基于新定义的二型模糊偏好关系及其在多准则决策中的应用  

Type-2 fuzzy preference relation based on new definition and itsapplication in multi-criteria decision-making

作　　者：徐婷婷 秦晋栋[1,2] XU Ting-ting;QIN Jin-dong(School of Management,Wuhan University of Technology,Wuhan 430070,China;Research Center for Data Science and Intelligent Decision Making,Wuhan University of Technology,Wuhan 430070,China)

机构地区：[1]武汉理工大学管理学院,武汉430070 [2]武汉理工大学数据科学与智能决策研究中心,武汉430070

出　　处：《控制与决策》2024年第10期3469-3478,共10页Control and Decision

基　　金：国家自然科学基金项目(72071151,71701158);湖北省自然科学基金项目(2020CFB773)。

摘　　要：二型模糊集本质上是将模糊集中的隶属度扩展为一型模糊集而产生的集合,是处理复杂不确定环境下决策分析问题的有效工具.首先,系统性回顾所提出的新的二型模糊集的数学表述定义,并进一步展示其在不同论域条件下的几何解释;其次,针对二型模糊偏好关系在处理复杂决策情景下的多准则决策问题时所具有的显著优势,开展针对二型模糊偏好关系及其在多准则决策中的应用基础研究,并基于新的数学表述方法分别给出二型模糊偏好关系的定义和决策解释,同时定义了加型和积型一致性二型模糊偏好关系的条件;然后,根据模糊偏好关系理论构建并分析二型模糊偏好关系的相关方法和性质来说明二型模糊偏好关系以及所提出的新的二型模糊集的数学表述定义的科学性和合理性;最后,通过旅游产品选择案例与对比分析验证所提出的新定义下的基于二型模糊偏好关系的多准则决策方法的有效性和可行性.A type-2 fuzzy set(T2FS)is essentially a set generated by expanding the membership degree of a fuzzy set into a type-1 fuzzy set,and it is an effective tool to deal with decision analysis problems in complex and uncertain environment.First,this paper systematically reviews the proposed new mathematical representation definition of type-2 fuzzy sets(T2FSs),and further demonstrates its geometric interpretations under different universe conditions.Second,aiming at the significant advantages of type-2 fuzzy preference relations in dealing with multi-criteria decision-making problems in complex decision-making scenarios,basic research is conducted on type-2 fuzzy preference relations and their applications in multi-criteria decision-making.More specifically,the definition and decision interpretations of type-2 fuzzy preference relations are given based on the new mathematical representation method,and the additive as well as multiplicative consistency conditions of type-2 fuzzy preference relations are defined simultaneously.Then,according to the theory on fuzzy preference relations,the related methods and properties of type-2 fuzzy preference relations are constructed and analyzed to illustrate the scientificity and rationality of type-2 fuzzy preference relations and the proposed new mathematical representation definition of T2FSs.Finally,the effectiveness and feasibility of the multi-criteria decision-making method based on type-2 fuzzy preference relations under the new definition are verified by a case study on tourism product selection and a comparative analysis.

关 键 词：二型模糊集 二型模糊偏好关系 决策解释 旅游产品选择 

分 类 号：C934[经济管理—管理学]