Institute of Numerical Sciences, Gomal University, D. I. Khan, KPK, Pakistan.
Institute of Numerical Sciences, Kohat University of Science and Technology, Kohat, KPK, Pakistan.
Sci Rep. 2023 Feb 16;13(1):2789. doi: 10.1038/s41598-023-29932-y.
q-ROPFLS, including numeric and linguistic data, has a wide range of applications in handling uncertain information. This article aims to investigate q-ROPFL correlation coefficient based on the proposed information energy and covariance formulas. Moreover, considering that different q-ROPFL elements may have varying criteria weights, the weighted correlation coefficient is further explored. Some desirable characteristics of the presented correlation coefficients are also discussed and proven. In addition, some theoretical development is provided, including the concept of composition matrix, correlation matrix, and equivalent correlation matrix via the proposed correlation coefficients. Then, a clustering algorithm is expanded where data is expressed in q-ROPFL form with unknown weight information and is explained through an illustrative example. Besides, detailed parameter analysis and comparative study are performed with the existing approaches to reveal the effectiveness of the framed algorithm.
q-ROPFLS 包括数字和语言数据，在处理不确定信息方面有广泛的应用。本文旨在基于所提出的信息能量和协方差公式，研究 q-ROPFL 相关系数。此外，考虑到不同的 q-ROPFL 元素可能具有不同的标准权重，进一步探讨了加权相关系数。还讨论并证明了所提出的相关系数的一些理想特性。此外，还通过所提出的相关系数提供了一些理论发展，包括组合矩阵、相关矩阵和等价相关矩阵的概念。然后，扩展了一个聚类算法，其中数据以 q-ROPFL 形式表示，并且权重信息未知，并通过一个实例进行了解释。此外，还对现有的方法进行了详细的参数分析和比较研究，以揭示所提出算法的有效性。
