Soft Set Extensions via Isotonic Spaces: Theory and Application to Risk-Based Decision Making

Abstract

This paper investigates the theoretical structure and practical implications of isotonic extensions of soft sets. It utilizes isotonic operators—functions satisfying groundedness and order-preserving properties—to derive new soft sets that reflect observed attributes and potential latent associations within a system. This study presents foundational results on preserving key soft set structures under isotonic extension and examines how internal approximation relations evolve under such operators. The study provides an application to infectious disease risk modeling in a hospital environment as a practical demonstration. Here, isotonic extensions enable the identification of asymptomatic but exposed individuals, offering a novel mathematical approach to decision-making under uncertainty.

Keywords

• Soft sets
• closure operators
• isotonic spaces
• decision making
• medical diagnosis

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