高维简单关联函数:定义、性质与数值模拟

    High-dimensional Simple Dependent Function: Definition, Property and Numerical Simulation

    • 摘要: 关联函数作为定量化的数学工具,在可拓集合与可拓策略的生成与评价中发挥关键作用,能够描述对象在论域内是否具有某种性质的程度。本文提出了一种可操作性强的高维简单关联函数构造方法,并对该高维简单关联函数的关键数学性质进行了严格证明。通过数值模拟与实例分析,展示了该方法在多维评价场景中的适用性与优越性,并对比分析了不同类型的实例。研究结果表明,该方法在高维情形下保持良好可操作性与理论可行性,能够更准确地刻画多评价特征之间的耦合关系,为多评价特征优度评价提供了一种实用的理论和方法工具,同时可用于进一步完善矛盾问题的定量化判定方法。

       

      Abstract: Dependent functions serve as a quantitative mathematical tool, playing a key role in the generation and evaluation of extension sets and extension strategies. They characterize the degree to which an object possesses a given property within a universe of discourse. This paper proposes an easily-to-operate operable construction method for high-dimensional simple dependent functions and provides rigorous proofs of their key mathematical properties. Numerical simulations and case analyses demonstrate the applicability and superiority of this method in multi-dimensional evaluation scenarios, with comparative analyses conducted across various case types. The results indicate that the proposed method maintains high operability and theoretical feasibility even in high-dimensional situations, while more accurately characterizing the coupling relationships among multiple evaluation features. This work provides a practical theoretical and methodological tool for superiority evaluation and can further improve the quantitative assessment of contradictory problems.

       

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