Research On Regret Theory Approach To Multiple Attribute Decision Making With Hybrid Data

The Study on theory and method of multiple attribute decision making is considered to be an important content of cybernetics and operational research,and it is widely used in engineering analysis,project evaluation management and economic planning decisions,and many other fields.In actual decision circumstance,due to the change of research object parameters and some subjective factors such as human disturbance,the decision-making information is always uncertain.With further study on interval theory,it shows that two-parameter interval number can effectively be used to describe the most decision-making information in multiple attribute decision making problems,but for complex decision problems,three-parameter interval number is applied to describe the decision-making information.As the rapid development of Big Data,the research in multiple attribute decision making problems facing some new challenges,which mainly come from diversity of the decision attribute types and sharp increase in the number of decision attributes,so that hybrid data with different types in multiple attribute decision making becomes one of the hotspot and difficulty in decision making theory research.With the development of behavioral decision theory,the psychological activities of decision-makers need to be considered in a growing number of decision-making problems,therefore the psychological factors would be as an important condition of decision-making.Consequently,this paper conducts research aiming at multiple attribute decision making problems with different types of data on the following two aspects:For multiple attribute decision making problems with three parameters interval number under some different states.Firstly,three-parameter interval number is converted into two-parameter interval number before comparison between two three-parameter interval numbers for avoiding loss of uncertain information.Secondly,regret-rejoice value and overall perceived utility value of alternatives are obtained by the utility value of each attribute for alternatives and the positive ideal alternative according to the decision information with two-parameter interval number under different states.Thirdly,if weight information is completely unknown,the attribute weights are got by water-filling theory.Finally comprehensive utility values of alternatives are calculated with weighted summethod,therefore,a ranking of alternatives can be determined by comparison of overall utility value of alternatives.In order to solve the multiple attribute decision making problems with hybrid Data,the method of attribute reduction and regret theory are applied to solve those problems.Firstly,hybrid data of decision information is converted into the type of two-parameter interval number in a unified way,which reduces the loss of uncertain information in comparison with the type of real number.Then the two-parameter interval numbers are normalized into interval [0,1].Secondly,attribute weights are got by water-filling theory and the weight threshold is set for the attribute reduction.Furthermore,regret-rejoice value and comprehensive perceived utility value of alternatives are obtained by utility value of each attribute for alternatives and the positive ideal alternative according to the decision information after attribute reduction.Finally comprehensive utility values of alternatives are calculated with the weighted sum method;therefore,a ranking of alternatives can be determined by comparison of comprehensive utility values of alternatives.