Abstract
Since their introduction, fuzzy sets and systems have become an important area of research known for its versatility in modelling, knowledge representation and reasoning, and increasingly its potential within the context explainable AI. While the applications of fuzzy systems are diverse, there has been comparatively little advancement in their design from a machine learning perspective. In other words, while representations such as neural networks have benefited from a boom in learning capability driven by an increase in computational performance in combination with advances in their training mechanisms and available tool, in particular gradient descent, the impact on fuzzy system design has been limited. In this paper, we discuss gradient-descent-based optimisation of fuzzy systems, focussing in particular on automatic differentiation--crucial to neural network learning--with a view to free fuzzy system designers from intricate derivative computations, allowing for more focus on the functional and explainability aspects of their design. As a starting point, we present a use case in FuzzyR which demonstrates how current fuzzy inference system implementations can be adjusted to leverage powerful features of automatic differentiation tools sets, discussing its potential for the future of fuzzy system design.
Abstract (translated)
自它们被引入以来，模糊集合和系统已成为一个重要的研究领域，以其在建模、知识表示和推理方面的灵活性而闻名，并且随着越来越多的应用于可解释性AI，其在该背景下的潜力也越来越受到关注。虽然模糊系统的应用领域各不相同，但从机器学习角度来看，它们的設計并没有取得太多進展。换句话说，虽然像神經网络這樣的表示形式从計算性能的提高以及訓練機制和可用工具的進步中受益，但在特別是大於神經網絡訓練強度的梯度下降的影響下，模糊系統的設計影響有限。在本文中，我們討論了基於梯度下降的模糊系統優化，重點關注自動 differentiation--關鍵於神經網絡學習--以 free fuzzy system designers from intricate derivative computations， allowing for more focus on the functional and explainability aspects of their design. 作為開始，我們在FuzzyR中展示了如何將 current fuzzy inference system implementations調整以利用自動 differentiation工具集的強大功能，探討其對未來模糊系統設計的潛力。
URL
https://arxiv.org/abs/2403.12308
