用区间直觉模糊集方法对属性权重未知的群求解其多属性决策

本文首先提出群区间直觉模糊有序加权几何(groupinterval-valuedintuitionistic fuzzy orderedweighted geometric,GIVIFOWG)算子和群区间直觉模糊有序加权平均(group interval-valued intuitionistic fuzzy ordered weighted averaging,GIVIFOWA)算子.利用GIVIFOWG算子或GIVIFOWA算子聚集群的决策矩阵以获得方案在属性上的综合区间直觉模糊决策矩阵(collectiveinterval-valuedintuitionistic fuzzy decision-matrix,CIVIFDM).然后定义了一个考虑犹豫度的区间直觉模糊熵(interval-valuedintuitionistic fuzzyentropy,IVIFE);通过熵衡量每个属性所含的信息来求解属性权重.最后,提出基于可能度的接近理想解的区间排序法(interval technique for order preference by similarity to an ideal solution,ITOPSIS)和区间得分函数法.在ITOPSIS法中,依据区间距离公式计算候选方案和理想方案的属性加权区间距离,进而采用ITOPSIS准则对各方案进行排序;在区间得分函数法中,算出CIVIFDM中各方案的得分值以及精确值,然后利用区间得分准则对各方案进行排序.实验结果验证了决策方法的有效性和可行性.

Interval-valued intuitionistic fuzzy set method for group multi-attribute decision-making with unknown attribute weights

We introduce the group interval-valued intuitionistic fuzzy ordered weighted geometric (GIVIFOWG) operator and the group interval-valued intuitionistic fuzzy ordered weighted averaging (GIVIFOWA) operator. All the decision matrices of group are integrated into a collective interval-valued intuitionistic fuzzy decision matrix (CIVIFDM) by GIVIFOWG or GIVIFOWA operator. Next, the interval-valued intuitionistic fuzzy entropy (IVIFE) with hesitancy degree is defined and used to calculate attribute weights according to the information of every attribute. Finally, the interval technique for order preference by similarity to an ideal solution (ITOPSIS) method and the interval score function method both based on possibility degree are presented. In the ITOPSIS method, the attribute weighted interval distance between every alternative and the ideal-positive alternative is calculated by the interval distance formula; then, the ITOPSIS criterion is applied to determine the ranking order of all the alternatives. In the method of interval score function, the score values and accuracy values of all the alternatives in CIVIFDM are calculated, and the ranking order of all the alternatives is determined through the interval score criterion. The simulation shows the validity and feasibility of the proposed decision-making method.