改进的直觉模糊加权Heronian几何平均算子及其在徽酒评价中的应用  

Improved Intuitionistic Fuzzy Weighted Heronian Geometric Averaging Operator and Its Application to Anhui Liquor

作　　者：毕太苗 施明华 BI Taimiao;SHI Minghua(Department of Finance and Mathematics,West Anhui University,Lu'an 237012,China)

机构地区：[1]皖西学院金融与数学学院,安徽六安237012

出　　处：《皖西学院学报》2020年第5期47-54,共8页Journal of West Anhui University

基　　金：安徽省自然科学基金项目(1908085QG306);安徽省科技创新战略与软科学研究专项项目(1706a02020037);安徽省优秀青年人才基金项目(gxyq2017058);国家级大学生创新创业训练计划项目(201910376045);大别山绿色发展研究中心招标课题资助(WXZB201903)。

摘　　要：Heronian几何平均算子因具有良好的捕获变量间关联性的特性,一直被广泛用于解决多属性决策问题。通过对现有的加权Heronian几何平均算子分析,可知其不具有退化性和幂等性。为此,在直觉模糊环境下,提出一种改进的直觉模糊加权Heronian几何平均(IIFWGHM)算子,证明了新算子具有退化性、幂等性、单调性、有界性等优良性质,并探讨新算子的一些特殊形式。在此基础上,给出一种直觉模糊多属性决策方法,并对徽酒产品进行评价分析。Heronian geometric averaging operator has been widely used to solve multi-attribute decision-making problems because of its good ability to capture the correlation between variables. By analyzing the existing weighted Heronian geometric average operators, we can see that they are not degenerate and idempotent. Thus, we proposed a new geometric Heronian mean operator under intuitionistic fuzzy environment, and proved it can satisfy some desirable properties, such as reducibility, idempotency, monotonicity and boundedness. On this basis, we developed the MADM problems with intuitionistic fuzzy information and the evaluation and analysis were carried out based on liquor brands in Anhui province.

关 键 词：Heronian几何平均算子 幂等性 退化性 直觉模糊数 

分 类 号：O156[理学—数学]