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

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.