区间数刻画属性值下的两种多属性决策新算法

Two new algorithms for multi-attribute decision making under attribute values are described by interval number

为了解决区间信息多属性决策问题,建立了两种多属性决策算法(算法1和算法2).算法1:首先利用区间数的积型贴近度公式将属性的区间信息数据转换为精确数值,然后使用Maclaurin对称平均算子集结属性的精确数值,进而通过比较其数值大小来判断方案的优劣.算法2:首先利用区间数的积型贴近度公式算出各方案在所有属性上的积型模糊互补判断矩阵,然后通过求解积型模糊互补判断矩阵的排序向量来判断方案的优劣.研究表明,两种算法的决策路径虽然不同,但其排序结果相同,即不同决策路径不会影响方案的排序结果,因此决策者可以根据实际问题需要选择适当的决策算法及排序规则,以更好地满足决策需求.

In order to solve the problem of interval information multi-attribute decision making,two algorithms(Algorithm 1 and Algorithm 2)of multi-attribute decision making are established in this paper.Algorithm 1:firstly converting the interval information data of attributes into exact values by using the product approximation formula of interval numbers,then aggregating the exact values of attributes by using MacLaurin symmetric average operator,and then the optimal scheme is decided by comparing the exact values of attributes after aggregation.Algorithm 2:firstly constructing a product fuzzy complementary judgment matrix on all attributes of each scheme by using the product approximation formula of interval number,then calculating the ranking vectors of the matrix,and then the optimal scheme is decided according to the ranking vectors.The research shows that although the decision paths of the two algorithms are different,their ranking results are the same,that is,the decision paths will not affect the ranking results of the scheme.So the decision makers can choose the appropriate decision algorithms and sorting rules according to the actual needs of the problems to better meet the decision requirements.