Several Multiple Attribute Decision-Making Models Of Interval Grey Number Models And Its Application

Grey decision-making is an important part of grey system theory and it is widely used in various fields.Due to the limitations of people's awareness,the complexity of the environment and so on,the information we collect may not be accurate but the number of interval grey number.This paper studies the multiple attribute decisionmaking problem of interval grey number.The main contents are as follows:(1)Because of the different attributes of index,we need to normalize the index before making decision or forecast research.Aiming at the two kinds of normalization methods of interval grey number used at present,this paper studies three aspects: the normalized meaning,the kernel and the greyscale.(2)Decision making model of multi-attribute interval grey number based on the distance of general consistency.Firstly,based on the thought of kernel and greyscale of interval grey number,the paper introduced a series of concept such as consistency coefficient,general consistency coefficient and general consistency distance,who trade off the corresponding distance between kernel,greyscale of each scheme and kernel and greyscale of ideal scheme.And this paper gives their respective solutions.Secondly,on the basis of this,a new method of forming the optimal scheme by using the general consistency distance is proposed.Finally,the example is given to illustrate the feasibility and effectiveness of the method.(3)Decision making model of interval grey number based on the close degree of synthesis grey incident.Firstly,the interval grey number sequence is decomposed into“white part sequence” and “grey part sequence” by the method of information decomposition,namely the interval grey number matrix is transformed into two real number matrices.Secondly,this paper constructs a relation degree of nearness which is used to evaluate the degree of nearness of the grey part of the white part.Thirdly,compares the merits and demerits of the scheme with the size of the correlation degree,so as to determine the choice of the scheme.Finally the application examples s given to illustrate the rationality and effectiveness of the method,and the calculation is simple and easy to apply.(4)Decision-making model of the relation degree of nearness based on Lagrange Interpolation polynomial.Firstly,to calculate the Lagrange interpolation polynomial of each scheme and ideal scheme,and calculate the area between the two curves of each scheme and the ideal scheme by using Riemann integral.The new relation degree of the degree of approximation between the two curves is constructed,and it is proved to bethe relation degree of nearness.The size of the relation degree is used to compare the merits and demerits of the scheme,so as to determine the choice of the scheme.Secondly,for the case of the interval grey number,to calculate relation degree of nearness of the sequence of lower bounds of each scheme to the lower bound of the ideal scheme,and relation degree of nearness of the sequence of upper bounds of each scheme to the upper bound of the ideal scheme,then calculate the new synthesis degree of grey incident,and by comparing the new synthesis degree of grey incident to choose the optimal scheme.Finally,through two different examples of real number and interval grey number to verify the feasibility,reasonable and effective of the method.