Fuzzy Filter Research Articles

Distributed square root fuzzy cubature information filter for object tracking on the possibilistic framework

AbstractIn this study, a distributed fuzzy filter is proposed for a non‐linear state estimation problem on the possibilistic framework. Firstly, instead of Gaussian distribution on the probability framework, the process and observation noises are modelled as fuzzy random variables with trapezoidal possibility distributions. Secondly, a novel square root fuzzy cubature information filtering (SRFCIF) algorithm is proposed to deal with non‐linear state estimation with fuzzy noise; a fuzzy variable fusion (FVF) algorithm is used for fuzzy random variables fusion. Consequently, a distributed square root fuzzy cubature information filter (DSRFCIF) is proposed by embedding SRFCF and FVF into the consensus frame. Finally, consistency analysis and simulation demonstration are executed for the proposed filter.

Improved adaptive type-2 fuzzy filter with exclusively two fuzzy membership function for filtering salt and pepper noise

Image denoising is one of the preliminary steps in image processing methods in which the presence of noise can deteriorate image quality. This paper presents an improved two-stage fuzzy filter for filtering salt and pepper noise from the images to enhance the image quality. In the first stage, the pixels in the image are categorized as good or noisy based on adaptive thresholding using type-2 fuzzy logic with exclusively two different membership functions in the filter window. In the second stage, the noisy pixels are denoised using modified ordinary fuzzy logic in the respective filter window. The proposed filter is validated on standard images with various noise levels. The proposed filter removes the noise and preserves beneficial image characteristics, i.e., edges and corners at higher noise levels. The performance of the proposed filter is compared with the various state-of-the-art methods in terms of peak signal-to-noise ratio and computation time. The average PSNR values for the noise percentage 20%, 50% and 80% are the 37%, 31% and 27%. To show the effectiveness of statistical filter tests, i.e., the Friedman test and Bonferroni−Dunn (BD) test are also carried out, which ascertain that the proposed filter outperforms in comparison to various filtering approaches.

A Neighborhood Impact Driven K-Medoid Clustering and Fuzzy Logic Blended Approach for High Density Impulse Noise Detection and Removal

In the field of image processing, removing impulse noise has been regarded as one of the most important tasks, primarily because of the noise pattern it presents. Existing filters used the effect of only those non-noisy pixels which were present inside the specified windows ignoring the effect of the non-noisy pixels present in the surrounding windows. So, the least distant non-noisy pixels in the present window as well as in the surrounding windows may have an influence on the present window's noisy pixels. Hence, considering the above factors, in this paper, a two-step technique named KMDCIFF (K-medoid clustering identified fuzzy filter) is proposed for removing impulse noise from digital images. In the proposed KMDCIFF algorithm, the first step is noise detection using K-medoid clustering, followed by a fuzzy logic-acquainted noise reduction strategy that utilizes the least distant local and non-local non-noisy pixels for removal operation. The detection process involves the application of K-medoid clustering on all 5×5 windows produced by centering each pixel of the considered image. In order to remove noise, a 7×7 window is constructed with each detected noisy pixel in the center. Analyzing the impact of the least distant local and non-local pixel on each noisy pixel, the same is replaced by an estimated pixel’s intensity value obtained from the most influential non-noisy pixels. KMDCIFF is evaluated using well-known metrics for diverse types of images. At a high noise density of 80%, KMDCIFF exhibited significant peak-signal-to-noise-ratios (PSNRs) of 26.97 dB and 29.67 dB and structural similarity indexes (SSIMs) of 0.8045 and 0.9288 on random and fixed valued impulse noise impacted Lena image, respectively. Comparing the results of the contemporary study to those of previous studies of a similar kind in this sector, the results are unswervingly astounding.

