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

Abdurrahman Dayioglu (), Fatma Ozen Erdogan and Basri Celik
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Abdurrahman Dayioglu: Department of Mathematics, Bursa Uludag University, Nilufer, Bursa 16059, Turkiye
Fatma Ozen Erdogan: Department of Mathematics, Bursa Uludag University, Nilufer, Bursa 16059, Turkiye
Basri Celik: Department of Mathematics, Bursa Uludag University, Nilufer, Bursa 16059, Turkiye

Mathematics, 2025, vol. 13, issue 16, 1-27

Abstract: 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.

Keywords: soft set theory; relational membership function; decision-making algorithms; uncertainty modeling; decision support systems; open-source AI tools (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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