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<p>Hypersoft set theory has become an essential mathematical framework for modeling multi-parameter uncertainty; however, most of its current extensions, including fuzzy and intuitionistic hypersoft sets, still depend on the decision-maker’s subjective evaluation when assigning (non-)membership degrees within the interval (0,&#xa0;1). This dependence restricts objectivity, reproducibility, and analytical robustness in uncertainty-based decision processes. To address this limitation, this paper introduces the novel concepts of relational and inverse relational hypersoft (non-)membership degrees, which enable the <i>objective computation</i> of these values through relational mappings that fully eliminate subjective numerical input. The proposed theoretical model is rigorously analyzed to ensure internal consistency, boundedness, and interpretability. Building on these concepts, two relational decision-making algorithms are developed to demonstrate their practical applicability. Experimental evaluation on an uncertainty problem reveals that the proposed relational hypersoft framework yields more reliable, consistent, and closer-to-ideal decisions compared to fuzzy-hypersoft and intuitionistic-hypersoft models. Moreover, the relational structure enhances information granularity and computational transparency by deriving (non-)membership degrees directly from binary expert judgments. Overall, this study contributes a mathematically grounded and decision-maker-independent approach that strengthens the theoretical foundation of hypersoft set theory and expands its practical capability in complex decision-making under uncertainty.</p>

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Relational assessment in hypersoft sets: a decision-maker driven approach

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月7日

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  • Orhan Dalkılıç

摘要

Hypersoft set theory has become an essential mathematical framework for modeling multi-parameter uncertainty; however, most of its current extensions, including fuzzy and intuitionistic hypersoft sets, still depend on the decision-maker’s subjective evaluation when assigning (non-)membership degrees within the interval (0, 1). This dependence restricts objectivity, reproducibility, and analytical robustness in uncertainty-based decision processes. To address this limitation, this paper introduces the novel concepts of relational and inverse relational hypersoft (non-)membership degrees, which enable the objective computation of these values through relational mappings that fully eliminate subjective numerical input. The proposed theoretical model is rigorously analyzed to ensure internal consistency, boundedness, and interpretability. Building on these concepts, two relational decision-making algorithms are developed to demonstrate their practical applicability. Experimental evaluation on an uncertainty problem reveals that the proposed relational hypersoft framework yields more reliable, consistent, and closer-to-ideal decisions compared to fuzzy-hypersoft and intuitionistic-hypersoft models. Moreover, the relational structure enhances information granularity and computational transparency by deriving (non-)membership degrees directly from binary expert judgments. Overall, this study contributes a mathematically grounded and decision-maker-independent approach that strengthens the theoretical foundation of hypersoft set theory and expands its practical capability in complex decision-making under uncertainty.