Adaptive event‐triggered quantized H∞ fuzzy filtering for T‐S fuzzy systems via fuzzy Lyapunov–Krasovskii functional method

SummaryThis article is concerned on the problem of adaptive event‐triggered quantized fuzzy filtering for networked T‐S fuzzy control systems under imperfect premise matching. First, a novel adaptive event‐triggered communication scheme for networked fuzzy control systems is built to save more limited network bandwidth, where the event‐triggered parameter is changed with the output fluctuation. Second, a fuzzy filter with the imperfect premise matching is designed. Under consideration of event‐triggered scheme and quantization method, an unified filtering error model is well constructed, which contains time delay and parameter uncertainties. Then, a new augmented fuzzy Lyapunov–Krasovskii functional including a fuzzy Lyapunov matrix and a delay product term is established, and sufficient conditions are derived to guarantee the asymptotic stability of the filtering error system with a given performance. Moreover, the corresponding filter can be designed by solving a set of linear matrix inequalities. Finally, a numerical example is put forward to illustrate the effectiveness and advantages of the proposed method.

Reduced-Order Extended Dissipative Filtering for Nonlinear Systems With Sensor Saturation via Interval Type-2 Fuzzy Model

The system nonlinearity, sensor saturation, and the uncertainty will hamper the analysis and affect the control performance. Filtering is a signal processing method which facilitates the system analysis and synthesis by signal estimation or noise suppression. To achieve generalized filtering problem for nonlinear systems with sensor saturations with lower computational burden, this article addresses the reduced-order extended dissipative filter design for nonlinear sensor-saturated system which is modeled by interval type-2 (IT2) T–S fuzzy system. For IT2 T–S fuzzy systems, the main challenge exists in the acquisition of the information in IT2 membership functions (MFs) for analysis and design. A membership-function-dependent (MFD) method is applied to capture the information of the MFs for reducing the conservativeness introduced by MFs not involved in the analysis. An extended dissipative filtering method, under imperfect premise matching (IPM) concept that the membership functions of the filter are different from those of the model, is proposed for sensor-saturated IT2 fuzzy systems. The proposed method has a high flexibility in parameters adjustment of both the filter and the design condition, including extended dissipative matrices, approximation MFs, and sensor saturation degree, one can freely choose the parameters according to the required performance of the fuzzy filter. A numerical example is given to demonstrate the effectiveness of the results.

Event-Triggered Fault Detection Filtering of Fuzzy-Model-Based Systems With Prescribed Performance

This article deals with the fault detection filtering problem for a nonlinear dynamic system in the Takagi–Sugeno fuzzy framework. An event-triggered scheme considering network bandwidth utilization rate and fault occurrence probability is utilized, which can conserve communication resources and reduce computational burden. The fault detection fuzzy filter is used as a residual generator, and the proposed event-based fault detection scheme is formulated as a fuzzy filtering problem. Moreover, the generated residual is robust against exogenous disturbances while being sensitive to system faults, and the resulting fault detection system has asymptotic stability with a specified <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> error property. The corresponding solvability conditions of the fault detection filter are constructed by converting the nonconvex feasibility problem into a series of optimization problems. Finally, a numerical simulation is conducted to demonstrate the feasibility and validity of the proposed scheme.

Robust Filtering for Fuzzy Systems With Bounded Disturbances via Premise-Region-Dependent Event-Triggered Mechanisms

This article studies the problem of robust filtering for continuous-time Takagi–Sugeno (T–S) fuzzy systems with bounded external disturbances via premise-region-dependent event-triggered mechanisms (ETMs). First, attention is focused on the analysis and design of piecewise fuzzy filters (PFFs) without considering the ETMs. Then, based on the established PFF, ET PFF with time regularization is designed, such that the new augmented system is Zeno free and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L_{\infty }$</tex-math></inline-formula> stable, in which new ET conditions that depend on the different regions where the premise variables of the T–S model and the PFF are located are designed. Unlike the existing results, the designed observer gains in the absence of ETMs are also applicable to the case with ETMs, while the ones in the existing methods need to be redesigned. Finally, a simulation example is applied to verify the effectiveness of the proposed filtering scheme.

