Enhancing Business System Performance Through Confidence-Based Algebraic Aggregation and the p, q, r-Fraction Fuzzy Model for Robust Decision-Making

Effective business system management necessitates strategic planning, efficient resource monitoring, and consistent team coordination.In practice, decision-making (DM) processes are frequently challenged by uncertainty, imprecision, and the need to aggregate diverse information sources.To address these complexities, a confidence-based algebraic aggregation framework incorporating the p, q, r-Fraction Fuzzy model has been proposed to enhance decision accuracy under uncertain environments.Within this framework, four novel aggregation operators are introduced: the Confidence p, q, r-Fraction Fuzzy Weighted Averaging Aggregation (Cpqr-FFWAA) operator, the Confidence p, q, r-Fraction Fuzzy Ordered Weighted Averaging Aggregation (Cpqr-FFOWAA) operator, the Confidence p, q, r-Fraction Fuzzy Weighted Geometric Aggregation (Cpqr-FFWGA) operator, and the Confidence p, q, r-Fraction Fuzzy Ordered Weighted Geometric Aggregation (Cpqr-FFOWGA) operator.These operators are designed to capture the inherent vagueness and subjectivity in business-related decision inputs, thereby facilitating robust assessments.The theoretical properties of the proposed operators-such as idempotency, boundedness, and monotonicity-are rigorously analyzed to ensure mathematical soundness and operational reliability.To illustrate the practical applicability of the model, a detailed case study is provided, demonstrating its effectiveness in maintaining resource sufficiency, preventing financial disruptions, and ensuring organizational coherence.The use of these aggregation mechanisms allows for systematic integration of expert confidence levels with varying degrees of fuzzy information, resulting in optimized decisions that are both data-informed and uncertainty-resilient.The methodological contributions are positioned to support real-world business contexts where dynamic inputs, incomplete data, and human judgment intersect.Consequently, the proposed approach offers a substantial advancement in intelligent decision-support systems, providing a scalable and interpretable tool for business performance enhancement.