Research On Grey Decision Model With Three-Parameter Interval Grey Number

Multi-attribute decision making is a systemic analysis method to solve the uncertain decision making problem.Through the comprehensive evaluation of the alternatives,we can find out the optimal scheme,which has a wide range of applications in the field of Decision Science.With the development of society,there are more and more uncertain factors,and the decision information is usually not in the form of accurate numbers,but in the form of interval grey numbers,Therefore,the grey multi-attribute decision making method is an important method to solve the problem of uncertain decision making,and it has been widely used in engineering decision-making,equipment selection and investment optimization and so on.Due to the complex and uncertain nature of the objective environment,the three-parameter interval grey number is used to describe the decision-making problem more in line with the real situation,Therefore,it is of theoretical and practical value to apply the gray system theory to the decision problem of the three parameter interval gray numbers.In this paper,three-parameter interval gray number is used to describe the decision information,based on the classical grey relational decision and grey target decision,grey relational decision and grey target decision methods are proposed based on the three-parameter interval grey number decision information.Furthermore,based on the bounded rationality of decision makers,considering the subjective risk preference,grey relational decision method and grey target decision method for the three-parameter interval grey number are proposed based on the prospect theory,which broaden the application fields of grey decision model.The main contents of this paper are as follows:(1)Three-parameter interval gray number distance measure and ranking problem.A new type of three-parameter interval grey number distance measure formula is proposed,which takes into account the importance of the center of gravity in the grey decision information of the three-parameter interval;On the basis of the definition of the general interval grey number kernel,the kernel of three-parameter interval grey numbers is defined,and the three-parameter interval grey number ranking method is given based on kernel and distance measure.(2)The research of the grey relational decision model of three-parameter interval gray number based on prospect theory.Based on the grey relational decision making method of traditional interval grey numbers and the particularity of three parameter interval grey number,the grey relational coefficient and grey relational degree of three parameter interval grey numbers are given.Firstly,a grey relational decision model of three-parameter interval grey number is established.An example is given to verify its feasibility.Furthermore,considering the subjective preferences of decision makers,the grey relational decision making model with three-parameter interval grey number based on foreground theory is established.Normalizing the original decision information through rewarding good and punishing bad [-1,1] linear transformation operator to construct three-parameter interval grey number,making the decision more practical decision.Then According to the size of the comprehensive prospect value of the decision result,the scheme is selected,and an example is used to analyze.(3)The research of grey target decision model of three-parameter interval grey numbers based on prospect theory.Combined with the grey target decision method of the existing three-parameters interval grey numbers,the three parameter interval grey number distance formula of target.Firstly,the grey target decision model with three parameters interval number is constructed.Furthermore,based on the idea of n prospect theory,the grey target decision model of the three-parameter interval numbers based on prospect theory is established and analyzed with examples.This paper combines the main idea of prospect theory and grey relational decision making and grey target decision making.On the one hand,The grey relational decision model and grey target decision model of interval grey numbers with three parameters are established;on the other hand,considering the subjective risk preference,It combines the advantages of grey decision model in dealing with uncertain decision problems.In this paper,The grey decision making method based on prospect theory are proposed to solve the problem that the decision information is three-parameter interval grey number.