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

Tang Long; Li Xingsen; Zhang Lingling; Tian Yingjie

doi:10.12052/gdutxb.250173

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

更新时间：2026-08-04

- High-dimensional Simple Dependent Function: Definition, Properties and Numerical Simulation
- Vol. 43, Issue 4, Pages: 115-121(2026)
- 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：
- 基金信息：
- DOI：10.12052/gdutxb.250173
  CLC： O174.4
- Published：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

杨春燕, 蔡文, 汤龙. 可拓学[M]. 2版. 北京: 科学出版社, 2024.

TIAN Y J, LIU D L, LI X S. Extension classification method for label variability[J]. Journal of Guangdong University of Technology, 2025, 42(4): 1-7.

蔡文. 物元分析[M]. 广州: 广东高等教育出版社, 1994.

LI Q X, LIU S F. The method to construct interval elementary dependent function based on the interval distance and side-distance[J]. Journal of Harbin Institute of Technology, 2006, 38(7): 1097-1100.

YANG C Y, CAI W. Recent research progress in dependent functions in extension sets[J]. Journal of Guangdong University of Technology, 2012, 29(2): 7-14.

LI Q X, YANG C Y. One-dimensional dependent function based on three nested intervals with finite positive in extension set[J]. Science Technology Review, 2014, 32(36): 48-51.

CHEN X G, BIAN X F, WANG C Q. Construction method of uncertain type elementary dependent function in three nested intervals[J]. Journal of Heilongjiang University of Science Technology, 2016, 26(1): 106-109.

HU B Q, HE J J. Interval extension set and its dependent function on interval domain[J]. Journal of Guangdong University of Technology, 2001, 18(1): 48-54.

TANG L, YANG C. A novel establishing method for 1-dimensional elementary dependent function by standard interval transformation[C] //2016 International Conference on Oriental Thinking and Fuzzy Logic: Celebration of the 50th Anniversary in the era of Complex Systems and Big Data. Cham: Springer International Publishing, 2016: 563-575.

SMARANDACHE F. Extenics in higher dimensions [M]. Des Moines, USA: Infinite Study, 2012.

LI Z M, YANG C Y. Construction method of two-dimensional elementary dependent function in three nested regions[J]. Journal of Liaoning Technical University (Natural Science) , 2015, 34(2): 267-272.

CHEN X G, BIAN X F, PENG M H, et al . Construction method of uncertain type elementary correlation function under three nested regions[J ] . Journal of Heilongjiang University of Science Technology, 2018, 28(2): 124-128.

杨春燕. 可拓创新方法[M]. 北京: 科学出版社, 2017.

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