Constructing interval-valued generalized partitioned Bonferroni mean operator with several extensions for MAGDM

In group decision making, each expert’s background and the level of knowledge and ability differ, which makes the expert’s information inputs to the decision-making process heterogeneous. Such heterogeneity in the information can affect the outcome of the selection of the decision alternatives. This paper therefore attempts to partition the heterogeneous information into homogeneous groups to elicit similar (related) and dissimilar (unrelated) data using a clustering algorithm. We then develop an aggregation approach to gather the collective opinions from the homogeneous clusters to accurately model the decision problem in a group setting. The proposed aggregation approach, labeled as the generalized partitioned Bonferroni mean (GPBM), is studied to investigate the characteristics of the aggregation operator. Further, we extend the GPBM concept to an interval-valued fuzzy set context using the additive generators of the strict t-conorms and we develop two other new aggregation operators: the interval-valued GPBM (IVGPBM) and the weighted IVGPBM (WIVGPBM). We analyze the aggregation of fuzzy numbers by the IVGPBM operator using interval arithmetic involving \(\alpha\)-cuts and the \(\alpha\)-cut-based decomposition principle of fuzzy numbers. Two practical examples are presented to illustrate the applicability of these operators, and a comparison is conducted to highlight the effects of the confidence level and the sensitivity of the parameters chosen, analyzing the results with the parameterized strict t-conorm. Finally, we compare the experimental results of the proposed method with existing methods.