Employing the concept and function of tangency with similarity measures and counterpart distances for reliable medical consultations has been extensively studied in the past decades and results in lots of isomorphic measures for application. We compared the majority of such isomorphic measures proposed by various researchers and classified them into (a) maximum norm and (b) one-norm categories. Moreover, we found that previous researchers used monotonic functions to transform an identity function and resulted in complicated expressions. In this study, we provide a theoretical foundation to explain the isomorphic nature of a newer measure proposed by the following research paper against its studied existing one in deriving the same pattern recognition results. Specifically, this study initially proposes two similarity measures using maximum norm, arithmetic mean, and aggregation operators and followed by a detailed discussion on their mathematical characteristics. Subsequently, a simplified version of such measures is presented for easy application. This study completely covers two previous methods to point out that the complex approaches used were unnecessary. The findings will help physicians, patients, and their family members to obtain a proper medical diagnosis during multiple examinations.

中文翻译：

---

单值中智集下的多期健康诊断方法学的进一步研究

在过去的几十年中，采用相切的概念和功能以及相似的度量和对应距离来进行可靠的医疗咨询，这已经得到了广泛的研究，并导致了许​​多同构度量的应用。我们比较了各种研究人员提出的大多数此类同构测度，并将它们分为（a）最大范数和（b）一范数类别。此外，我们发现以前的研究人员使用单调函数来转换恒等函数并导致复杂的表达式。在这项研究中，我们提供了一个理论基础，以解释以下研究论文提出的一种较新的度量的同构性质，而不是其在获得相同模式识别结果时所研究的现有度量。具体来说，本研究最初使用最大范数提出了两种相似性度量，算术平均值和聚集运算符，然后对其数学特性进行详细讨论。随后，提出了此类措施的简化版本，以方便实施。这项研究完全涵盖了之前的两种方法，以指出所使用的复杂方法是​​不必要的。这些发现将帮助医生，患者及其家属在多次检查中获得正确的医学诊断。