Multi-attribute Decision-making Method With Three-Parameter Interval Grey Number

Grey decision-making refers to the decision-making that contains grey elements in the decision-making model or combines the general decision-making model with the grey decision-making model,it's focuses on the selection of alternatives.Grey decision-making is an important part of the theoretical system of grey system.This paper studies the grey decision-making model.The main research contents are as follows:(1)Research on three-parameter interval grey number.According to the algorithm of two-parameter interval grey number,the algorithm of three-parameter interval grey number is given.Since the "center of gravity" point of the three-parameter interval grey number plays an important role in the evaluation information,and the subjective risk preference of decision makers will affect the accuracy of decision results,the kernel,relative kernel and distance measure of three-parameter interval grey number are given.(2)Research on grey relational decision-making model with three-parameter interval grey number.Considering the bounded rational behavior of decision makers when facing decision-making,a grey relational decision model with three-parameter interval grey number information is constructed based on the prospect theory.The original linear transformation operator of "rewarding good and punishing bad" is improved,and a linear transformation operator with more detailed discrimination degree is proposed.The relative kernel of three-parameter interval grey number is used as the judgment basis to judge the size of the three-parameter interval grey number.The relative kernel of three-parameter interval grey number is used as the evaluation value to define the prospect value function and the weight function,and thus the positive and negative ideal alternatives are determined.The positive and negative relational coefficients are determined according to the grey relational analysis method,and the relative closeness degree is determined by the positive and negative relational coefficients to sort the alternatives.On the basis of prospect theory and grey relational analysis,a dynamic grey relational decision-making model based on prospect theory is proposed by taking time dimension into consideration in multi-attribute decision-making.According to the relative kernel of three-parameter interval grey number to judge the three-parameter interval grey number,the prospect value function is determined by taking the decision information at different time points as the reference points,and an optimization model is constructed to solve the attribute weight and the time weight by combining the grey entropy principle,and the ranking of the alternatives is realized by the comprehensive prospect value of the alternatives.(3)Research on grey target decision-making model with three-parameter interval grey number.In the process of decision-making,decision-makers are often risk-averse when they get benefits,risk-biased when they suffer losses,and they are more sensitive to losses than benefits.In view of this characteristic of decision makers in the real decision-making process,this paper combines the traditional range transformation method with the logarithm function based on e and constructs a nonlinear transformation operator to depict the psychological change behavior of decision makers in the decision-making process.When the evaluation information is normalized,the nonlinear transformation operator can be used.When determining the positive and negative bull's-eye of the decision-making alternatives,the distance and relative kernel of three-parameter interval grey number can be used as the judgment basis,and the alternatives can be sorted and optimized according to the ratio between the positive and negative bull's-eye distances.Combining the prospect theory and grey target decision analysis method,a grey target decision model based on prospect theory is proposed.The distance formula between the three-parameter interval grey numbers is determined by the relative kernel of three-parameter interval grey numbers,the relative kernel of three-parameter interval grey numbers is integrated into the prospect value function,the maximized comprehensive prospect value is set as the expected target,a mathematical model for solving the attribute weight is constructed,the solved optimal attribute weight is brought into the comprehensive prospect value function,and the alternatives are sorted by comparing the sizes of the comprehensive prospect values.(4)Research on cosine similarity decision model based on three-parameter interval grey number.Combining cosine similarity decision method with three-parameter interval grey number,an extended form of grey decision model is constructed.When dealing with the three-parameter interval grey numbers,the three-parameter interval grey numbers can be decomposed by the idea of interval decomposition method,i.e.expressed as a form consisting of real number and two-parameter interval grey numbers,the real number and the kernels of two-parameter interval grey numbers are fused to give the kernels of the three-parameter interval grey numbers,the three-parameter interval grey numbers are expressed in the form of vectors,and the kernels and precision of three-parameter interval grey numbers are projected onto the horizontal axis and the vertical axis of the two-dimensional coordinate plane respectively,and the cosine similarity is used to describe the similarity between evaluation indexes.The alternatives are sorted according to the cosine similarity between all adjacent attributes between the alternatives and ideal alternatives.