The Takagi-Sugeno-Kang fuzzy system has wide applications across different areas, e.g., regression, classification and decision making, attributed to its high precision and interpretability. However, the existing Takagi-Sugeno-Kang fuzzy system is not an ideal solution to some special scenarios, particularly for those that are constrained monotonically. To this end, a monotonic relation-constrained Takagi-Sugeno-Kang fuzzy system classifier is proposed in this paper. The proposed method introduces a monotonic relation between the inputs and the outputs, where the objective function is expressed in a monotonically constrained form and a strategy for generating monotonicity constraint pairs is developed. Furthermore, to address the convexity loss caused by the increasing monotonicity constraints, the proposed method introduces the Tikhonov regularization strategy to ensure the uniqueness and boundedness of the solution. The results from extensive experiments show that the proposed method exhibits better classification performance than the original Takagi-Sugeno-Kang fuzzy system and state-of-the-art monotonic classification methods in handling monotonic datasets.

Takagi-Sugeno-Kang 模糊系统由于其高精度和可解释性，在回归、分类和决策等不同领域具有广泛的应用。然而，现有的 Takagi-Sugeno-Kang 模糊系统对于一些特殊场景，尤其是单调约束的场景，并不是一个理想的解决方案。为此，本文提出了一种单调关系约束的Takagi-Sugeno-Kang模糊系统分类器。所提出的方法在输入和输出之间引入了单调关系，其中目标函数以单调约束形式表示，并采用生成策略单调性约束对被开发出来。此外，为了解决单调性约束增加引起的凸性损失，所提出的方法引入了Tikhonov正则化策略来确保解的唯一性和有界性。大量实验的结果表明，所提出的方法在处理单调数据集时表现出比原始的 Takagi-Sugeno-Kang 模糊系统和最先进的单调分类方法更好的分类性能。