A Hamacher operator in a q-rung orthopair trapezoidal fuzzy linguistic environment is studied based on the definition of the q-rung orthopair fuzzy set and the Hamacher aggregation operator. First, we define a new fuzzy variable called q-rung orthopair trapezoidal fuzzy linguistic sets, and the operational laws, score function, accuracy function, comparison rules, and distance measures of the IVPFLVS are defined. Second, based on the Hamacher operator and the q-rung orthopair trapezoidal fuzzy linguistic sets, we propose several q-rung trapezoidal fuzzy linguistic Hamacher operator information aggregation operators, such as the generalized q-rung orthopair trapezoidal fuzzy linguistic Hamacher weighted averaging (q-GROTrFLHWA) operator, and the generalized q-rung orthopair trapezoidal fuzzy linguistic Hamacher weighted geometric (q-GROTrFLHWG) operator. Third, some desirable properties of the correlation operators, such as idempotency, boundedness, and monotonicity are discussed. Finally, there are two group decision schemes based on q-rung orthopair trapezoidal fuzzy information with known attribute weights. The decision-making scheme is applied to the evaluation of school teaching quality, and the practicability and effectiveness of the scheme are demonstrated by different methods.

中文翻译：

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一些q-rung orthopair梯形模糊语言hamacher聚合算子及其应用

基于q-rung orthopair模糊集的定义和Hamacher聚合算子，研究了q-rung orthopair梯形模糊语言环境下的Hamacher算子。首先，我们定义了一个新的模糊变量，称为 q-rung orthopair 梯形模糊语言集，并定义了 IVPFLVS 的运算法则、评分函数、准确度函数、比较规则和距离度量。其次，基于Hamacher算子和q-rung orthopair梯形模糊语言集，我们提出了几种q-rung梯形模糊语言Hamacher算子信息聚合算子，如广义q-rung orthopair梯形模糊语言Hamacher加权平均（q- GROTrFLHWA) 操作员，和广义 q-rung orthopair 梯形模糊语言 Hamacher 加权几何 (q-GROTrFLHWG) 算子。第三，讨论了相关算子的一些理想特性，例如幂等性、有界性和单调性。最后，有两种基于已知属性权重的 q-rung orthopair 梯形模糊信息的群决策方案。将该决策方案应用于学校教学质量的评价，通过不同的方法论证了该方案的实用性和有效性。