Ying Changyan, Slamu Wushour, Ying Changtian
School of Information Science and Engineering, Xinjiang University, Urumqi 830046, China.
Laboratory of Multi-Lingual Information Technology, Xinjiang University, Urumqi 830046, China.
Entropy (Basel). 2022 Oct 19;24(10):1494. doi: 10.3390/e24101494.
The purpose of our research is to extend the formal representation of the human mind to the concept of the complex q-rung orthopair fuzzy hypersoft set (Cq-ROFHSS), a more general hybrid theory. A great deal of imprecision and ambiguity can be captured by it, which is common in human interpretations. It provides a multiparameterized mathematical tool for the order-based fuzzy modeling of contradictory two-dimensional data, which provides a more effective way of expressing time-period problems as well as two-dimensional information within a dataset. Thus, the proposed theory combines the parametric structure of complex q-rung orthopair fuzzy sets and hypersoft sets. Through the use of the parameter , the framework captures information beyond the limited space of complex intuitionistic fuzzy hypersoft sets and complex Pythagorean fuzzy hypersoft sets. By establishing basic set-theoretic operations, we demonstrate some of the fundamental properties of the model. To expand the mathematical toolbox in this field, Einstein and other basic operations will be introduced to complex q-rung orthopair fuzzy hypersoft values. The relationship between it and existing methods demonstrates its exceptional flexibility. The Einstein aggregation operator, score function, and accuracy function are used to develop two multi-attribute decision-making algorithms, which prioritize based on the score function and accuracy function to ideal schemes under Cq-ROFHSS, which captures subtle differences in periodically inconsistent data sets. The feasibility of the approach will be demonstrated through a case study of selected distributed control systems. The rationality of these strategies has been confirmed by comparison with mainstream technologies. Additionally, we demonstrate that these results are compatible with explicit histograms and Spearman correlation analyses. The strengths of each approach are analyzed in a comparative manner. The proposed model is then examined and compared with other theories, demonstrating its strength, validity, and flexibility.
我们研究的目的是将人类思维的形式化表示扩展到复杂q阶正交对模糊超软集（Cq - ROFHSS）的概念，这是一种更通用的混合理论。它能够捕捉到大量人类解释中常见的不精确性和模糊性。它为基于顺序的矛盾二维数据模糊建模提供了一种多参数化数学工具，为表达时间周期问题以及数据集中的二维信息提供了更有效的方式。因此，所提出的理论结合了复杂q阶正交对模糊集和超软集的参数结构。通过使用参数 ，该框架捕捉到了超出复杂直觉模糊超软集和复杂毕达哥拉斯模糊超软集有限空间的信息。通过建立基本的集合论运算，我们展示了该模型的一些基本性质。为了扩展该领域的数学工具箱，将爱因斯坦运算和其他基本运算引入到复杂q阶正交对模糊超软值中。它与现有方法之间的关系证明了其卓越的灵活性。利用爱因斯坦聚合算子、得分函数和准确性函数开发了两种多属性决策算法，这些算法在Cq - ROFHSS下基于得分函数和准确性函数对理想方案进行排序，以捕捉周期性不一致数据集中的细微差异。将通过对选定的分布式控制系统进行案例研究来证明该方法的可行性。通过与主流技术比较，证实了这些策略的合理性。此外，我们证明这些结果与显式直方图和斯皮尔曼相关性分析兼容。以比较的方式分析了每种方法的优势。然后对所提出的模型进行检验并与其他理论进行比较，展示了其优势、有效性和灵活性。
