Gradient-based Fuzzy System Optimisation via Automatic Differentiation -- FuzzyR as a Use Case

TL;DR

This paper explores using automatic differentiation to optimize fuzzy systems with gradient descent, aiming to simplify their design process and enhance explainability, demonstrated through a FuzzyR use case.

Contribution

It introduces a method to incorporate automatic differentiation into fuzzy system optimization, bridging the gap with neural network training techniques.

Findings

Automatic differentiation enables gradient-based fuzzy system optimization.

FuzzyR can be adapted to leverage automatic differentiation tools.

Potential for more efficient and explainable fuzzy system design.

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.