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A similarity measure under Pythagorean fuzzy soft environment with applications
Computational and Applied Mathematics ( IF 2.998 ) Pub Date : 2020-09-11 , DOI: 10.1007/s40314-020-01321-5
Muhammad Riaz , Khalid Naeem , Deeba Afzal

A novel similarity measure (SM) based upon cosine similarity measure and Frobenius inner product of matrices, and a weighted SM for Pythagorean fuzzy soft sets (PFS-sets/PFSSs) are coined in this article. Some fundamental characteristics of the proposed SM are also brought into light, including that SM of any two PFS-sets equals unity iff the two PFS-sets coincide. Employing this SM, a relation \(\thickapprox ^\lambda \) amongst two PFS-sets is demarcated. Further, it is demonstrated that this relation does not enjoy the status of an equivalence relation. Moreover, the efficacy of the proposed SM is established with the aid of numerical examples. Comparison analysis of the proposed method with some of the prevailing similarity measures is also given, both numerically and diagrammatically. In the end, an application from psychological disorder accompanied by algorithm and flow chart have been put on display through a conjectural case study.

中文翻译:

毕达哥拉斯模糊软环境下的相似度量及其应用

本文提出了一种基于余弦相似度度量和矩阵Frobenius内积的新颖相似度度量(SM),以及勾股勾股模糊软集(PFS-sets / PFSSs)的加权SM。还提出了所提出的SM的一些基本特征,包括如果两个PFS组重合,则任何两个PFS组的SM等于1。使用此SM,关系\(\ thickapprox ^ \ lambda \)在两个PFS集之间进行了划分。此外,证明了该关系不具有等价关系的状态。此外,借助于数值示例来建立所提出的SM的功效。还通过数字和图形方式对所提出的方法与一些主要的相似性度量进行了比较分析。最后,通过一个推测的案例研究,展示了来自心理障碍的应用以及算法和流程图。
更新日期:2020-09-11
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