联系向量距离与灰色关联度结合的理想解法

TOPSIS Method of Connecting Connection Vector Distance with Grey Correlation Degree

针对传统理想解法采用欧氏距离计算的缺陷,提出了联系向量距离与灰色关联度结合的理想解法.首先将理想点与负理想点均视为确定不确定系统中相互对立的集合,计算各待决策方案与理想解和负理想解的联系向量距离;然后采用灰色关联度方法计算各待决策方案与理想解和负理想解之间的相似程度;其次通过定义新的综合距离和综合距离贴近度构建联系向量距离与灰色关联度结合的理想解法.该方法在有效地解决传统理想解法缺陷的基础上,还包含了待决策方案在趋势上的差异性,同时综合距离在权重分配上充分考虑了决策者的偏好或者专家意见,使评价结果更加有效.最后采用算例验证了该方法的可行性和有效性.

Aiming at the defects of traditional TOPSIS method,this paper presents a new TOPSIS method combining the connection vector distance and grey correlation degree.Firstly,the connection vector distance between each scheme to be decided and the ideal solution and the negative ideal solution is calculated,in which the ideal solution and the negative ideal solution are regarded as the opposite sets in the certain or uncertain system;Secondly,the similarity degree between each scheme to be decided and the ideal solution and the negative ideal solution is calculated by using the grey correlation degree method;Thirdly,by defining the new comprehensive distance and the close degree of the comprehensive distance,TOPSIS method of connecting connection vector distance with grey correlation degree is constructed.This method not only solves the defect of traditional ideal solution method effectively,but also contains the difference in the trend of the scheme to be selected,and at the same time,the comprehensive distance fully considers the preference of decision makers or expert opinion in weight allocation,making the evaluation result more effective.Finally,the validity of the method is proved by a classical example.