Regret Theory-based Multi-attribute Group Decision-making Method With Interval Grey Number

Multi-attribute group decision-making is an important part of decision-making theory,which has a wide range of practical background in the economy,management and other fields.On the one hand,due to the uncertainty of the decision-making environment,the quantification of the evaluation index often has the characteristics of "explicit extension and unclear connotation".Accordingly,interval gray number is an information form which can effectively express the uncertainty and ambiguity of the evaluation information.On the other hand,a large number of experiments show that: facing some complex decision-making problems,the decision maker is not a "completely rational person" and will show some characteristics of bounded rationality.At present,the research on multi-attribute group decision-making method in which the attribute values are interval gray numbers has some difficulties in practical application and needs futher study.Because it takes into the psychological behavior of the decision maker,but is based on the prospect theory.As a theory of bounded rational behavior,regret theory has some advantages in its application.In view of this,based on the theory of regret theory,it is of the theoretical and pratical significance to study the multi-attribute group decision problem in which the attribute values are interval gray numbers.The research work mainly includes the following three parts.(1)Research on the deterministic multi-attribute group decision-making problem in which the attribute values are interval gray numbers.A multi-attribute group decision-making method based on regret theory and the gray-target decision-making method is proposed for deterministic multi-attribute group decision-making problem in which the attribute value are two-parameter interval gray numbers.A multi-attribute group decision-making method based on regret theory and the gray relational decision method is given for the deterministic multi-attribute group problem in which the attribute value are three-parameter interval gray numbers.The validity and rationality of the method are verified by two application examples.(2)Research on the risky multi-attribute group decision-making problem in which the attribute values are interval gray numbers.A multi-attribute group decision-making method based on regret theory and the gray-target decision-making method is proposed for risky multi-attribute group decision-making problem in which the attribute value are two-parameter interval gray numbers.A multi-attribute group decision-making method based on regret theory and the gray relational decision method is given for the risky multi-attribute group problem in which the attribute value are three-parameter interval gray numbers.Finally,the application of examples to illustrate the effectiveness and rationality of this method.(3)Research on the uncertain multi-attribute group decision-making problem in which the attribute values are interval gray numbers.Combined with the gray entropy method,a new decision-making method is proposed to solve the uncertain multi-attribute group decision-making problem in which the attribute values are two-parameter interval gray numbers.Combined with the minimum maximum regret value method,a new decision-making method is proposed to solve the uncertain multi-attribute group decision-making problem in which the attribute values are three-parameter interval gray numbers.Finally,the application of examples verifies the feasibility of the proposed methods.The proposed multi-attribute group decision-making method can be applied to solve the multi-attribute group decision-making problems which need to consider of decision makers' psychological behavior and in which the attribute values are interval gray numbers,such as risk investment problem,R&D partner selection problem,emergency response problems and so on.This paper not only enriches the content of gray decision theory but also provides a new solution to solve such problems,which has certain theoretical and practical significance.