ADONiS—Adaptive Online Nonsingleton Fuzzy Logic Systems

Nonsingleton fuzzy logic systems (NSFLSs) have the potential to capture and handle input noise within the design of input fuzzy sets (FSs). In this article, we propose an online learning method that utilizes a sequence of observations to continuously update the input FSs of an NSFLS, thus providing an improved capacity to deal with variations in the level of input-affecting noise, common in real-world applications. The method removes the requirement for both
a priori
knowledge of noise levels and relying on offline training procedures to define input FS parameters. To the best of our knowledge, the proposed ADaptive, ONline Nonsingleton (ADONiS) fuzzy logic system (FLS) framework represents the first end-to-end framework to adaptively configure nonsingleton input FSs. The latter is achieved through online uncertainty detection applied to a sliding window of observations. Since real-world environments are influenced by a broad range of noise sources, which can vary greatly in magnitude over time, the proposed technique for combining online determination of noise levels with associated adaptation of input FSs provides an efficient and effective solution which elegantly models input uncertainty in the FLS's input FSs, without requiring changes in any other part (e.g., antecedents, rules or consequents) of the FLS. In this article, two common chaotic time series (Mackey–Glass, Lorenz) are used to perform prediction experiments to demonstrate and evaluate the proposed framework. Results indicate that the proposed adaptive NSFLS framework provides significant advantages, particularly in environments that include high variation in noise levels, which are common in real-world applications.