Fuzzy mathematics，1914篇，综述60偏

1 Fuzzy C-Means Clustering: A Review of Applications in Breast Cancer Detection

基本的FCM方法依赖于欧几里得距离，这对于测量非球面结构不是最优的。Mahalanobis-distance-based FCM (FCM-M)。马氏距离是使用协方差矩阵计算的相异性指标，因此考虑了数据点的方差和相关性。通过将FCM中的欧几里得距离替换为马氏距离，模糊c-means算法可以减轻其局限性，因为它允许采用多变量方法进行乳腺癌检测。

Developed in 2008 by Xin-She Yang, the firefly algorithm (FA) is an optimization algorithm based on the behaviour of fireflies。

First introduced in 1975 by Holland , the genetic algorithm imitates the process of natural selection to determine the best potential solution to the problem。

基于生物地理学的优化（BBO）是指一类基于生物地理学的算法，研究物种在栖息地的分布模式[26]。受最初基于生物地理学的算法的启发，Simon 提出了元启发式算法来确定给定问题的最佳解决方案。优化问题的每种解决方案都被称为“栖息地”。已知对该物种适应性较高的栖息地具有较高的栖息地适宜性指数（HSI）。使栖息地适宜的因素称为适宜性指数变量 （SIV）。在优化问题中，HSI 表示解决方案的适应度值，而 SIV 是其组件。该数学模型是BBO的基础，考虑了影响野外物种分布的因素：栖息地之间的迁移率、灭绝率和物种突变率。

2 Improved Cattle Disease Diagnosis Based on Fuzzy Logic Algorithms

模糊集允许更灵活和细致的决策方法，因为它们解释了医学诊断中经常存在的不确定性和不精确性。

Unlike Mamdani’s algorithm, the rules containing disjunctions in the left parts of implications are not used. The advantages of the Sugeno algorithm lie in the lower labor intensity of calculationsbased on it, as well as in the ability to model very complex systems, the adequate description of which using the Mamdani scheme is almost impossible due to the extremely large number of emerging relationships between fuzzy parameters.

A neutrosophic fuzzy set (NFS)is a mathematical construct that can be used to model the uncertainty and indeterminacy that often arises in real-world systems.

Recently, many works have proposed various algorithms and methods for single-valued neutrosophic fuzzy sets and interval neutrosophic fuzzy sets. In these works, some basic operations are introduced on single-valued and interval neutrosophic fuzzy sets, such as addition and multiplication, as well as some corresponding aggregation operators. Some basic operational laws of elementary neutrosophic fuzzy sets are defined, which include single-valuedneutrosophic fuzzy sets and interval neutrosophic fuzzy sets[12].

Currently, FL is used in control and decision support systems, where the problem description approach cannot be accurate. A fuzzy inference system comprises output and input variables. For each variable, fuzzy sets that characterize it are expressed and a membership functionis constructed for each fuzzy set. Afterward, rules that connect the output and input variables with the corresponding fuzzy sets are defined. The computational evaluation of a fuzzy inference system comprises fuzzification (building output variables that define a study), inferencing (applying fuzzy reasoning to fuzzy output data), and defuzzification (translating a linguistic value into a numerical value). 

最近的机器学习建模，包括多层感知器人工神经网络(MLP-ANN)、数据处理分组方法(GMDH)、径向基函数(RBF)、人工神经模糊推理系统(ANFIS)、支持向量机(SVM)

3 The applications of MCDM methods in COVID-19 pandemic: A state of the art review

层次分析法AHP(包括模糊AHP)是最常用的MCDM方法，37.5%的论文使用了AHP，其次是TOPSIS（Technique for order of preference by similarity to ideal solution）和VIKOR。模糊MCDM方法的计算量很大，并且在解质量方面模糊方法比清晰方法的明显优势并没有普遍的共识。分析网络过程。

一般来说，MCDM方法在决策空间方面分为两组：MADM和MODM。MADM（多属性决策）方法解决了具有预定备选方案（备选方案数量有限）的离散决策问题，为了处理备选方案数量无限的连续问题，使用了多目标决策（MODM）方法。在文献中，术语“MCDM”通常用于表示离散MCDM，许多论文将“MCDM”和“MADM”作为可互换的。在本文的其余部分，当我们使用术语“MCDM”时，我们指的是“离散 MCDM”。事实上，MCDM方法是指一套分析方法，这些方法处理对一组有限的备选方案的评估，涉及不可比较和相互冲突的标准。

4 Is fractional-order chaos theory the new tool to model chaotic pandemics as Covid-19?（分数阶微积分）

本文提出使用具有记忆容量和遗传特性的分数阶(FO)混沌理论作为一种潜在的工具，以更准确和更接近其真实的物理动力学。我们通过阶段画像、时间序列、李亚普诺夫指数和分岔分析对孟买鼠疫、癌症和Covid-19大流行的8种FO模型进行了研究。基于模糊逻辑、自适应滑模(adaptive sliding mode)和主动反步控制(active backstepping control)的概念设计了FO controllers(FOCs)来稳定混沌。此外，基于自适应滑模和主动后退同步的FOCs设计用于将混沌流行病与非混沌流行病同步，以减轻传播过程中混沌造成的不可预测性。

5 Intrinsically disordered proteins: modes of binding with emphasis on disordered domains

Interactions involving intrinsically disordered proteins (IDPs) have indicated a significant degree of disorder present in the bound state, ranging from static disorder to complete disorder, termed 'random fuzziness'

6 An epidemic model through information-induced vaccination and treatment under fuzzy impreciseness

Using graded mean integration value (GMIV)method, the fuzzy model is transformed into defuzzified model to represent the solutions avoiding the difficulties.  The positivity and the boundedness of the crisp model are discussed elaborately and also the equilibrium analysis is accomplished.  The stability analysis for both the infection free and the infected equilibrium are established for the crisp model.  Application of optimal control of the crisp system is explored.  Using Pontryagin's Maximum Principle, the optimal control is explained.  

7 A Path Toward Explainable AI and Autonomous Adaptive Intelligence: Deep Learning, Adaptive Resonance, and Models of Perception, Emotion, and Action

自适应共振理论(ART)算法克服了反向传播和深度学习的计算问题。ART是一种自组织的生产系统，它使用无监督和有监督学习的任意组合以及仅在局部可计算的数量进行增量学习，以快速分类大型非平稳数据库，而不会经历灾难性的遗忘。ART分类和预测可以使用它们所依赖的STM中的关键特征模式来解释。模糊ARTMAP算法的LTM自适应权重产生模糊IF-THEN规则，解释哪些特征组合可以预测成功的结果。ART已成功地应用于多个大规模的现实世界应用，包括遥感、医学数据库预测和社交媒体数据聚类。同样可以解释的还有强化学习和认知-情感互动的MOTIVATOR模型，以及接触、语音产生、空间导航和自主适应智能的VITE、DIRECT、DIVA和SOVEREIGN模型。这些生物模型体现了互补计算，并使用局部规律进行匹配学习和不匹配学习，从而避免了深度学习的问题。