Automatic clustering is a challenging problem, especially when the decision-maker has little or no information about the nature of the dataset and the criteria of interest. There is a lack of generalizability in the current validity indexes (VI) for automatic clustering algorithms, as each considers a limited number of objectives and mostly ignores the other aspects of clustering validation. The proposed framework benefits from collaboration among selected evolutionary algorithms. A mixed-integer non-linear programming model is developed, and a framework is proposed for a six-step decision support system to solve it. The decision-maker (DM) selects the quantitative (primary) VIs and the evolutionary algorithms. Given DM's knowledge on the dataset and VIs, DM can incorporate qualitative (secondary) VIs. DM determines the quality threshold for each VI and runs the evolutionary algorithms separately. The DSS then saves the best obtained value of VIs in order to prepare the input necessary to construct the aggregated function. Based on the selected primary VIs, a new normalized aggregated function is developed and solved repeatedly using the randomly selected or predefined weights of importance. Eventually, DM employs a proper DEA model to define the final clustering output among all possible solutions. Given multiple efficient solutions, the best-worst method and a multi-criteria decision-making approach are applied to find the final output. The applicability of the proposed approach is illustrated on a synthetic and two secondary datasets, and the result at each step is discussed in detail.

自动聚类是一个具有挑战性的问题，尤其是当决策者对数据集的性质和感兴趣的标准知之甚少或没有信息时。当前自动聚类算法的有效性指标 ( VI )缺乏普遍性，因为每个算法考虑的目标数量有限，并且大多忽略了聚类验证的其他方面。提议的框架受益于选定的进化算法之间的协作。开发了混合整数非线性规划模型，并提出了六步决策支持系统的框架来解决它。决策者 (DM) 选择定量（主要）VI和进化算法。鉴于 DM 对数据集和VI的了解s，DM 可以包含定性（次要）VI s。DM 确定每个VI的质量阈值并分别运行进化算法。然后，DSS 保存获得的最佳VI值，以便准备构建聚合函数所需的输入。基于选定的主要VIs，使用随机选择或预定义的重要性权重开发和解决新的归一化聚合函数。最终，DM 使用合适的 DEA 模型来定义所有可能解决方案中的最终聚类输出。给定多个有效解决方案，应用最佳最差方法和多标准决策方法来找到最终输出。在合成数据集和两个辅助数据集上说明了所提出方法的适用性，并详细讨论了每个步骤的结果。