Abstract
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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