基于奇异值分解的多评价结论集结方法

针对综合评价中存在的“多评价结论非一致性”问题,提出了一种基于奇异值分解的多评价结论集结方法.对多个不一致评价结论组成的数值矩阵进行奇异值分解,并通过对定义的一致度与可信度两个性能指标的均衡确定出需保留奇异值的个数,运用奇异值分解的原理求出原评价结论的近似结论矩阵,而近似结论是对原有结论的优化.该方法具有提取多评价结论共性信息、削弱极端评价结论影响及对集结过程进行柔性控制等特点.最后,用一个算例验证了方法的有效性.

A Multi-evaluation Conclusion Aggregation Method Based on Singular Value Decomposition

A multi-evaluation conclusion aggregation method based on SVD(singular value decomposition) is put forward aiming at the inconsistency between the evaluation conclusions drawn by different methods.In this way,the SVD is done for the numerical matrix composed of multiple inconsistency conclusions.Then,the number of singular values to be kept are determined by equilibrating the two defined performance indices,i.e.,consistency and reliability.Based on the principle of singular value decomposition,an approximate conclusion matrix is given as the optimization of original conclusions.The method has advantages of picking up common information from multi-evaluation,weakening the impact due to extreme evaluation conclusions and controlling flexibly the aggregation process.A numerical example is given to verify the validity of the method.