基于Normative算子的HFS数值延拓方法及多属性决策应用

摘要

A numerical extending (NE) method for hesitant fuzzy sets (HFSs) based on normative operator is proposed to solve the problem that the membership number of the HFS is usually unequal .Meanwhile ,we point out the weakness of the existing NE extending method for HFS .In this new method ,without new deci-sion-making information adding ,it extends the shorter membership with the mean of the existing membership of the given HFSs until all of them have the same length .Furthermore ,we summarize the HFSs NE method with the help of the ordered weighted averaging (OWA) operators .Finally we apply the proposed methods in deci-sion-making problems for multi-sensor electronic reconnaissance intelligence processing .Then we make the de-cision based on the developed technique for the order preferences by similarity to ideal solution (TOPSIS )-ε method .Combined with the simulation example ,the effects of the different distance measures ,distance param-eters and attribute w eights on the decision result are demonstrated .It also show s the superiority of the proposed approach in stability and intuitiveness for the HFSs' NE in detail .%为解决犹豫模糊集(hesitant fuzzy set ,HFS)隶属度数值个数不一致的问题,讨论了现有数值延拓(numerical extending ,NE)方法的局限性,提出基于Normative算子的 HFS NE方法,在没有新息加入的条件下,依次选取现有 HFS隶属度可能值的均值作为一个新的延拓隶属度,直至所有 HFS隶属度个数相等为止,并基于有序加权平均(ordered weighted averaging ,OWA)算子归纳隶属度统一方法.最后将所提出的方法应用到多传感器电子侦察情报的多属性决策问题中,基于改进的逼近理想解(technique for order preferences by similarity to ideal solution ,TOPSIS-ε)法对各信源 HFS属性判决进行多属性决策.仿真试验分析了距离、距离参数、属性权重对决策结果的影响,并详细对比和验证了新方法在 HFS隶属度NE方面的稳定性和直观性.