In recent years, different higher order fuzzy sets have been introduced to better handle the uncertainty in many practical decision making and data mining problems. The recent proposal of higher order fuzzy set is q-rung picture fuzzy set (q-RPFS) modeled by three parameters positive, negative, and neutral membership function. One of the important topics in q-RPFS is distance measures which play a crucial role in many multi criteria decision making methods and data mining applications. In this paper, we introduce a novel distance measure for q-RPFS which is the combination of q-rung orthopair fuzzy set (q-ROFS) and picture fuzzy set (PFS). The proposed distance measure is used in q-rung picture fuzzy (q-RPF) ELECTRE integrated with TOPSIS as a new approach for group decision making in q-RPF environment. To demonstrate the effectiveness of our proposed method, a comparison is made with the q-RPF approach based on aggregation operators using a numerical example for decision making problem. Furthermore, the proposed distance measure is utilized in a q-RPF k nearest neighborhood (kNN) algorithm for classification. The proposed classification algorithm is applied to twenty UCI machine learning classification data sets. A comparison with other algorithms is performed and the results show that the proposed classification algorithm has the highest average classification accuracy.

近年来，引入了不同的高阶模糊集以更好地处理许多实际决策和数据挖掘问题中的不确定性。高阶模糊集的最新提议是通过三个参数正，负和中性隶属函数对q阶图片模糊集（q-RPFS）进行建模。q-RPFS中的重要主题之一是距离度量，它在许多多准则决策方法和数据挖掘应用程序中起着至关重要的作用。在本文中，我们介绍了一种新颖的q-RPFS距离度量，它是q阶正交对模糊集（q-ROFS）和图片模糊集（PFS）的结合。拟议的距离测度用于与TOPSIS集成的q-梯级图片模糊（q-RPF）ELECTRE中，作为q-RPF环境中群体决策的一种新方法。为了证明我们提出的方法的有效性，将基于聚合算子的q-RPF方法进行了比较，并使用一个数值示例来解决决策问题。此外，在q-RPF k最近邻（kNN）算法中利用提出的距离度量进行分类。提出的分类算法应用于20个UCI机器学习分类数据集。与其他算法进行了比较，结果表明该分类算法具有最高的平均分类精度。提出的分类算法应用于20个UCI机器学习分类数据集。与其他算法进行了比较，结果表明该分类算法具有最高的平均分类精度。提出的分类算法应用于20个UCI机器学习分类数据集。与其他算法进行了比较，结果表明该分类算法具有最高的平均分类精度。