Non-singleton Fuzzy Logic Systems Research Articles

Hybrid Nonsingleton Fuzzy Strong Tracking Kalman Filtering for High Precision Photoelectric Tracking System

This article presents a hybrid nonsingleton fuzzy strong tracking Kalman filter (H-NFSTKF) for the high-precision photoelectric tracking system (PTS) to improve state estimation performance in the complex case of measurement noise change and velocity state mutation. The proposed H-NFSTKF is composed of three parts: A strong tracking Kalman filter (STKF) and two fuzzy logic systems (FLSs) including a singleton FLS (SFLS) and a nonsingleton FLS (NFLS). To compare different nonsingleton firing strength approaches, standard method (Sta-NS), centroid-based method (Cen-NS), similarity-based method (Sim-NS), and subsethood-based method (Sub-NS) are discussed. In addition, two traditional control strategies, i.e, dual closed-loop and feed-forward control, as well as four filtering methods including Kalman filter (KF), STKF, fuzzy STKF (FSTKF), and single nonsingleton FSTKF (S-NFSTKF) are also designed to show the superiority of the proposed H-NFSTKF. Finally, by means of comparative simulation analyses and experimental results, the excellence of the proposed H-NFSTKF is verified.

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.

Improved Uncertainty Capture for Nonsingleton Fuzzy Systems

In nonsingleton fuzzy logic systems (NSFLSs), input uncertainties are modeled with input fuzzy sets in order to capture input uncertainty (e.g., sensor noise). The performance of NSFLSs in handling such uncertainties depends on both the appropriate modeling in the input fuzzy sets of the uncertainties present in the system's inputs and on how the input fuzzy sets (and their inherent model of uncertainty) interact with the antecedent and, thus, affect the inference within the remainder of the NSFLS. This paper proposes a novel development on the latter. Specifically, an alteration to the standard composition method of type-1 fuzzy relations is proposed and applied to build a new type of NSFLS. The proposed approach is based on employing the centroid of the intersection of input and antecedent sets as origin of the firing degree, rather than the traditional maximum of their intersection, thus making the NSFLS more sensitive to changes in the input's uncertainty characteristics. The traditional and novel approach to NSFLSs are experimentally compared for two well-known problems of Mackey-Glass and Lorenz chaotic time-series predictions, where the NSFLSs' inputs have been perturbed with different levels of Gaussian noise. Experiments are repeated for system training under noisy and noise-free conditions. Analyses of the results show that the new method outperforms the traditional approach. Moreover, it is shown that while formally more complex, in practice, the new method has no significant computational overhead compared with the standard approach.

Uncertain Rule-based Fuzzy Technique: Nonsingleton Fuzzy Logic System for Corrupted Time Series Analysis

In this paper, we present the modeling of time series data which are corrupted by noise via nonsingleton fuzzy logic system. Nonsingleton fuzzy logic system (NFLS) is useful in cases where the available data are corrupted by noise. NFLS is a fuzzy system whose inputs are modeled as fuzzy number. The abilities of NFLS to approximate arbitrary functions, and to effectively deal with noise and uncertainty, are used to analyze corrupted time series data. In the simulation results, we compare the results of the NFLS approach with the results of using only a traditional fuzzy logic system.

On Choosing Models for Linguistic Connector Words for Mamdani Fuzzy Logic Systems

We examine ten antecedent connector models in the framework of a singleton or nonsingleton fuzzy logic system (FLS), to establish which models can be used. In this work, a usable connector model must lead to a separable firing degree that is a closed-form and piecewise-differentiable function of the membership function parameters and also the parameter characterizing that connector model. Our analysis shows that: for a singleton FLS where the Mamdani-product or Mamdani-minimum implication method is used, all ten antecedent connector models are usable; for a nonsingleton FLS where the Mamdani-product implication method is used, only one antecedent connector model is usable; and for a nonsingleton FLS where the Mamdani-minimum implication method is used, none of the ten antecedent connector models is usable. We also show, by examples, that the parameter of the antecedent connector model provides additional freedom in adjusting a FLS, so that the FLS has the potential to achieve better performance than a FLS that uses the traditional product or minimum t-norm for the antecedent connections.

Neuro-fuzzy extraction of angular information from muscle afferents for ankle control during standing in paraplegic subjects: an animal model.

