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<p>Soft set theory has emerged as an effective mathematical tool for modeling and analyzing uncertainty in complex and ambiguous environments. Despite its conceptual flexibility, existing formulations of soft set theory encounter notable limitations in representing interdependent parameters and in deriving objective, interpretable solutions from ambiguous data. To address these deficiencies, this study introduces the novel concept of <i>condensed soft sets</i>, which provides a systematic mechanism for reducing redundant parameters and revealing the structural relationships among them. The proposed framework establishes new mathematical definitions and operations, extending the classical foundations of soft set theory through innovative notions such as <i>pulling</i> and <i>pushing forces</i>. These formulations enable the quantitative modeling of parameter interactions, offering a richer and more dynamic analytical structure. To demonstrate its effectiveness, the proposed approach is implemented in a medical decision-making scenario, highlighting its ability to capture complex dependencies among clinical parameters. Overall, this research contributes to the literature by introducing a new conceptual layer to soft set theory, establishing a unified and computationally efficient framework that can inspire further developments in uncertainty modeling and intelligent decision-making.</p>

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Opening new directions toward topological structures in condensed soft sets with applications to medical decision-making

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年7月14日

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  • Orhan Dalkılıç,
  • Naime Demirtaş,
  • Muhammad Riaz

摘要

Soft set theory has emerged as an effective mathematical tool for modeling and analyzing uncertainty in complex and ambiguous environments. Despite its conceptual flexibility, existing formulations of soft set theory encounter notable limitations in representing interdependent parameters and in deriving objective, interpretable solutions from ambiguous data. To address these deficiencies, this study introduces the novel concept of condensed soft sets, which provides a systematic mechanism for reducing redundant parameters and revealing the structural relationships among them. The proposed framework establishes new mathematical definitions and operations, extending the classical foundations of soft set theory through innovative notions such as pulling and pushing forces. These formulations enable the quantitative modeling of parameter interactions, offering a richer and more dynamic analytical structure. To demonstrate its effectiveness, the proposed approach is implemented in a medical decision-making scenario, highlighting its ability to capture complex dependencies among clinical parameters. Overall, this research contributes to the literature by introducing a new conceptual layer to soft set theory, establishing a unified and computationally efficient framework that can inspire further developments in uncertainty modeling and intelligent decision-making.