The evaluation of smart cities involves multiple stakeholder groups and has multiple objectives. Therefore, a multi-criteria approach is required to facilitate inclusive decisions. In view of covering classic fuzzy sets, the q-rung orthopair fuzzy set (q-ROFS) with parameters can provide a wider range to represent uncertain information. Considering the flexibility and robustness of the Frank aggregation method, this study investigates a new framework for smart city evaluation by integrating the Frank operator with q-ROFS. First, it defines the Frank operational rule of q-ROFS, and based on this rule, it presents q-rung orthopair fuzzy Frank weighted averaging/geometric operators. In addition, it analyzes some properties of the proposed operators and discusses their exceptional cases. Subsequently, by combining an improved TOPSIS model and the proposed operators, it presents a novel multi-attribute evaluation approach within q-ROF situations. Finally, it proves the feasibility of this method through its application in a smart city evaluation.

中文翻译：

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利益相关者包容的智慧城市多标准发展

智慧城市的评估涉及多个利益相关群体并具有多个目标。因此，需要采用多标准方法来促进包容性决策。鉴于覆盖经典模糊集，带参数的q-梯级正交模糊集（q-ROFS）可以提供更广泛的范围来表示不确定信息。考虑到 Frank 聚合方法的灵活性和鲁棒性，本研究通过将 Frank 算子与 q-ROFS 相结合，研究了一种新的智慧城市评估框架。首先定义了q-ROFS的Frank运算规则，并基于该规则提出了q-梯级正交模糊Frank加权平均/几何算子。此外，它还分析了所提出的算子的一些属性并讨论了它们的特殊情况。随后，通过结合改进的 TOPSIS 模型和所提出的算子，提出了一种在 q-ROF 情况下新颖的多属性评估方法。最后通过在智慧城市评价中的应用证明了该方法的可行性。