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近年来，三支决策在实际应用和理论研究方面均取得了迅速发展，尤其是作为三支决策独具价值的衍生脉络，三支决策空间已成为当前研究的热门主题之一。目前，关于三支决策空间的研究主要集中在2个方面：1）基于常用聚合函数的半三支决策空间到三支决策空间的转换方法；2）基于模糊集及其衍生集的（半）三支决策空间构造方法。与此同时，copula函数作为一类重要的聚合函数，已在金融、保险等领域得到广泛应用，却尚未被引入至三支决策空间中。因此，鉴于常用聚合函数为三支决策空间发展起到的推动作用，本文旨在基于copula函数，围绕三支决策空间中前述热点问题开展拓展研究。具体而言，首先，提出3种基于copula函数的半三支决策空间到三支决策空间的转换方法；其次，借助copula函数给出一些基于模糊集的（半）三支决策空间构造方法；最后，对所提方法进行包含数据集实验、对比分析及灵敏度分析的数值实验。实验结果表明，所提方法具备可行性和有效性，且所提方法中的参数也具备有效性和稳定性。
Abstract：In recent years, three-way decisions have achieved rapid development both in practical applications and theoretical research. In particular, as a distinctive and valuable extension of three-way decisions, three-way decision spaces have become one of the current research focuses. At present, research on three-way decision spaces mainly focuses on two aspects: 1) the transformation methods from semi-three-way decision spaces to three-way decision spaces based on common aggregation functions; 2) the construction methods of(semi-) three-way decision spaces based on fuzzy sets and their derived sets. Meanwhile, as a vital class of aggregation functions, copula functions have been widely applied in fields such as finance and insurance, yet they have not been introduced into three-way decision spaces. Therefore, given the significant role of common aggregation functions in advancing three-way decision spaces,this paper aims to conduct extended research on the aforementioned research topics in three-way decision spaces using copula functions. Specifically, firstly, three transformation methods from semi-three-way decision spaces to three-way decision spaces based on copula functions are proposed. Secondly, using copula functions, some construction methods of(semi-) three-way decision spaces based on fuzzy sets are proposed. Finally, comprehensive numerical experiments are conducted, including dataset experiments, comparative analysis, and sensitivity analysis of the proposed methods.The experimental results show that the proposed methods are feasible and effective, and the parameterin the proposed methods is also effective and stable.
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基本信息:
DOI：10.12194/j.ntu.20250611001
中图分类号:O225
引用信息:
[1]王一丁,乔军胜,李腾彪,等.基于copula函数的半三支决策空间到三支决策空间的转换方法及其应用[J].南通大学学报(自然科学版),2025,24(03):12-22.DOI:10.12194/j.ntu.20250611001.
基金信息:
国家自然科学基金地区科学基金项目（62166037）;国家自然科学基金重点基金项目（U2433216）; 甘肃省自然科学基金基础研究创新群体项目（25JRRA002）; 国家重点研发计划项目（2024YFE0202700）; 江苏省自然科学基金项目（BK20231337）; 江苏省高等学校自然科学研究面上项目（24KJB520032）