Research On Muti-attribute Decision Making Method With Three-Parameter Interval Grey Number

As an important content in decision making problems,Multi-attribute decision making has been widely researched,and the decision-making process of multi-attribute decision making in real life of is often with uncertainty.It includes the inadequacy of information,variability and instability of decision makers' attitude when they are at risk.To solve it,many scholars have come up with various kinds of methods with the form of interval number,fuzzy number and linguistic variables,etc.But the decision making methods with three-parameter interval grey number are still relatively limited.As an extension form of interval grey number,three-parameter interval grey number has a maximum possible parameter compared with interval grey number.So,it could be said a whitening form of interval grey number,and this form could characterize the interval distribution of decision information with a more intuitive way.Therefore,in order to further enrich and perfect the theory system of Grey System Theory and Multi-attribute Decision Making Theory,make up for the shortage of existing decision-making methods,this paper proposed a series of decision-making methods aiming at the muti-attribute decision and clustering problem with three-parameter interval grey number.The main contents of research are as follows:(1)Research on distance measuring and sorting problem.In order to make up the deficiency of existing distance measuring methods,this paper improve them and proposed a new method for distance measurement.The new method could take each parameter's proportion and the coverage length into consideration comprehensively.So,the features of grey information are fully grasped.For comparation and sorting problems,a sorting method based on SPD(Superiority Position Degree)is proposed.This method could consider the influence of interval length on realation of size and cover all situations with diffirent parameter sizes.(2)Research on grey relational decision making method.In order to make up the deficiency of existing grey relational decision making methods on solving process and computational complexity,grey relational TOPSIS decision method based on SPD is proposed.First,the parameters are assembled by solving the SPD of each decision value relative to positive and negative ideal alternatives;then,grey relational analysis is carried out based on SPD,and grey close correlation degree of decision alternative are calculated relative to positive and negative ideal alternatives;finally,examples are introduced for comparative analysis,so the scientificity and validity of the proposed method are verified.(3)Research on grey relational clustering decision making method.First,in order to solve the clustering and evaluation problem with three-parameter interval grey number,a new kind of grey relational clustering decision making method is proposed based on the research of traditional methods.Then,the comprehensive perceptional utility of grey relational degree is defined to lower the decision risk by introducing Regret theory.And the calculated perceptional values of three-parameter interval grey number is used for clustering to further reduce the uncertainty in process of clustering and evaluation analysis.Finally,example is introduced for comparative analysis to demonstrate the effectiveness and objectivity of the proposed methods.(4)Research on risk-type decision making method.First,in order to solve the risk-type decision making problem with three-parameter interval grey number,a TOPSIS decision making method is proposed.Then,considering the limited rationality of decision maker,Regret theory is introduced.Reducing risk on the minimized unit is realized by substituting the distance between decision values and positive-negative ideal points into the “regret-gratification” function.Finally,an example is introduced to compare the proposed decision making method and model,so the reliability and rationality of the proposed methods are verified.Aiming at the multi-attribute decision making problem with the information of three-parameter interval grey number,a series of decision making methods and models are proposed by this paper,by combining with Regret theory,TOPSIS methods,and some effective methods of Grey System theory,like Grey relational analysis methods,Grey clustering methods and SPD methods.On the one hand,the existing distance measurement and sorting methods of three-parameter interval grey numbers are improved,as well as the concept of relative kernel.And all these methods are used in decision making analysis effectively.On the other hand,considering the limited rationality and different attitudes for risk of decision makers when they are at risk,Regret theory is introduced for analysis,grey relational clustering decision model and risk-type decision model based on Regret theory are further proposed.Therefore,the some deficiencies in process of traditional decision making methods are made up,and the theory system of Grey decision making is enriched and perfected.