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
References
- D. A. Molodtsov, Soft set theory-First results, Computers and Mathematics with Application 37 (4-5) (1999) 19-31.
- M. M. Day, Convergence, closure, and neighborhoods, Duke Mathematical Journal 11 (1944) 181-199.
- F. Hausdorff, Gestufte raume, Fundamenta Mathematicae 25 (1) (1935) 486-502.
- K. Kuratowski, Topology, Academic Press, 1966.
- E. Čech, Z. Frolik, M. Katetov, Topological spaces, Publishing House of the Czechoslovak Academy of Sciences, 1966.
- S. Gnilka, On extended topologies I: Closure operators, Commentationes Mathematicae 34 (1994) 81-94.
- S. Gnilka, On extended topologies II: Compactness, quasi-metrizability, symmetry, Commentationes Mathematicae 35 (1995) 147-162.
- S. Gnilka, On continuity in extended topologies, Commentationes Mathematicae 37 (1997) 99-108.
- P. C. Hammer, Extended topology: Set-valued set functions, Nieuw Archief voor Wiskunde 10 (1962) 55-77.
- P. C. Hammer, Extended topology: Continuity I, Portugaliae Mathematica 25 (2) (1964) 77-93.