基于可能性理论的广义模糊数排序  

Ranking Generalized Fuzzy Numbers Based on Possibility Theory

作　　者：张莹 叶国菊[1] 刘尉[1] 赵大方 ZHANG Ying;YE Guoju;LIU Wei;ZHAO Dafang(College of Science,Hohai University,Nanjing 210098 China;School of Mathematics and Statistics,Hubei Normal University,Huangshi 435002 China)

机构地区：[1]河海大学理学院,江苏南京210098 [2]湖北师范大学数学与统计学院,湖北黄石435002

出　　处：《西华大学学报（自然科学版）》2022年第4期98-103,共6页Journal of Xihua University:Natural Science Edition

基　　金：江苏省自然科学基金青年项目(BK20180500);湖北省教育厅重点项目(D20192501)。

摘　　要：针对广义模糊数排序的问题,提出一种基于可能性理论和决策者风险态度的排序方法。利用可能变异系数与决策者风险态度定义广义模糊数大小,在此基础上建立一种新的广义模糊数排序方法,并用实例对该方法的合理性和有效性进行验证。该方法不仅可解决广义模糊数的可能均值与可能标准差相等时的排序问题,还可同时排序不同类型的广义模糊数,并且该方法计算简单,易于推广应用。经数值例子和上海银行间同业拆放利率实例验证,该方法合理有效。Aiming at the problem of sorting generalized fuzzy numbers,a ranking method based on possibility theory and the risk attitude of decision makers is proposed.The magnitude of generalized fuzzy numbers is defined by the possible coefficient of variation and the risk attitude of decision makers.On this basis,a new generalized fuzzy number ranking method is established,and the rationality and effectiveness of the method are verified by examples.This method can not only solve the ranking problem when the possible mean and possible standard deviation of generalized fuzzy numbers are equal,but also rank different types of generalized fuzzy numbers at the same time,and the method is simple to calculate and easy to popularize and apply.This method is reasonable and effective through numerical examples and an application of ranking the Shibor fuzzy numbers.

关 键 词：广义模糊数 排序 可能性理论 决策者风险态度 

分 类 号：O159[理学—数学]