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

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中图分类号：0159；TP18 文献标志码：A 文章编号：1673-2340（2025）03-0012-11

Transformation methods from semi-three-way decision spaces to three-way decision spaces based on copula functions and their applications

WANGYidingl，QIAO Junshengl，3*，LI Tengbiao²，DINGWeiping4 （1.College of Mathematics and Statistics，Northwest Normal University，Lanzhou 73oo7o，China;

2.School of Mathematics and Statistics，Lanzhou University，Lanzhou 73oooo， China;

3. Gansu Provincial Research Center for Basic Disciplines of Mathematics and Statistics，Lanzhou 73oo7o， China;

4.Schoolof Artificial Intelligence and Computer Science，Nantong University，Nantong 226ol9，China） Abstract： Inrecent years，three-waydecisions haveachieved rapid developmentboth in practical applications and theoreticalresearch.In particular，asa distinctiveandvaluable extension of three-waydecisions，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：l） 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

basedonfuzzysetsandtheirderivedsets.Meanwhile，asavitalclassofaggregation functions，copula functions have been widelyapplied in fields suchas financeand insurance，yet theyhave 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，someconstruction methods of （semi-）three-way decisionspaces based on fuzzysets are proposed.Finaly，comprehensive numerical experiments areconducted，including datasetexperiments，comparativeanalysis，and sensitivityanalysisof the proposed methods. The experimental results show that the proposed methods are feasible and efective，and the parameterin the proposed methods is also effective and stable.

Key words： （semi-）three-way decision spaces; （semi-） decision evaluation functions;copula functions;three-way decisions; fuzzy sets;aggregation functions

2010年，Yao基于决策理论粗糙集和决策情景提出了三支决策。（剩余14369字）