Generalized hesitant fuzzy information fusion using extended partitioned Bonferroni mean operator with application in decision-making

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 intra-partition 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 intra-partition 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.