Research On Three-way Multi-attribute Decision-making Methods In Incomplete Information Systems

Given the successful applications of three-way decision in multi-attribute decision-making problems,three-way multi-attribute decision-making methods have been become a hot topic in current researches.However,most of the existing three-way multi-attribute decision-making methods with classification and ranking functions are based on complete information systems,while the three-way multi-attribute decision-making methods based on incomplete information systems are rare.Considering the existence of a large number of incomplete multi-attribute decision-making problems in real life,this paper extends the existing research results to incomplete information systems,and proposes two novel three-way multi-attribute decision-making methods,which provide new solutions and research ideas for actual incomplete multi-attribute decision-making problems.The specific research content of this paper mainly includes the following two aspects:(1)A three-way multi-attribute decision-making method based on fuzzy rough sets in incomplete information systems is established.First,based on the defined fuzzy rough set model,a new method for calculating the relative loss functions is presented by considering the hesitation degree of each evaluation value.At the same time,by considering the information granularity of each object,a conditional probability measurement method is given.Based on these,we construct a three-way decision model with three strategies.Then,based on the real-value data provided by the incomplete multi-attribute decision-making problems in real life,the arithmetic mean approach is used to fill in the missing data.In consideration of the inaccuracy of the populated data,a three-way multi-attribute decision-making method is established by means of the proposed three-way decision model.Finally,according to a real case in UCI database,the feasibility,effectiveness,superiority and stability of the proposed method are verified through comparative analysis and experimental analysis.(2)A three-way multi-attribute decision-making method based on utility theory in incomplete information systems is constructed.Given the fact that the information in actual incomplete multi-attribute decision-making problems may be discrete and even some attribute values may be non-compensatory.For this kind of incomplete multi-attribute decision-making problem with decision attributes,firstly,we calculate the weighted conditional probability of each object by virtue of the defined similarity relations under each attribute.Meanwhile,according to the decision attribute,the utility theory is utilized to compute the relative utility functions of each alternative.Then,we establish a three-way multi-attribute decision-making model.Subsequently,the incomplete multi-attribute decision-making problems are modeled,and the key decision-making steps are given.Finally,based on an investment project example,we demonstrate the feasibility,effectiveness and stability of the proposed method by comparative and experimental analyses.