Despite the importance of cosine and cotangent function- based similarity measures, the literature has not provided a satisfactory formulation for the case of q-rung orthopair fuzzy set (qROFS). This paper criticizes the existing attempts in terms of respect of the basic axioms of a similarity measure and strict inclusion relation. In addition, the maximum operator-based similarity measures are criticized. Then, new improved, axiomatically supported cosine and cotangent function-based similarity measures for qROFSs are proposed. Additional properties of the new similarity measures are discussed to guarantee their good performance. Two algorithmic procedures of TOPSIS method that based on fixed and relative ideal solutions are discussed. The numerical examples are provided to support the findings

尽管基于余弦和余切函数的相似性度量很重要，但文献并未为 q-rung orthopair 模糊集 (qROFS) 的情况提供令人满意的公式。本文从相似性测度和严格包含关系的基本公理方面批评了现有的尝试。此外，基于最大算子的相似性度量受到批评。然后，提出了新的改进的、公理支持的、基于余弦和余切函数的 qROFS 相似性度量。讨论了新的相似性度量的其他属性，以保证它们的良好性能。讨论了基于固定和相对理想解的TOPSIS方法的两种算法过程。提供了数值例子来支持研究结果