Institute of Mathematics, Khwaja Fareed University of Engineering and Information Technology, Rahim Yar Khan 64200, Pakistan.
Department of Mathematics, Abdul Wali Khan University, Mardan 23200, Pakistan.
Comput Intell Neurosci. 2023 Mar 8;2023:9273239. doi: 10.1155/2023/9273239. eCollection 2023.
Fermatean fuzzy sets (FFSs) have piqued the interest of researchers in a wide range of domains. The striking framework of the FFS is keen to provide the larger preference domain for the modeling of ambiguous information deploying the degrees of membership and nonmembership. Furthermore, FFSs prevail over the theories of intuitionistic fuzzy sets and Pythagorean fuzzy sets owing to their broader space, adjustable parameter, flexible structure, and influential design. The information measures, being a significant part of the literature, are crucial and beneficial tools that are widely applied in decision-making, data mining, medical diagnosis, and pattern recognition. This paper aims to expand the literature on FFSs by proposing many innovative Fermatean fuzzy sets-based information measures, namely, distance measure, similarity measure, entropy measure, and inclusion measure. We investigate the relationship between distance, similarity, entropy, and inclusion measures for FFSs. Another achievement of this research is to establish a systematic transformation of information measures (distance measure, similarity measure, entropy measure, and inclusion measure) for the FFSs. To accomplish this aim, new formulae for information measures of FFSs have been presented. To demonstrate the validity of the measures, we employ them in pattern recognition, building materials, and medical diagnosis. Additionally, a comparison between traditional and novel similarity measures is described in terms of counter-intuitive cases. The findings demonstrate that the innovative information measures do not include any absurd cases.
费马型模糊集（FFSs）引起了众多领域研究人员的兴趣。FFS 的显著框架热衷于提供更大的偏好域，以便通过隶属度和非隶属度来对模糊信息进行建模。此外，FFSs 优于直觉模糊集和 Pythagorean 模糊集理论，因为它们具有更广泛的空间、可调参数、灵活的结构和有影响力的设计。信息测度作为文献的重要组成部分，是决策、数据挖掘、医学诊断和模式识别等领域广泛应用的关键和有益工具。本文旨在通过提出许多基于 FFS 的创新费马型模糊集信息测度（距离测度、相似性测度、熵测度和包含测度）来扩展 FFS 的文献。我们研究了 FFS 中距离、相似性、熵和包含测度之间的关系。这项研究的另一个成果是为 FFS 建立了信息测度（距离测度、相似性测度、熵测度和包含测度）的系统变换。为了实现这一目标，提出了 FFS 信息测度的新公式。为了验证这些测度的有效性，我们将它们应用于模式识别、建筑材料和医学诊断。此外，还描述了传统和新颖相似性测度在反直觉情况下的比较。结果表明，新的信息测度不包含任何荒谬的情况。
