幂调和平均算子及其在模糊偏好关系群决策中的应用

Power-Harmonic Average Operators and Its Application to Group Decision Making with Fuzzy Preference Relations

传统的加权算术平均算子的权重没有考虑集成数据之间相互关系,是一种线性加权平均算子。本文将在幂平均算子和幂有序加权平均算子的基础上,考虑了集成数据之间相互支撑程度对权重的影响,提出幂调和平均算子、幂加权调和平均算子和幂有序加权调和平均算子等概念,并且研究了它们相应的性质。最后,探讨了幂调和平均算子在模糊偏好关系的群决策中的应用,结果表明此方法是可行的和有效的。

Traditional weighted arithmetic averaging operator is a linear one,in which the relations among the aggregation arguments are not considered in its weights.Based on power-average（PA）,the power ordered weighted average（POWA）operator and the weights affecting from the support between the aggregation arguments,we propose power-harmonic（PH）operator,power weighted harmonic（PWH）average operator and power ordered weighted harmonic（POWH）average operator,and we also study their properties.Finally,we use the developed approaches to the application to group decision making with fuzzy preference relations.The results show that the method proposed in this paper is feasible.