Satisfaction with life scale is a comprehensive cognitive judgement of individual’s own life and becomes the dominant measure of life satisfaction. However, the individual may hesitate to assess his/her life satisfaction with a single value due to multiple criteria. Consequently, we propose the hesitant fuzzy satisfaction with life scale (HFSWLS) with the same form as hesitant fuzzy element (HFE), consisting of several possible values of the cognitive judgements to describe the uncertainties and hesitancies. In this paper, we propose a novel aggregation method for large scale HFEs and apply it to HFSWLSs. Primarily, we present the necessary requirements of the extension rules for HFEs to guarantee the reversibility and linearity of the proposed operators. In the proposed aggregation method, we cluster the individuals based on their feature values and further define the hesitant fuzzy feature pair to find out the abnormal HFEs. We generate each cluster’s center HFE by the proposed operators in the first-round aggregation. Based on the orness degree relating to the cluster’s feature value and the decision makers’ preferences to cluster’s feature value, we derive the weights of the center HFEs by O’Hagan’s nonlinear optimization, leading to the final aggregation result taking into account the actual demand. Finally, the validity and effectiveness of the proposed aggregation method for HFEs are testified by the application of HFSWLSs of the citizens.

对生活量表的满意是对个人生活的全面认知判断，并成为生活满意度的主要衡量指标。然而，由于多个标准，个人可能会犹豫以单个值来评估他/她的生活满意度。因此，我们提出了犹豫模糊的生活满意度量表（HFSWLS），其形式与犹豫模糊元素（HFE）一样，由认知判断的几种可能值组成，以描述不确定性和犹豫性。在本文中，我们提出了一种针对大型HFEs的新型聚合方法，并将其应用于HFSWLSs。首先，我们提出了HFE扩展规则的必要要求，以保证所提议算子的可逆性和线性。在建议的汇总方法中，我们根据特征值对个体进行聚类，并进一步定义犹豫的模糊特征对，以找出异常的HFE。我们在第一轮汇总中由建议的运营商生成每个集群的中心HFE。基于与集群特征值相关的折衷度以及决策者对集群特征值的偏好，我们通过O'Hagan的非线性优化得出中心HFE的权重，从而在考虑到实际需求的情况下得出最终的聚合结果。最后，通过对居民的HFSWLSs的应用证明了所提出的HFEs聚集方法的有效性和有效性。基于与集群特征值相关的折衷度以及决策者对集群特征值的偏好，我们通过O'Hagan的非线性优化得出中心HFE的权重，从而在考虑实际需求的情况下得出最终的聚合结果。最后，通过对居民的HFSWLSs的应用，证明了所提出的HFEs聚合方法的有效性和有效性。基于与集群特征值相关的折衷度以及决策者对集群特征值的偏好，我们通过O'Hagan的非线性优化得出中心HFE的权重，从而在考虑到实际需求的情况下得出最终的聚合结果。最后，通过对居民的HFSWLSs的应用证明了所提出的HFEs聚集方法的有效性和有效性。