基于对偶犹豫模糊几何Heronian平均算子的多属性决策方法及其应用

针对需要同时考虑变量隶属度、非隶属度以及关联性的融合问题，本文将对偶犹豫模糊集与Heronian平均算子相结合，定义了对偶犹豫模糊几何Heronian平均算子和对偶犹豫模糊几何加权Heronian平均算子，讨论了新算子的一些优良特性，包括幂等性、置换不变性、有界性、单调性等性质，并针对属性值为对偶犹豫模糊语言信息关联系的多属性决策问题，建立了基于对偶犹豫模糊几何加权Heronian平均算子的多属性决策模型，基于所定义的算子和建立的数学模型，提出了一种新的基于对偶犹豫模糊Heronian平均算子的多属性决策方法。最后，通过多属性决策算例验证了方法的有效性和可行性。

A Multiple-attribute Decision-making Method Based on the Dual Hesitant Fuzzy Geometric Heronian Means Operator and Its Application

Motivated by the problem that aggregates the membership, nonmembership and association, the dual hesitant fuzzy information is combined with the geometric Heronian means operator in this paper, and the dual hesitant fuzzy geometric Heronian means (DHFGHM) operator and dual hesitant fuzzy geometric weighted Heronian means (DHFGWHM) operator are defined. Meanwhile, the properties of these new operators are investigated, including Idempotency, Commutativity, Monotonicity and Boundedness. Then, for the multi-attribute decision-making problem with the dual hesitant fuzzy attributes, the model based on the dual hesitant fuzzy geometric weighted Heronian means (DHFGWHM) operator is established. Furthermore, based on this model, a multi-attribute decision-making method with the DHFGWHM operator is proposed. Finally, an example is shown to verify the effectiveness and feasibility of the given method.