基于Lagrange插值多项式的接近性关联度决策模型及其应用

Decision-making Model and Application of the Relation Degree of Nearness Based on Lagrange Interpolation Polynomial

针对实数情形的灰色关联决策问题，提出了一种选择最优方案的新方法：首先计算出各个方案和理想方案的Lagrange插值多项式，并利用黎曼积分计算出各个方案和理想方案两曲线之间的面积，进而构造接近性关联度，通过比较接近性关联度来选择最优方案．然后针对区间灰数情形，提出分别计算出各方案的下界序列到理想方案的下界序列的接近性关联度，各方案的上界序列到理想方案的上界序列的接近性关联度后再计算两者的新型综合关联度，并通过比较综合关联度来选择最优方案．最后通过实数和区间灰数两个不同的算例来进一步验证了该方法的可行性、合理性和有效性．

For the grey relational decision problems in the real number situation, this paper proposes a new method to choose the optimum scheme： 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, construct relation degree of nearness, and through the comparison of relation degree of nearness to choose the optimum 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 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.