In view of the good properties of copulas and their effective use in various fuzzy environments, the goal of the current study is to develop a series of aggregation operators for hesitant fuzzy information based on Archimedean copula and cocopula, which are applied to the MADM problems. Firstly, operational laws of hesitant fuzzy elements on the basis of copulas and cocopulas are defined which can show the relevance between hesitant fuzzy values. Secondly, four aggregation operators (AC-HFWA, AC-GHFWA, AC-HFWG, and AC-GHFWG) under hesitant fuzzy environment are developed according to the proposed operational laws. The properties of these operators are also studied in detail, including idempotence, monotonicity, boundedness, etc. Subsequently, five special cases of copula are also given and the special forms of aggregation operator are obtained. In the end, an example is used to illustrate the application of the proposed approach in MADM problems. The influences of different generated functions and parameters are shown, and the feasibility of the proposed method is validated through comparative analyses.

中文翻译：

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基于阿基米德Copula的犹豫模糊信息聚合算子用于多属性决策

鉴于copulas的良好特性以及它们在各种模糊环境中的有效使用，当前的研究目标是开发一系列基于Archimedean copula和cocopula的犹豫模糊信息的聚合算子，并将其应用于MADM问题。首先，定义了基于copulas和copulas的犹豫模糊元素的运算规律，可以显示犹豫模糊值之间的相关性。其次，根据拟议的运行规律，在犹豫的模糊环境下，开发了四个聚合算子（AC-HFWA，AC-GHFWA，AC-HFWG和AC-GHFWG）。还详细研究了这些算子的性质，包括幂等性，单调性，有界性等。随后，给出了五个算子的特殊情况，并获得了聚合算子的特殊形式。最后，通过一个例子说明了该方法在MADM问题中的应用。给出了不同生成函数和参数的影响，并通过比较分析验证了该方法的可行性。