This paper is part of a project whose aim is the implementation of closed-loop control of ankle angular position during functional electrical stimulation (FES) assisted standing in paraplegic subjects using natural sensory information. In this paper, a neural fuzzy (NF) model is implemented to extract angular position information from the electroneurographic signals recorded from muscle afferents using cuff electrodes in an animal model. The NF model, named dynamic nonsingleton fuzzy logic system is a Mamdani-like fuzzy system, implemented in the framework of recurrent neural networks. The fuzzification procedure implemented was the nonsingleton technique which has been shown in previous works to be able to take into account the uncertainty in the data. The proposed algorithm was tested in different situations and was able to predict reasonably well the ankle angular trajectories especially for small excursions (as during standing) and when the stimulation sites are far from the registration sites. This suggests it may be possible to use activity from muscle afferents recorded with cuff electrodes for FES closed-loop control of ankle position during quite standing.

Uncertainty, fuzzy logic, and signal processing

In this paper we focus on model-based statistical signal processing and how some problems that are associated with it can be solved using fuzzy logic. We explain how uncertainty (which is prevalent in statistical signal processing applications) can be handled within the framework of fuzzy logic. Type-1 singleton and non-singleton fuzzy logic systems (FLSs) are reviewed. Type-2 FLSs, which are relatively new, and are very appropriate for signal processing problems, because they can handle linguistic and numerical uncertainties, are overviewed in some detail. The output of a type-2 FLS is a type-2 fuzzy set. Using a new operation called type-reduction, the type-2 set can be reduced to a type-1 set – the type-reduced set – which plays the role of a confidence interval for linguistic uncertainties. No such result can be obtained for a type-1 FLS. We demonstrate, by means of examples, that a type-2 FLS can outperform a type-1 FLS for one-step prediction of a Mackey–Glass chaotic time series whose measurements are corrupted by additive noise, and equalization of a nonlinear time-varying channel.

Comments on "Nonsingleton fuzzy logic systems: theory and applications" and Reply

The original paper by Mouzouris and Mendel (ibid., vol.5, p.56-71, 1997) explains nonsingleton fuzzifiers and their application. Neto and Le-Huy assert that there are errors in their expressions for triangular functions, and suggest correct expressions. The original authors reply that the apparent errors arise from their use of a different convention for expressing triangular membership functions.

Dynamic non-Singleton fuzzy logic systems for nonlinear modeling

We investigate dynamic versions of fuzzy logic systems (FLSs) and, specifically, their non-Singleton generalizations (NSFLSs), and derive a dynamic learning algorithm to train the system parameters. The history-sensitive output of the dynamic systems gives them a significant advantage over static systems in modeling processes of unknown order. This is illustrated through an example in nonlinear dynamic system identification. Since dynamic NSFLS's can be considered to belong to the family of general nonlinear autoregressive moving average (NARMA) models, they are capable of parsimoniously modeling NARMA processes. We study the performance of both dynamic and static FLSs in the predictive modeling of a NARMA process.

Nonsingleton fuzzy logic systems: theory and application

In this paper, we present a formal derivation of general nonsingleton fuzzy logic systems (NSFLSs) and show how they can be efficiently computed. We give examples for special cases of membership functions and inference and we show how an NSFLS can be expressed as a "nonsingleton fuzzy basis function" expansion and present an analytical comparison of the nonsingleton and singleton fuzzy logic systems formulations. We prove that an NSFLS can uniformly approximate any given continuous function on a compact set and show that our NSFLS does a much better job of predicting a noisy chaotic time series than does a singleton fuzzy logic system (FLS).

A Singular-Value-QR Decomposition Based Method for Training Fuzzy Logic Systems in Uncertain Environments

We extend the theory of nonsingleton fuzzy logic systems NSFLSs by presenting an algorithm to design and train such systems. Since NSFLSs are a generalization of singleton fuzzy logic systems, the algorithm is equally applicable to both types of systems. The proposed SVD-QR method selects subsets of independent basis functions which are sufficient to represent a given system, through operations on a nonsingleton fuzzy basis function matrix. In addition, it provides an estimate of the number of necessary basis functions. We present several examples to illustrate the ability of the SVD-QR method to operate in uncertain environments.