Fuzzy Ideals in Pseudo-Hoop Algebras

In this study, fuzzy ideals in pseudo-hoop algebras are presented. Also, we investigate fuzzy congruences relations on pseudo-hoop algebras induced by fuzzy ideals. By using fuzzy ideals, we create the fuzzy quotient pseudo-hoop algebras and identify and demonstrate the one-to-one relationship between the set of all normal fuzzy ideals of a pseudo-hoop algebra H with conditions p D N and the set of all fuzzy congruences relation on H . Additionally, we investigate the relationship between fuzzy ideals and fuzzy filters in pseudo-hoop algebras by considering the set of complement elements of pseudo-hoop algebras. Lastly, we study fuzzy prime ideals and fuzzy ⊙ -prime ideals and their relation.

Fuzzy Ideals and Fuzzy Filters on Topologies Generated by Fuzzy Relations

Recently, Mishra and Srivastava have introduced and studied the notion of fuzzy topology generated by fuzzy relation and several properties were proved. In this paper, we mainly investigate the lattice structure of fuzzy open sets in this topology, and show its various properties and characteristics. Additionally, we extend to this lattice the notions of fuzzy ideal and fuzzy filter. For each of these notions, we fully characterize them in terms of this lattice meet and join operations.

Image Noise Reduction by Means of Bootstrapping-Based Fuzzy Numbers

Removing or reducing noise in color images is one of the most important functions of image processing, which is used in many sciences. In many cases, nonlinear methods significantly reduce the noise in the image and are widely used today. One of these methods is the use of fuzzy logic. In this paper, we want to introduce a fuzzy filter by using the fuzzy metric for fuzzy sets. For this purpose, we define fuzzy color pixels by using the mean of neighborhoods. Due to the noise in the image, we use the bootstrap resampling method to reduce the effect of outliers. The concept of the strong law of large numbers for the bootstrap mean in fuzzy metric space helps us to use the resampling method.

Filter-Based Event-Triggered Adaptive Fuzzy Control for Discrete-Time MIMO Nonlinear Systems With Unknown Control Gains

In this article, an event-triggered output feedback adaptive fuzzy control scheme is developed for a class of uncertain discrete-time multiinput–multioutput (MIMO) nonlinear systems with immeasurable states and unknown control gains. Due to the existence of unmeasured states, a set of fuzzy filters are designed, then a filter-based event-triggered adaptive fuzzy control scheme is developed for discrete-time MIMO nonlinear systems. To solve the problem of state estimation caused by the coupling of control input and unknown control gains, a fuzzy filters-based state observer is developed by combining filter states. And then, a parameterized state observer is constructed to effectively estimate immeasurable state signals by the combination of the fuzzy filter states and the gradient-based fuzzy parameter updating law. Based on filter states and estimation states, an event-based adaptive fuzzy control scheme is proposed by novel intermediate errors and backstepping. To overcome the causal problem caused by the low-triangular structure, the variable substitution and a predictor are, respectively, employed to forecast the future state and reference signals. A series of stability analyses illustrates that the proposed scheme achieves immeasurable state estimations, guarantees the ultimately uniformly boundedness of the closed-loop system, and obtains the good tracking performance, while reducing communication occupancy. Finally, simulation studies on a numerical and a practical example are conducted to demonstrate the effectiveness of the proposed scheme.

Fuzzy logic approach in salt and pepper noise

This paper describes a new method based on fuzzy logic to denoising images corrupted by the salt and pepper noise. In this approach, noisy pixels are detected via fuzzy IF-THEN rules and restored with a multi-level fuzzy filter. To reduce the amount of noise corruption, the filtering process begins with a window of size 3 × 3 centered on the noisy pixels. Then, a floating window in the form of fuzzy compositions is used for the remaining unrestored noisy pixels. A fuzzy logic controller is employed to improve the restoration results. By comparing this method with many well-established denoising methods, we have shown that the mentioned technique has high accuracy and reasonably low complexity at very high noise densities while preserving the structure and edge information of the images.

