高维简单关联函数：定义、性质与数值模拟

汤龙; 李兴森; 张玲玲; 田英杰

doi:10.12052/gdutxb.250173

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高维简单关联函数：定义、性质与数值模拟

可拓学与创新方法 | 更新时间：2026-08-04

- 高维简单关联函数：定义、性质与数值模拟
- High-dimensional Simple Dependent Function: Definition, Properties and Numerical Simulation
- 广东工业大学学报 2026年43卷第4期页码：115-121
- 作者机构：
  
  1. 南京信息工程大学人工智能学院,江苏,南京,210044
  2. 广东工业大学可拓学与创新方法研究所,广东,广州,510006
  3. 中国科学院大学经济与管理学院,北京,100190
- 作者简介：
  
  汤龙(1985–)，男，副教授，博士，主要研究方向为数据挖掘、可拓智能，E-mail：longt@nuist.edu.cn
- 基金信息：
  
  江苏省自然科学基金资助项目 (BK20221341)
- DOI：10.12052/gdutxb.250173
  中图分类号： O174.4
- 纸质出版：2026
- 稿件说明：
移动端阅览
汤龙, 李兴森, 张玲玲, 等. 高维简单关联函数：定义、性质与数值模拟[J]. 广东工业大学学报, 2026, 43(4): 115-121.
汤龙, 李兴森, 张玲玲, 等. 高维简单关联函数：定义、性质与数值模拟[J]. 广东工业大学学报, 2026, 43(4): 115-121. DOI： 10.12052/gdutxb.250173.

DOI： 10.12052/gdutxb.250173

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的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 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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references

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