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Zander et al. Complex Eng Syst 2023;3:9 Complex Engineering
DOI: 10.20517/ces.2023.11 Systems

Research Article Open Access

Reinforcement learning with Takagi-Sugeno-Kang fuzzy
systems

Eric Zander, Ben van Oostendorp, Barnabas Bede

DigiPen Institute of Technology, Redmond, WA 98012, USA.

Correspondence to: Eric Zander, DigiPen Institute of Technology, 9931 Willows Rd. NE.Redmond, WA 98012, USA.
E-mail: eric.zander@digipen.edu

How to cite this article: Zander E, van Oostendorp B, Bede B. Reinforcement learning with Takagi-Sugeno-Kang fuzzy systems.
Complex Eng Syst 2023;3:9. http://dx.doi.org/10.20517/ces.2023.11

Received: 17 Mar 2023 First Decision: 12 Apr 2023 Revised: 16 May 2023 Accepted: 19 May 2023 Published: 14 Jun 2023
Academic Editor: Hamid Reza Karimi Copy Editor: Fanglin Lan Production Editor: Fanglin Lan

Abstract
We propose reinforcement learning (RL) architectures for producing performant Takagi-Sugeno-Kang (TSK) fuzzy
systems. The first employs an actor-critic algorithm to optimize existing TSK systems. An evaluation of this approach
with respect to the Explainable Fuzzy Challenge (XFC) 2022 is given. A second proposed system applies Deep Q-
Learning Network (DQN) principles to the Adaptive Network-based Fuzzy Inference System (ANFIS). This approach
is evaluated in the CartPole environment and demonstrates comparability to the performance of traditional DQN.
In both applications, TSK systems optimized via RL performed well in testing. Moreover, the given discussion and
experimental results highlight the value of exploring the intersection of RL and fuzzy logic in producing explainable
systems.

Keywords: Explainable AI, Fuzzy systems, Takagi-Sugeno-Kang fuzzy systems, Adaptive neuro-fuzzy inference sys-
tems, Reinforcement learning

1. INTRODUCTION
Fuzzy sets have been introduced in [1] as a mathematical framework for modeling under uncertainty. Fuzzy
systems employ a fuzzy inference engine to solve control problems in various frameworks and applications [2,3] .
In a majority of fuzzy control applications, a dynamic model joins a fuzzy system to create a dynamic fuzzy
[4]
control system . However, there are various applications where dynamic models are either not available or

© The Author(s) 2023. Open Access This article is licensed under a Creative Commons Attribution 4.0
International License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, shar-
ing, adaptation, distribution and reproduction in any medium or format, for any purpose, even commercially, as long as you
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