The partitioned Bonferroni mean (PBM) operator, which was oriented as an elementary attempt to outstretch the Bonferroni mean (BM) operator, has enlarged the class of BM‐type aggregation operators for information accumulation by modeling interrelationship among pairwise disjoint partition sets with the presupposition that the criteria of intra‐partition are homogeneously related to each other, while no relationship exists among criteria of inter‐partition. Although PBM has encountered a lot of attraction from the researchers due to its versatility in information aggregation technique, the principal disadvantage of the existing PBM definitions evolution is that they do not provide any specification regarding the relationship among criteria of partition structure during design, development, and applications of PBM over unalike situations of information fusion. This consideration propels us to focus on the systematic investigation of different variations of PBM operators based on various mandatory requisites to be imposed on information retrieved from the partition sets. In this regard, we propose the construction of novel generalized partitioned Bonferroni mean (GPBM) operator by befitting its suitable components to provide a descriptive configuration, which is quite interpretable, understandable and thus facilitates the ability to model specific mandatory prerequisites in a single operator. To enrich the capacity for modeling real‐life decision situations, the PBM operator is customized to propose optional partitioned Bonferroni mean (OPBM) operator that captures partition‐wise interrelationship among attributes while taking into consideration optional conditions jumbled in each partition set. Furthermore, we demonstrate the construction methodology of generalized OPBM operator that amalgamate the concept of GPBM and OPBM operator to enhance and model‐specific requirements along with optional requirements as per the desires of decision makers.

中文翻译：

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分区 Bonferroni 均值算子对可选先决条件建模的泛化和扩展

分区 Bonferroni 均值 (PBM) 算子是扩展 Bonferroni 均值 (BM) 算子的基本尝试，通过对成对不相交分区集之间的相互关系进行建模，从而扩大了用于信息积累的 BM 类型聚合算子的类别。分区内的标准之间是同质相关的，而分区间的标准之间不存在任何关系。尽管 PBM 由于其在信息聚合技术方面的多功能性而受到了研究人员的广泛关注，但现有 PBM 定义演变的主要缺点是它们在设计、开发、PBM 在信息融合的不同情况下的应用。这种考虑促使我们专注于基于对从分区集中检索的信息强加的各种强制性要求，对 PBM 算子的不同变体进行系统调查。在这方面，我们建议构建新颖的广义分区 Bonferroni 均值 (GPBM) 算子，使其适合其合适的组件以提供描述性配置，该配置非常可解释、易于理解，从而有助于在单个算子中对特定的强制性先决条件进行建模。为了丰富对现实生活中的决策情况进行建模的能力，PBM 算子被定制为提出可选的分区 Bonferroni 均值 (OPBM) 算子，该算子捕获属性之间的分区相互关系，同时考虑到每个分区集中混乱的可选条件。此外，我们展示了广义 OPBM 算子的构造方法，该方法融合了 GPBM 和 OPBM 算子的概念，以根据决策者的愿望增强和模型特定的要求以及可选的要求。