Clinical Assessment of Diabetic Foot Ulcers Using GWO-CNN based Hyperspectral Image Processing Approach

ABSTRACT Diabetes Mellitus has turned out to be a complicated disease and as of 2016 one out of eleven humans suffer from this disease leading to Diabetic Foot Ulcers (DFU). When not treated, DFUs lead to amputation and in this work, a novel image processing method is proposed for the efficient assessment and classification of DFU images. Initially, pre-processing is done by cascaded fuzzy filter followed by nonlinear partial differential equation (NPDE) based segmentation that segments the foot ulcer regions. Consequently, the local binary pattern (LBP) is employed to extract the useful features. Then the proposed hybrid Grey Wolf Optimization-Convolutional Neural Network (GWO-CNN) model uses these features to identify the DFU regions. The performance evaluation is done by the estimation of the performance metrics and the results are compared with existing algorithms indicating the efficacy of the proposed technique. The obtained results reveal that the proposed work generates an accuracy of 98.5% with a reduced error percentage of 1.4%.

Decentralized sampled-data [formula omitted] fuzzy filtering with exponential time-varying gains for nonlinear interconnected systems

This study proposes a technique to design a decentralized sampled-data H∞ fuzzy filter for nonlinear interconnected systems. Unlike previous studies, a novel sampled-data fuzzy filter design includes exponential time-varying gains, which leads to enlargement of the sampling period and improvement in the decay rate performance of the filter. The filter design technique includes both measurable and immeasurable premise variable cases. In the latter case, the H∞ performance criterion is newly defined to minimize the effect of immeasurability on filtering performance. This study also focuses on deriving less conservative design conditions of the filter. First, a novel two-sided looped Lyapunov–Krasovskii functional (LKF) is constructed to make full use of the actual sampling pattern. Then, by utilizing an extended reciprocally convex matrix inequality along with Writinger-based integral inequality, less conservative design conditions are derived as linear matrix inequalities (LMIs)-based optimal problem. Finally, the effectiveness and superior performance of the proposed filtering design techniques are demonstrated through two simulation examples.

Fuzzy Closed Filters in Bounded BE-Algebras

ABSTRACT In this paper we use the method of fuzzification of crisp set to fuzzy set as extension of crisp set to fuzzy set. In particular the concepts of fuzzy closed filters of a bounded BE-algebra are introduced; and also some related properties are investigated. As a result a new concept of fuzzy closed filters of a bounded BE-algebras are discussed. Using the idea of fuzzy closed filters of a bounded BE-algebras, some related properties are investigated. In general characterization theorems that related fuzzy closed filters and fuzzy filter are proved. Furthermore, characterization theorem that relate closed filter and fuzzy closed filter in abounded BE-algebra is investigated.

Adaptive event-triggered [formula omitted] fuzzy filter design for nonlinear networked systems via asymmetric LKF approach

This paper studies the problem of the fuzzy H∞ filter design for nonlinear networked control systems through event-triggered communication (ETC) scheme. Firstly, an improved adaptive ETC scheme is proposed to save communication resources. Secondly, an asymmetric Lyapunov-Krasovskii functional (LKF) method is introduced in the H∞ performance analysis of filter error systems. Then, a new sufficient condition is obtained to meet the H∞ performance by combining the method with membership-function-dependent approach. Further, a relaxed co-design method of the corresponding filter and event-triggering parameters is obtained. Finally, two numerical examples are provided to verify the advantage of the new approaches.

