Sevastjanov Pavel, Dymova Ludmila, Kaczmarek Krzysztof
Department of Computer Science, Czestochowa University of Technology, Dabrowskiego 73, 42-201 Czestochowa, Poland.
Entropy (Basel). 2021 Nov 10;23(11):1485. doi: 10.3390/e23111485.
In this short paper, a critical analysis of the Neutrosophic, Pythagorean and some other novel fuzzy sets theories foundations is provided, taking into account that they actively used for the solution of the decision-making problems. The shortcomings of these theories are exposed. It is stated that the independence hypothesis, which is a cornerstone of the Neutrosophic sets theory, is not in line with common sense and therefore leads to the paradoxical results in the asymptotic limits of this theory. It is shown that the Pythagorean sets theory possesses questionable foundations, the sense of which cannot be explained reasonably. Moreover, this theory does not completely solve the declared problem. Similarly, important methodological problems of other analyzed theories are revealed. To solve the interior problems of the Atanassov's intuitionistic fuzzy sets and to improve upon them, this being the reason most of the criticized novel sets theories were developed, an alternative approach based on extension of the intuitionistic fuzzy sets in the framework of the Dempster-Shafer theory is proposed. No propositions concerned with the improvement of the Cubic sets theory and Single-Valued Neutrosophic Offset theory were made, as their applicability was shown to be very dubious. In order to stimulate discussion, many statements are deliberately formulated in a hardline form.
在这篇短文中，对中庸模糊集、毕达哥拉斯模糊集及其他一些新型模糊集理论的基础进行了批判性分析，考虑到它们被积极用于解决决策问题。这些理论的缺点被揭示出来。文中指出，作为中庸模糊集理论基石的独立性假设不符合常识，因此在该理论的渐近极限中会导致矛盾的结果。研究表明，毕达哥拉斯模糊集理论的基础存在问题，其意义无法得到合理的解释。此外，该理论并未完全解决其所宣称要解决的问题。同样，其他被分析理论的重要方法问题也被揭示出来。为了解决阿塔纳索夫直觉模糊集的内部问题并对其进行改进（这也是大多数受到批评的新型模糊集理论得以发展的原因），提出了一种基于在邓普斯特 - 谢弗理论框架下扩展直觉模糊集的替代方法。由于立方模糊集理论和单值中庸模糊偏移理论的适用性被证明非常可疑，所以未对其改进提出任何建议。为了激发讨论，许多陈述都特意以强硬的形式表述。
