The aggregation of Z-numbers based on overlap functions and grouping functions and its application on group decision-making

In this paper, we propose a series of novel aggregation techniques based on overlap and grouping functions for group decision-making (GDM) issues in the Z-number environment. Firstly, we introduce an optimization model to determine the underlying distribution for Z-numbers, meanwhile, the mean function of Z-numbers is revised to better reflect the three-dimensional structure of the Z-numbers. And then, a series of operations for Z-numbers using overlap and grouping function are defined, and their properties are also investigated. Subsequently, we construct the overlap function-based Z-number weighted Bonferroni mean (OZWBM) operator to integrate the information in the Z-number environment. Furthermore, to verify the efficiency of novel aggregation techniques, a new energy investment selection issue is addressed. Besides giving the rankings of alternatives, by analyzing the calculation results, we can also derive the degree of preference from investment experts in scoring each investment object. Finally, by comparing the existing methodologies, we confirm that the new approach is effective and reasonable for the multi-criteria group decision-making (MCGDM).