Application of Bipolar Single-Valued Neutrosophic Graphs in Decision-Making Problems

Abstract Objectives: Real-world decision-making environments often involve complex information that is multi-layered, vague, ambiguous, contradictory, or indeterminate, posing significant challenges for traditional decision-making frameworks. This study aims to address these limitations by developing a robust multi-criteria decision model capable of effectively processing such complexity. Methods: An integrated multi-criteria decision model is proposed based on Bipolar Single-Valued Neutrosophic Graphs (BSVNG). In this model, decision alternatives and criteria are represented as vertices, and relational assessments between them are depicted as edges. The approach incorporates six distinct membership classifications—positive truth, negative truth, indeterminate truth, positive indeterminate, negative indeterminate, and false—to better capture diverse and ambiguous information. Two novel operational functions are introduced: the Bipolar Single-Valued Neutrosophic Weighted Arithmetic Average (BSVNWAA) and the Bipolar Single-Valued Neutrosophic Weighted Geometric (BSVNWG). These are used to formulate a comprehensive decision metric for identifying the optimal alternative. Findings: Illustrative examples and empirical results validate the effectiveness of the BSVNG-based model in gathering both supporting and contradictory evidence for decision alternatives. The model consistently yields reliable and robust conclusions, even in multi-dimensional and conflicting information environments, demonstrating its practical utility. Novelty: This research introduces a singular, adaptable, and computationally efficient decision support system that uniquely integrates bipolar uncertainty modeling with graph-based neutrosophic structures. It advances multi-criteria decision-making, risk management, and evaluation methodologies by effectively handling contradictory and ambiguous information through a novel combination of membership classifications and aggregation operators. Keywords: Bipolar Single-Valued Neutrosophic Graphs, Multi-criteria decision-making, aggregation operators, Decision analysis