Navigating ambiguity: A novel neutrosophic cubic shapley normalized weighted Bonferroni Mean aggregation operator with application in the investment environment

Abstract

The Neutrosophic Cubic Shapley Normalized Bonferroni (NC-SNWBM) method represents a cutting-edge approach to decision making theory, combining three distinct mathematical frameworks the neutrosophic cubic sets (NCS), Shapley values, and the Bonferroni aggregation operator. This innovative method addresses the challenges posed by uncertainty, vagueness, and imprecision in decision-making (DM) processes, offering a comprehensive and versatile tool for handling complex and dynamic scenarios. Neutrosophic cubic sets offers a strong platform to handle ambiguous and vague data due to three components Membership Grade (MG), Non-Membership Grade (NMG) and Indeterminancy Grade (IG) in data. By adding Shapley Fuzzy Measures (SFM), which come from cooperative game theory, distribute values among cooperative agents equally and to account for each agent's contributions to all potential coalitions. The Bonferroni aggregation operator—a statistical aggregative tool that regulates the likelihood of many types in error in statistical tests and the interdependence of the input arguments by allowing different values to parameters involved. These values are further improved by normalization in the framework of the NC-SNWBM approach in order to consider the various degrees of impact that agents exert in various circumstances. This operator is smoothly combined with normalized Shapley values and neutrosophic cubic sets in the NC-SNWBM approach to enable the aggregation of data with different levels of imprecision and uncertainty from various sources using NCS. The MG, NMG and IG connected to NCS are important elements of the NC-SNWBM approach. To evaluate each element's contribution to the overall value distribution SFM are used, and the Bonferroni aggregation operator maintains a careful balance between conservatism and significance. Together, these components provide a thorough framework that successfully tackles the problems caused by ambiguity, imprecision, and uncertainty in scenarios involving decision-making. The NC-SNWBM operator is applied to a numerical problem as an application in investment environment and sensitive and comparative analysis are conducted. The recommendation based on sensitive and comparative analysis proposed.

Keywords

• Neutrosophic cubic set (NCS)
• Shapley fuzzy measure (SFM)
• Bonferroni Mean (BM)
• Decision making (DM)