Design hybrid filter technique for mixed noise reduction from synthetic aperture radar imagery

For military and civilian applications, synthetic aperture radar (SAR) imaging is an essential instrument for obtaining images of the Earth's surface. Speckle noise, a form of noise that is multiplicative, generated by conflicting echoes returned from each pixel, has a significant impact on the SAR picture. On SAR pictures, a hybrid filter for mixed noise reduction is used to remove the mixed noises that are present in the data during capture and transmission. Specifically, speckle noise and salt and pepper noises from SAR images. Both are being worked on at the same time to minimize mixed noise in SAR pictures without revealing edges or other features. This study proposes a technique that combines a hybrid filter derived from a statistics filters with nonlinear functions (SFNF). When comparing to mean, median as no adaptive filters, and frost filter, a lee filter, and fuzzy filters as adaptive filters, this hybrid filter produces good results. MATLAB was used to carry out the simulation. To illustrate the filtering technique's performance, quantitative measurements like signal to noise ratio (SNR) procedure, the mean square error (MSE) method, and edge measurement (β) mechanization are used.

Event-Triggered and Asynchronous Reduced-Order Filtering Codesign for Fuzzy Markov Jump Systems

This article is devoted to the investigation of reduced-order dissipative filtering for Takagi&#x2013;Sugeno (T&#x2013;S) fuzzy Markov jump systems with the event-triggered mechanism. For the proposed event-triggered mechanism, its threshold parameter is constructed as a special diagonal matrix which can improve system performance by flexibly adjusting the matrix elements. Due to the impact of the sampling behaviors and the environmental disturbance, the asynchronization between the filter and the estimated system is considered in this article, which can be characterized by the hidden Markov model. Through handling the linear matrix inequalities (LMIs) with some slack matrices, event-triggered fuzzy filters are designed to guarantee the resulting system is stochastically stable and strictly dissipative. The proposed filter parameters are obtained by solving LMIs. Ultimately, both the effectiveness and advantages of the proposed reduced-order filter with the event-triggered mechanism are verified by a practical example.

Further Results on Sampled-Data $H_{\infty }$ Filtering for T–S Fuzzy Systems With Asynchronous Premise Variables

This article presents a new sampled-data fuzzy filter design method for Takagi–Sugeno fuzzy systems with the asynchronous premise variables. In the new fuzzy filter design method, the membership functions of the filter are affine transformed by scaling and biasing the system’s membership functions. Taking the advantage of the newly proposed method, the asynchronous problem of the premise variables between the system and filter is easily resolved. Based on the looped function and a modified free-weighting matrix inequality, the sampled system’s output is handled, and the filter design condition is formulated in terms of a parameterized linear matrix inequality with affine matched fuzzy parameter vectors. Additionally, a modified Finsler’s lemma is devised to handle the affine matched fuzzy parameter vectors. By utilizing the relationship between the transformed membership functions, the filter design condition for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> performance is enhanced with larger allowable maximum bounds of variable sampling intervals. Lastly, the superiority of the presented method is verified by comparing the numerical simulations with existing methods.

Fault Detection for Interval Type-2 T-S Fuzzy Networked Systems via Event-Triggered Control

This paper investigates the event-triggered fault diagnosis (FD) problem for interval type-2 (IT2) Takagi–Sugeno (T-S) fuzzy networked systems. Firstly, an FD fuzzy filter is proposed by using IT2 T-S fuzzy theory to generate a residual signal. This means that the FD filter premise variable needs to not be identical to the nonlinear networked systems (NNSs). The evaluation functions are referenced to determine the occurrence of system faults. Secondly, under the event-triggered mechanism, a fault residual system (FRS) is established with parameter uncertainty, external disturbance and time delay, which can reduce signal transmission and communication pressure. Thirdly, the progressive stability of the fault residual system is guaranteed by using the Lyapunov theory. For the energy bounded condition of external noise interference, the performance criterion is established using linear matrix inequalities. The matrix parameters of the target FD filter are obtained by the convex optimization method. A less conservative fault diagnosis method can be obtained. Finally, the simulation example is provided to illustrate the effectiveness and the practicalities of the proposed theoretical method.