直觉判断矩阵的直觉模糊数型权重研究

Deriving intuitionistic fuzzy number priority weights from intuitionistic judgment matrix

研究了确定直觉判断矩阵的权重问题,并对与权重的可靠性密切相关的直觉判断矩阵的一致性问题进行了探讨.从直觉模糊数的得分函数和精确度函数角度给出直觉判断矩阵的加型一致性的新定义,并导出加型一致性的等价条件.为了充分利用原直觉判断矩阵的信息以及使决策符合一致性要求,根据加型一致性的等价条件运用转换函数将原直觉判断矩转换为两个加型模糊一致性互补判断矩阵,然后对这两个加型模糊一致性互补判断矩阵运用行和归一的方法分别求出原直觉判断矩阵权重的隶属度和非隶属度,从而得到直觉模糊数型权重,并利用直觉模糊数的排序方法进行排序.最后讨论了决策方法的优良性质,并通过实例验证了决策方法的有效性和实用性.

The problem of the weights of intuitionistic judgment matrix （IGM） was discussed, and the consistency of IGM, which is related to the reliability of the weights, was explored. From the perspectives of the score function and accuracy function of intuitionistic fuzzy value, a new definition of additive consistency of IGM was given, and an equivalent condition for additive consistency was achieved. To make full use of the information of the original IGM and make the decision meet the consistency, the original IGM was converted into two additive consistency fuzzy judgment matrices, which was achieved by the transformation function arising from the equivalent condition. The membership degree and the non membership degree of the original IGM＇s weights were respectively achieved by normalizing rank aggregation to the two additive consistency fuzzy judgment matrices. Thus the intuitionistic fuzzy number priority weights of the IGM were obtained, and ranked with a seauencing rule for intuitionistic fuzzyvalues. The excellent properties of the proposed method were discussed, and its validity and practicability were illustrated in an example.