Gandotra Neeraj, Kizielewicz Bartłomiej, Anand Abhimanyu, Bączkiewicz Aleksandra, Shekhovtsov Andrii, Wątróbski Jarosław, Rezaei Akbar, Sałabun Wojciech
Yogananda School of AI, Computers and Data Science, Shoolini University, Solan 173229, Himachal Pradesh, India.
Research Team on Intelligent Decision Support Systems, Department of Artificial Intelligence and Applied Mathematics, Faculty of Computer Science and Information Technology, West Pomeranian University of Technology in Szczecin, ul. Żołnierska 49, 71-210 Szczecin, Poland.
Entropy (Basel). 2021 Nov 29;23(12):1600. doi: 10.3390/e23121600.
The purpose of this paper is to propose a new Pythagorean fuzzy entropy for Pythagorean fuzzy sets, which is a continuation of the Pythagorean fuzzy entropy of intuitionistic sets. The Pythagorean fuzzy set continues the intuitionistic fuzzy set with the additional advantage that it is well equipped to overcome its imperfections. Its entropy determines the quantity of information in the Pythagorean fuzzy set. Thus, the proposed entropy provides a new flexible tool that is particularly useful in complex multi-criteria problems where uncertain data and inaccurate information are considered. The performance of the introduced method is illustrated in a real-life case study, including a multi-criteria company selection problem. In this example, we provide a numerical illustration to distinguish the entropy measure proposed from some existing entropies used for Pythagorean fuzzy sets and intuitionistic fuzzy sets. Statistical illustrations show that the proposed entropy measures are reliable for demonstrating the degree of fuzziness of both Pythagorean fuzzy set (PFS) and intuitionistic fuzzy sets (IFS). In addition, a multi-criteria decision-making method complex proportional assessment (COPRAS) was also proposed with weights calculated based on the proposed new entropy measure. Finally, to validate the reliability of the results obtained using the proposed entropy, a comparative analysis was performed with a set of carefully selected reference methods containing other generally used entropy measurement methods. The illustrated numerical example proves that the calculation results of the proposed new method are similar to those of several other up-to-date methods.
本文旨在为毕达哥拉斯模糊集提出一种新的毕达哥拉斯模糊熵，它是直觉模糊集毕达哥拉斯模糊熵的延续。毕达哥拉斯模糊集延续了直觉模糊集，并且具有额外的优势，即它能够很好地克服其不足之处。其熵决定了毕达哥拉斯模糊集中的信息量。因此，所提出的熵提供了一种新的灵活工具，在考虑不确定数据和不准确信息的复杂多准则问题中特别有用。在一个实际案例研究中展示了所引入方法的性能，包括一个多准则公司选择问题。在这个例子中，我们提供了一个数值示例，以区分所提出的熵测度与一些现有的用于毕达哥拉斯模糊集和直觉模糊集的熵。统计示例表明，所提出的熵测度对于证明毕达哥拉斯模糊集（PFS）和直觉模糊集（IFS）的模糊程度是可靠的。此外，还提出了一种多准则决策方法——复杂比例评估法（COPRAS），其权重基于所提出的新熵测度进行计算。最后，为了验证使用所提出的熵获得的结果的可靠性，与一组精心挑选的包含其他常用熵测量方法的参考方法进行了比较分析。所示的数值示例证明，所提出的新方法的计算结果与其他几种最新方法的结果相似。
