Mao Haiyi, Cai Rui
School of Computer and Information Science, Southwest University, No. 2 Tiansheng Road, BeiBei District, Chongqing 400715, China.
Business College, Southwest University, No.160 Xueyuan Road, Rongchang District, Chongqing 402460, China.
Entropy (Basel). 2020 Feb 7;22(2):195. doi: 10.3390/e22020195.
The Pythagorean fuzzy number (PFN) consists of membership and non-membership as an extension of the intuitionistic fuzzy number. PFN has a larger ambiguity, and it has a stronger ability to express uncertainty. In the multi-criteria decision-making (MCDM) problem, it is also very difficult to measure the ambiguity degree of a set of PFN. A new entropy of PFN is proposed based on a technique for order of preference by similarity to ideal solution (Topsis) method of revised relative closeness index in this paper. To verify the new entropy with a good performance in uncertainty measure, a new Pythagorean fuzzy number negation approach is proposed. We develop the PFN negation and find the correlation of the uncertainty measure. Existing methods can only evaluate the ambiguity of a single PFN. The newly proposed method is suitable to systematically evaluate the uncertainty of PFN in Topsis. Nowadays, there are no uniform criteria for measuring service quality. It brings challenges to the future development of airlines. Therefore, grasping the future market trends leads to winning with advanced and high-quality services. Afterward, the applicability in the service supplier selection system with the new entropy is discussed to evaluate the service quality and measure uncertainty. Finally, the new PFN entropy is verified with a good ability in the last MCDM numerical example.
毕达哥拉斯模糊数（PFN）由隶属度和非隶属度组成，是直觉模糊数的一种扩展。PFN具有更大的模糊性，并且具有更强的表达不确定性的能力。在多准则决策（MCDM）问题中，测量一组PFN的模糊度也非常困难。本文基于一种通过与理想解相似性排序技术（TOPSIS）方法的修正相对接近度指标，提出了一种新的PFN熵。为了验证新熵在不确定性度量方面具有良好性能，提出了一种新的毕达哥拉斯模糊数否定方法。我们开发了PFN否定并找到了不确定性度量的相关性。现有方法只能评估单个PFN的模糊性。新提出的方法适用于在TOPSIS中系统地评估PFN的不确定性状态。目前，衡量服务质量没有统一的标准。这给航空公司的未来发展带来了挑战。因此，把握未来市场趋势才能以先进和高质量的服务取胜。随后，讨论了新熵在服务供应商选择系统中的适用性，以评估服务质量并度量不确定性。最后，通过最后一个MCDM数值示例验证了新的PFN熵具有良好的能力。
