Aczel–Alsina Weighted Aggregation Operators of Neutrosophic Z-Numbers and Their Multiple Attribute Decision-Making Method

Abstract

The new operations based on the Aczel–Alsina t-norm and t-conorm show the advantage of flexible operations by adjusting different parameter values. Motivated based on the new operations, we propose the Aczel–Alsina operations and weighted aggregation operators of neutrosophic Z-numbers (NZNs) to solve the flexible decision-making problem by adjusting different parameter values depending on the decision maker’s preference under the environment of NZNs. To do so, this paper first proposes the Aczel–Alsina t-norm and t-conorm operations of NZNs and develops the NZN Aczel–Alsina weighted arithmetic averaging (NZNAAWAA) and NZN Aczel–Alsina weighted geometric averaging (NZNAAWGA) operators to aggregate NZNs. Then, a multiple attribute decision-making (MADM) method is developed by the NZNAAWAA and NZNAAWGA operators under the NZN environment. Finally, a numerical example is provided to verify the influence of different parameter values on decision-making results. Compared with existing MADM methods, the new MADM method shows its feasibility and flexibility in MADM applications. Moreover, the new MADM approach can not only extend the existing MADM methods, but also overcome the lack of decision-making flexibility of the existing MADM methods.