RMVC: A Validated Algorithmic Framework for Decision-Making Under Uncertainty

• Published in: Mathematics (Basel) Vol. 13; no. 16; p. 2693
• Main Authors: Dayioglu, Abdurrahman, Erdogan, Fatma Ozen, Celik, Basri
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.08.2025
• Subjects: Algorithms; Artificial intelligence; Decision making; decision support systems; decision-making algorithms; Expert systems; Fuzzy sets; Methods; Missing data; Multiple criteria decision making; open-source AI tools; Python; relational membership function; Sensitivity analysis; Set theory; soft set theory; uncertainty modeling; Turkey
• ISSN: 2227-7390; 2227-7390
• DOI: 10.3390/math13162693

The reliability of decision-making algorithms within soft set theory is fundamentally constrained by their underlying membership functions. Traditional binary approaches overlook the implicit connections between the attributes a candidate possesses and those it lacks—connections that can be inferred from the wider candidate pool. To address this core challenge, this paper puts forward the Relational Membership Value Calculation (RMVC), an algorithmic framework whose core is a fine-grained relational membership function. Our approach moves beyond binary logic to capture these nuanced interrelationships. We provide a rigorous theoretical analysis of the proposed algorithm, including its computational complexity and robustness, which is validated through a comprehensive sensitivity analysis. Crucially, a comparative analysis using the Gini Index quantitatively demonstrates that our method provides significantly higher granularity and discriminatory power on a representative case study. The RMVC is implemented as an open-source Python program, providing a foundational tool to enhance the reasoning capabilities of AI-driven decision support and expert systems.