区间值犹豫模糊集群决策模型及其应用

Interval-valued hesitant fuzzy set group decision making model and its application

为了更好地解决区间值犹豫模糊集(IVHFS)群决策问题,利用平面向量建立了一种可以从多个角度判定方案优劣的群决策模型.首先,在IVHFS中定义了区间值隶属度的中位数、区间值隶属度的清晰度,并以此通过构造平面向量来刻画IVHFS.其次,通过利用平面向量簇刻画IVHFS建立了区间值犹豫模糊元(IVHFE)的外部固定函数模型和内部稳定函数模型,给出比较2个IVHFE大小的准则和计算二者距离的方法,并根据所有方案的外部固定函数值和内部稳定函数值分别计算了测评准则的外部权重和内部权重(依据外部权重与内部权重的相离程度值来确定测评准则的综合权重).再次,通过利用参数调整方案的外部固定函数值与内部稳定函数值的比例计算了各个方案的综合决策值.最后,利用数值算例验证了本文方法的可行性.

To solve the interval-value hesitant fuzzy set group decision making problem,a group decision model which can observe the scheme ordering results from multiple perspectives was established by using plane vector knowledge.Firstly,the median and clarity of interval-valued membership degree were defined in the intervalvalued hesitant fuzzy set,and the interval-valued hesitant fuzzy set was described by forming a plane vector.Secondly,the external fixed function model,the internal stable function model,the size comparison criterion and the distance measure model of two interval-valued hesitant fuzzy elements were established by describing the interval-valued hesitant fuzzy sets with the plane vector clusters.The external weight and internal weight of the evaluation criteria were calculated respectively according to the external fixed function values and internal stability function values of all schemes(the comprehensive weight of the evaluation criteria was determined according to the degree of separation between the external weight and the internal weight).Thirdly,the ratio between the external fixed function value and the internal stable function value of the scheme was adjusted by parameter,and the comprehensive decision value of each scheme was calculated.Finally,a numerical example was used to verify the feasibility of the proposed method.