Khan Madad, Ullah Safi, Zeeshan Muhammad, Shafqat Ramsha, Kebaili Imen, Bedada Tola Bekene, Anis Saima
Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus, Abbottabad, Pakistan.
Department of Mathematics, COMSATS University Islamabad, Islamabad Campus, Islamabad, Pakistan.
Sci Rep. 2024 Jun 20;14(1):14243. doi: 10.1038/s41598-024-64112-6.
A complex fuzzy distance measure (CFDMs) plays a significant role in applications involving complex or high-dimensional data where traditional distance measures may not adequately capture the nuances of the data relationships. The significance of CFDMs lies in their ability to handle uncertainty, imprecision, and complexity in various domains. Numerous researchers introduced different concepts of CFDMs, yet these CFDMs fails to convey any information regarding the hesitancy degree associated with an element. The main objective of this paper is to introduce some new distance measures based on complex fuzzy sets, called complex fuzzy hesitance distance measure and complex fuzzy Euclidean Hesitance distance measure, which is the generalization of complex fuzzy normalized Hamming distance measure and complex fuzzy Euclidean distance measure. Some new operations and primay results are discussed in the environment of proposed CFDMs and complex fuzzy operations. Moreover, we discussed the applications of the proposed CFDMs in addressing decision-making problems. We introduced a new decision-making algorithm that integrates CFDMs into decision-making processes, providing a robust methodology for handling real-world complexities. Further, the comparative study of the proposed CFDMs is discussed with some existing CFDMs.
一种复模糊距离度量（CFDMs）在涉及复杂或高维数据的应用中起着重要作用，在这些应用中，传统距离度量可能无法充分捕捉数据关系的细微差别。CFDMs的重要性在于它们能够处理各个领域中的不确定性、不精确性和复杂性。众多研究人员引入了不同的CFDMs概念，但这些CFDMs未能传达与元素相关的犹豫度的任何信息。本文的主要目的是引入一些基于复模糊集的新距离度量，称为复模糊犹豫距离度量和复模糊欧几里得犹豫距离度量，它们是复模糊归一化汉明距离度量和复模糊欧几里得距离度量的推广。在提出的CFDMs和复模糊运算的环境中讨论了一些新运算和初步结果。此外，我们还讨论了所提出的CFDMs在解决决策问题中的应用。我们引入了一种新的决策算法，该算法将CFDMs集成到决策过程中，为处理现实世界的复杂性提供了一种稳健的方法。此外，还将所提出的CFDMs与一些现有的CFDMs进行了比较研究。
