One worthwhile way of expressing imprecise information is the q‐rung orthopair fuzzy sets (q‐ROFSs), which extend intuitionistic fuzzy sets and Pythagorean fuzzy sets. The main goal of this contribution is to further extend the concept of similarity measure for q‐ROFSs, which not only endows the similarity framework with more ability to create new ones but also inherits all essential properties of a logical similarity measure. This contribution proposes a class of novel similarity measures for q‐ROFSs by drawing a general framework of existing q‐ROFS similarity and q‐ROFS distance measures. These q‐ROFS similarity measures enable us to overcome the theoretical drawbacks of the existing measures in the case where they are used individually. In the application part of the contribution, a pattern recognition problem on classification of building materials with a number of known building materials is reconsidered. The study of this particular case shows that the proposed family of similarity measures consistently classify the unknown building material pattern with the same known building material pattern. Then, an experimental case study regarding a problem of classroom teaching quality is re‐examined for the comparison of the performance of proposed similarity measures against the existing ones. The salient features of the proposed similarity measures in comparison to the existing qROFS similarity measures, are as follows: (i) a number of existing q‐ROFS similarity measures are inherently correlation coefficients, and they satisfy only a limited number of essential properties of a comprehensive similarity measure; (ii) several existing q‐ROFS similarity measures lead sometimes to nonlogical results, more specifically, to the same maximum similarity value for different q‐ROFSs; (iii) a variety of existing q‐ROFS similarity measures depend on subjective parameters, which either hinder their application in practice or increase their computational cost. In brief, following this direction of research, we will prove the superiority of the developed similarity measures over the existing ones from both theoretical and experimental viewpoints.

中文翻译：

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q-阶邻对对模糊集的相似度度量及其在多准则决策中的应用

表达不精确信息的一种有价值的方法是q阶正交对模糊集（q-ROFS），它扩展了直觉模糊集和勾股模糊集。此贡献的主要目标是进一步扩展q-ROFS的相似性度量的概念，这不仅赋予相似性框架更多的创建新相似性的能力，而且还继承了逻辑相似性度量的所有基本属性。通过绘制现有q-ROFS相似度和q-ROFS距离测度的一般框架，本文为q-ROFS提出了一类新颖的相似性测度。这些q-ROFS相似性度量使我们能够克服单独使用它们时现有度量的理论缺陷。在贡献的应用部分中，重新考虑了用多种已知建筑材料对建筑材料进行分类的模式识别问题。对这种特殊情况的研究表明，拟议的相似性度量标准系列始终将未知的建筑材料样式与相同的已知建筑材料样式进行分类。然后，重新审查了有关课堂教学质量问题的实验案例研究，以比较拟议的相似性措施与现有措施的性能。与现有的qROFS相似性度量相比，拟议的相似性度量的显着特征如下：（i）许多现有的q-ROFS相似性度量固有地具有相关系数，并且它们仅满足a的有限数量的基本属性。全面的相似性度量；（ii）几种现有的q-ROFS相似性度量有时会导致非逻辑结果，更具体地说，是针对不同q-ROFS的相同最大相似性值；（iii）各种现有的q-ROFS相似性度量取决于主观参数，这会阻碍其在实践中的应用或增加其计算成本。简而言之，遵循这一研究方向，我们将从理论和实验的角度证明已开发的相似性度量方法优于现有的相似性度量方法。