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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.

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The partitioned Bonferroni mean operator (PBM), which was formulated to outspread the family of the Bonferroni mean operator, has augmented the class of aggregation functions for information accumulation by modeling interrelationship among pairwise disjoint partition sets. It is constructed with the presupposition that the criteria set is subdivided into mutually disjoint partition sets, with homogeneous interconnection among input arguments of intrapartition sets. The PBM operator has accomplished a lot of desirability from the researchers due to its capability of apprehending interconnection among arguments in the information accumulation technique. The central idea of this study is to amplify the existing PBM definition systematically so that heterogeneous interconnections among the criteria of intrapartition sets can be captured. This contemplation prompted us to focus on the systematized proposition of extended partitioned Bonferroni mean (EPBM) operator based on heterogeneous connections of the information retrieved from the partition sets. In this aspect, we also propose the hesitant fuzzy extended partitioned Bonferroni mean (HFEPBM) operator, along with its weighted generalization (WHFEPBM operator), by fitting the concept of strict t-norms and t-conorms into it. To intensify the capacity for modeling real-life decision situations, the extended TOPSIS method and the proposed operator have been employed to detect the weights of decision-makers. A numerical example has been presented to demonstrate the experimental results obtained by utilizing the WHFEPBM operator. The contribution ends by providing a detailed comparative analysis of the proposed method with other existing methods by availing data through the simulation experiment. Keywords Extended partitioned Bonferroni mean (EPBM) • Hesitant fuzzy set (HFS) • Hesitant fuzzy extended partitioned Bonferroni mean (HFEPBM) • Multi-attribute group decision-making (MAGDM) Mathematics Subject Classification 03E72 Communicated by Anibal Tavares de Azevedo.

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