An Algorithmic MADM Framework for Risk Assessment Based on Complex Einstein Aggregation Operators

Business risk assessment is a critical component of effective decision making, as it requires the systematic evaluation of multiple alternatives under diverse and often uncertain criteria. With the rapid growth of complex and heterogeneous business data, conventional decision making approaches may face difficulties in simultaneously representing incomplete information, uncertainty, and periodic behavior. These challenges highlight the need for flexible and computationally effective algorithmic frameworks capable of supporting structured risk assessment under uncertain and phase-dependent decision information. To address these challenges, this study developed an Einstein aggregation framework for complex single-valued neutrosophic soft sets (CSvNSSs). This research introduced neutrosophic Einstein weighted average and neutrosophic Einstein weighted geometric aggregation operators to enable nonlinear aggregation of uncertain decision information. The proposed framework provides a flexible mechanism for effectively integrating complex, periodic, and incomplete information in risk assessment and decision-making problems. Fundamental properties of the proposed operators are established to verify their mathematical consistency and applicability. Subsequently, a risk-aware MADM algorithm is developed to aggregate expert assessments, incorporate attribute weights, and rank competing alternatives under simultaneous data and parametric uncertainty. A hypothetical business-location case study is presented to illustrate the computational applicability of the proposed framework, and additional synthetic decision problems are used to examine numerical scalability and internal consistency. The resulting rankings are further examined through comparative analysis with existing aggregation-based decision-making approaches. Finally, this article is concluded with complete research findings, its limitations and future research direction.