A Normalized Weighted Bonferroni Mean Aggregation Operator in Neutrosophic Vague Multi-Criteria Decision- Making

Abstract

Decision-making problems involve uncertain and incomplete information, which can be well represented by the Neutrosophic set (NS). Various extensions of NS are available in the literature for solving such problems. However, the published extensions of NS have some restrictions such as single based membership degree. Neutrosophic vague set (NVS) is a newly developed theory to address the shortcomings of previous set theory. NVS is structured based on interval membership in the context of dependent membership functions. Beside uncertainty information, aggregation operators (AOs) are critical components in real-world decision-making issues. As a generalization to the conventional aggregation functions defined on the set of real numbers, numerous AOs have been presented in the literature. Each AO provides a distinct purpose in effectively resolving decision-making problems. Recently, Bonferroni meant (BM) operator has received great attention among scholars because of its ability to consider interrelationship among criteria available in decision-making problems. Based on the advantages of the NV and BM operator, we would like to fill in the gaps by developing a Neutrosophic vague normalized weighted Bonferroni mean (NV-NWBM). In addition, five mathematical properties related to proposed AO are also examined. Besides that, a three-phase decision-making framework is presented to clarify that the proposed AO can be applied to real world decision-making issues. The NV-NWBM operator along with decision-making framework is applied to the example of investment selection under NV environment. The finding shows a computer company is the best alternative for investment. Finally, influence of parameter is performed to validate the effect of parameter towards ranking order.