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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.

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To improve the accuracy of decision results in complex fuzzy environments, complex cubic fuzzy sets are studied, which can not only measure the periodicity of decision-making data, but also use interval values and single values to act together on the data. However, the fuzzy sets do not provide a reasonable explanation for some special cases of input arguments. Thus, the power average operator is used to eliminate the influence of extreme input arguments on decision results, and the Maclaurin symmetric mean operator considers the correlation between inputs in this paper. Firstly, we define the operation rules, distance measures, evaluation index function, and evaluation criteria in a complex cubic q-rung orthopair fuzzy environment. Then, some aggregation operators are proposed to aggregate complex cubic q-rung orthopair fuzzy numbers, and their desirable properties and some special cases are discussed. Next, we use the subjective and objective fusion method to determine the weight of attributes. Further, a multi-attribute decision-making method is established by combining aggregation operator, evaluation function, and weight determination method. Finally, the proposed method is applied to a specific quality evaluation problem, and the effectiveness and practicability of the proposed method are illustrated by other methods and parameter analysis.