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arXiv 2102.01538cs.AI
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毕达哥拉斯模糊集的一种基于矩阵的距离及其在医学诊断中的应用

A Matrix-based Distance of Pythagorean Fuzzy Set and its Application in Medical Diagnosis

Key Laboratory of High Confidence Software Technologies (Peking University)(高可信软件技术重点实验室(北京大学));School of Computer Science, Peking University(北京大学计算机学院);University of Macau(澳门大学)

Yuanpeng He, Lijian Li, Tianxiang Zhan

AI总结:

针对现有毕达哥拉斯模糊集距离度量方法的不足,提出一种满足距离公理的新距离度量方法,能有效区分模糊集,并在医学诊断中验证了其优越性与可行性。

摘要:

毕达哥拉斯模糊集(PFS)是在直觉模糊集基础上发展而来的,在处理和解决不确定情境中的模糊性方面更为有效,这也是PFS被广泛应用于各个领域的重要原因。如何度量两个毕达哥拉斯模糊集之间的距离仍然是一个悬而未决的问题。以往的研究中已提出了多种方法来解决该问题。然而,并非所有现有方法都能准确体现毕达哥拉斯模糊集之间的差异并满足相似性性质。还有一些其他类型的方法忽略了毕达哥拉斯模糊集三个变量之间的关系。为解决这一问题,本文提出了一种新的距离度量方法,该方法满足距离度量的公理要求,并能很好地体现PFS之间的区分程度。随后,通过若干数值算例验证了该距离度量方法能够避免产生一些反直觉和不合理的结果,并且比其他类似方法更有效、更合理、更先进。此外,所提出的PFS间距离度量方法被应用于医学诊断这一实际环境中,并与之前的方法进行了比较,以展示其优越性和高效性。同时,也证明了该方法在实际处理不确定性方面的可行性。

英文摘要:

The pythagorean fuzzy set (PFS) which is developed based on intuitionistic fuzzy set, is more efficient in elaborating and disposing uncertainties in indeterminate situations, which is a very reason of that PFS is applied in various kinds of fields. How to measure the distance between two pythagorean fuzzy sets is still an open issue. Mnay kinds of methods have been proposed to present the of the question in former reaserches. However, not all of existing methods can accurately manifest differences among pythagorean fuzzy sets and satisfy the property of similarity. And some other kinds of methods neglect the relationship among three variables of pythagorean fuzzy set. To addrees the proplem, a new method of measuring distance is proposed which meets the requirements of axiom of distance measurement and is able to indicate the degree of distinction of PFSs well. Then some numerical examples are offered to to verify that the method of measuring distances can avoid the situation that some counter? intuitive and irrational results are produced and is more effective, reasonable and advanced than other similar methods. Besides, the proposed method of measuring distances between PFSs is applied in a real environment of application which is the medical diagnosis and is compared with other previous methods to demonstrate its superiority and efficiency. And the feasibility of the proposed method in handling uncertainties in practice is also proved at the same time.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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