and without calculating the conditional probabilities that the object belongs to all object sets,thereby,the computational efficiency of the traditional three-way decision model is improved to some extent.The model is applied successfully to the students’ comprehensive quality evaluation system,and the validity and practical significance of the model are further explained.(2)In the three-way decisions model for incomplete neighborhood systems,the neighborhood asymmetric similarity relationship is proposed to compute the neighborhood granularity of incomplete continuous data.By comparing with the classical rough set and the 0.5 probabilistic rough set and the neighborhood tolerance relationship for incomplete neighborhood system in the experiment,it is verified that the model can obtain higher partition accuracy and lower misclassification loss and provide an effective and feasible method for the processing of incomplete neighborhood data.(3)In the three-way decisions model for incomplete composite decision systems.This paper proposes a new complete neighborhood tolerance relationship and threshold calculation formula for incomplete composite data,and constructs three-way rules under“optimistic”,“compromise” and “pessimism” decision.The theoretical analysis and an example about medical diagnosis illustrate the effectiveness and interpretability of the algorithm,and experimental analysis verified that the constructed model is morereasonable than other related models for the classification process of incomplete composite data,and the classification effect is better.(4)In the algorithm of three-way probabilistic attribute reducts for class-specific,the heuristic attribute reduction algorithm under algebra theory and information theory is constructed based on relative dependence and information entropy.The reduction process and operation steps of the algorithms in consistent and inconsistent decision systems are given in detail through a medical diagnosis example.The reduction results of the algorithms are interpreted reasonably.The validity and feasibility of the algorithm are also illustrated,and the scope of application of the three-way reduction attributes is expanded.