The paper "ADONiS—Adaptive Online Nonsingleton Fuzzy Logic Systems" (by Direnc Pekaslan, Christian Wagner and Jonathan M. Garibaldi) has been published on IEEE Transactions on Fuzzy Systems.
Real-world environments are subject to different uncertainty sources which can be impactful at different levels and/or at different duration which can inevitably cause a variation in uncertainty levels over time. Due to the heterogeneity and diversity of real-world conditions, measurement devices (e.g. sensors) may not be able to provide absolute true perfect value, rather approximations which in turn processed as inputs to systems. Thus, given inputs are exposed to different effects (e.g. quadcopters subjected to varying wind gusts) which lead to input uncertainty to be a principal source of uncertainty and inseparable components of decision-making systems.
Non-Singleton Fuzzy Logic Systems have the potential to capture and handle input uncertainty within the design of input fuzzy sets. In this paper, we propose a complete ADaptive, Online Non-Singleton (ADONiS) framework which incorporates online uncertainty detection and associated parameterization of the Non-Singleton input fuzzy sets, thus providing an improved capacity to adapt to variations in the level of input-affecting noise, common in real-world applications.
The proposed approach avoids both the need for a priori knowledge of the uncertainty levels experienced at runtime and the need for offline training while providing the means for systems to continuously adapt to changing levels of uncertainty. Specifically, in the proposed approach, input fuzzy set parameters are continuously adapted based on information gained from an uncertainty level estimation process which iteratively estimates uncertainty levels over a sequence of recent observations.
The proposed ADONiS framework for combining online determination of uncertainty levels with associated adaptation of input fuzzy sets provides an efficient and effective solution which elegantly models input uncertainty ‘where it arises’ without requiring changes in any other part (e.g. antecedents, rules or consequents) of the FLS. In doing so, ADONiS limits tuning to the fuzzification stage and remain rules ‘untouched’ (which can be generated based on experts insights or in a data-driven way), thus providing a fundamental requirement for good interpretability. –if rules and sets were understood well initially.
As time series forecasting provides an ideal test bed for the systematic evaluation (offering the potential to accurately control the levels of uncertainty/noise affecting system inputs at any given time) of techniques designed to deal with input uncertainty, in this paper, we focus on applying the proposed ADONiS framework to the context of two common chaotic time series (Mackey-Glass, Lorenz) prediction as an initial area of the application enabling efficient evaluation and demonstration.
An animated illustration of the ADONiS adaptive behaviour to variation in the levels of uncertainty affecting a system’s inputs can be seen below.
At each time step, inputs are associated with a given non-singleton FS, for which the parameters are determined directly by the levels of uncertainty detected within the preceding time frame. Employing an uncertainty detection technique to construct input FSs provides the capacity for adapting to changes in the levels of uncertainty affecting a system (e.g. in respect to varying environmental circumstances).
Acknowledging the fact that in the real world, sources of (varying levels of) uncertainty are pervasive, a variety of different training/testing scenarios were explored to systematically evaluate the proposed framework. The results from the comparison of the proposed Adaptive and Non-adaptive techniques suggest that the proposed ADONiS approach of dynamically changing input FSs provides significant advantages, particularly in environments that include high variation in noise levels, which are common in real-world applications. For more details, please see the paper 10.1109/TFUZZ.2019.2933787.
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