毕达哥拉斯三角模糊数密度算子及其应用  

Pythagorean Triangular Fuzzy Number Density Operator and Its Application

作　　者：易平涛[1] 王胜男 李伟伟[1] 王露[1] YI Pingtao;WANG Shengnan;LI Weiwei;WANG Lu(School of Business Administration,Northeastern University,Shenyang 110167,China)

机构地区：[1]东北大学工商管理学院,辽宁沈阳110167

出　　处：《运筹与管理》2023年第9期72-78,共7页Operations Research and Management Science

基　　金：国家自然科学基金资助项目(71701040,71701041)。

摘　　要：针对属性信息为毕达哥拉斯三角模糊数(PTFN)的多属性决策问题,考虑属性信息分布的疏密关系,提出毕达哥拉斯三角模糊数密度(PTF-DM)算子。首先介绍PTFN及其相关运算法则,并基于模糊参考理想法(FRIM)的基本思想以及得分函数,运用有序增量分割法以实现PTFN的有效聚类。然后,提出PTF-DM算子及相应的合成算子,并运用熵值法建立规划模型确定最终的密度权重。最后,通过一个算例对PTF-DM算子的应用做一简要说明,结果发现PTF-DM算子具有较好的稳定性,在辅助决策者做出决策方面可以发挥良好效用。该方法以PTFN数据类型为背景,呈现信息表达及信息集成理念的新发展趋势,并进一步拓展密度算子的实际应用范围与决策工具的选择空间。Multi-attribute decision-making is a decision-making theory and method that uses multiple attributes to help decision makers choose alternatives,and it has been widely used in many fields.In addition to many attribute characteristics that can assist decision-making,the type of attribute value is also one of the important branches of multi-attribute decision-making research.With the higher complexity of decision-making environment,the research on multi-attribute decision-making with accurate values as attribute values cannot meet the current changeable decision-making environment,and then the research on multi-attribute decision-making with fuzzy numbers as attribute values has attracted extensive attention of many scholars.Fuzzy set theory has experienced the development from fuzzy set to intuitionistic fuzzy set and then to Pythagorean fuzzy set,and the explicable decision-making problems have also been improved in breadth and depth.The development of fuzzy sets more clearly depicts the uncertain nature of decision-making and ensures the authenticity of attribute information.Pythagorean triangular fuzzy number(PTFN)is an expanded data form.Although it can cope with the complexity and uncertainty of decision-making problems,the distribution characteristics of data are not considered in the process of aggregation.However,the decision-maker’s preference for the density of data distribution will affect the final decision-making results in the face of realistic decision-making problems.Then,this is also the source of density operator.Density aggregation operator is the result of re-integration on the basis of classical integration operator,and it has also received some attention since it was put forward.It is a flexible aggregation method and can effectively enhance the accuracy of information aggregation process.Given this,this paper proposes a Pythagorean triangular fuzzy number density weighted operator(PTF-DM),which not only refines the fuzzy data types in multi-attribute decision-making,but also considers the

关 键 词：多属性决策 密度集结算子 毕达哥拉斯三角模糊数 聚类 模糊参考理想法 

分 类 号：C934[经济管理—管理学]