Fuzzy Transform Research Articles

Out-of-Sample Extension of the Fuzzy Transform

Out-of-Sample Extension of the Fuzzy Transform

Generalized Fuzzy Transform and Non-Local Laplace Operator

Generalized Fuzzy Transform and Non-Local Laplace Operator

Fuzzy Transform Image Compression in the YUV Space

This research proposes a new image compression method based on the F1-transform which improves the quality of the reconstructed image without increasing the coding/decoding CPU time. The advantage of compressing color images in the YUV space is due to the fact that while the three bands Red, Green and Blue are equally perceived by the human eye, in YUV space most of the image information perceived by the human eye is contained in the Y band, as opposed to the U and V bands. Using this advantage, we construct a new color image compression algorithm based on F1-transform in which the image compression is accomplished in the YUV space, so that better-quality compressed images can be obtained without increasing the execution time. The results of tests performed on a set of color images show that our color image compression method improves the quality of the decoded images with respect to the image compression algorithms JPEG, F1-transform on the RGB color space and F-transform on the YUV color space, regardless of the selected compression rate and with comparable CPU times.

A novel spatiotemporal prediction method based on fuzzy Transform: Application to demographic balance data

Many issues require the application of forecasting models applied to spatiotemporal data in Geographic Information Systems (GIS) to predict the spatial distribution and evolution of a specific feature. The use of soft computing techniques in the development of these forecasting models makes it possible to detect non-linear trends but has the disadvantage of increasing the computational complexity of the model. In this paper we present a GIS-based framework in which a fast soft computing forecasting model based on the multidimensional Fuzzy Transform (for short, MF-transform) is applied to evaluate the spatial distribution and the time evolution in a study area of a measurable entity (the feature). The study area is divided into homogeneous zones (the subzones) in which the feature was measured in each time frame. The time series of the feature are analyzed to assess the trend of the feature in subsequent time frames; furthermore, those sub-areas are detected in which the feature is higher than a maximum threshold (hot spots) or lower than a minimum threshold (cold spots) in this time range. A process of fuzzifying the values of the feature is carried out in order to facilitate the interpretation of the results by expert users. The framework was tested on a study area provided by the province of Naples (Italy) to predict and analyze the spatial distribution and temporal trend of the monthly rate of births compared to deaths. Furthermore, the thematic map of the hot and cold spots detected in the three months following the time period of measurements was built. The results show that our method provides reliable results both in terms of forecast error and similarity between the detected hot and cold spots and those who have really formed.

A Novel Classification Algorithm Based on Multidimensional F1 Fuzzy Transform and PCA Feature Extraction

The bi-dimensional F1-Transform was applied in image analysis to improve the performances of the F-transform method; however, due to its high computational complexity, the multidimensional F1-transform cannot be used in data analysis problems, especially in the presence of a large number of features. In this research, we proposed a new classification method based on the multidimensional F1-Transform in which the Principal Component Analysis technique is applied to reduce the dataset size. We test our method on various well-known classification datasets, showing that it improves the performances of the F-transform classification method and of other well-known classification algorithms; furthermore, the execution times of the F1-Transform classification method is similar to the ones obtained executing F-transform and other classification algorithms.

PQ Event Detection After Noise Removal Using Fuzzy Transform and Hilbert Spectral Analysis on EMD

In this paper, a noise removal technique from Power Quality (PQ) signals is proposed which is based on a soft thresholding method. Thresholding is accomplished by using Fuzzy Membership Function (MF) and Empirical Mode Decomposition (EMD). To assess the denoising performance, the proposed technique is applied to detect PQ disturbances from the denoised power system signals. The EMD is applied to decompose the signal into different components. Next, the Intrinsic Mode Functions (IMFs) obtained from the EMD are utilized to determine the IMF dependent thresholding parameters, which are used into the modified fuzzy MF for the noise removal. For improved performance, several random versions of the first IMF are created, independently soft thresholded, and averaged to yield the final denoised version of the first IMF. A separate measurement is used to decide how many IMFs are required to be thresholded. For the evaluation of the noise removal performance, 1) the proposed method is compared with a wavelet-transform-based state of art technique, and 2) an application is presented on the denoised signal for the detection of PQ events from real and simulated power system disturbance data. The denoised and processed IMFs are subjected to Hilbert spectral analysis for the identification of the localized features, which are then utilized for the detection of PQ events in smart grid signal.

A Multilevel Fuzzy Transform Method for High Resolution Image Compression

The Multilevel Fuzzy Transform technique (MF-tr) is a hierarchical image compression method based on Fuzzy Transform, which is successfully used to compress images and manage the information loss of the reconstructed image. Unlike other lossy image compression methods, it ensures that the quality of the reconstructed image is not lower than a prefixed threshold. However, this method is not suitable for compressing massive images due to the high processing times and memory usage. In this paper, we propose a variation of MF-tr for the compression of massive images. The image is divided into tiles, each of which is individually compressed using MF-tr; thereafter, the image is reconstructed by merging the decompressed tiles. Comparative tests performed on remote sensing images show that the proposed method provides better performance than MF-tr in terms of compression rate and CPU time. Moreover, comparison tests show that our method reconstructs the image with CPU times that are at least two times less than those obtained using the MF-tr algorithm.

Fuzzy Transform and Least-Squares Fuzzy Transform: Comparison and Application

Fuzzy Transform and Least-Squares Fuzzy Transform: Comparison and Application

Continuous Fuzzy Transform as Integral Operator

The fuzzy transform (F-transform) is ubiquitous in different research fields and applications, such as image and data compression, data mining, knowledge discovery, and the analysis of linguistic expressions. As a generalization of the F-transform, in this article, we introduce the continuous F-transform and its inverse, as an integral operator induced by a kernel function. Through the relation between membership functions and integral kernels, we show that the main properties (e.g., continuity and symmetry) of the membership functions are inherited by the continuous F-transform. Then, the relation between the continuous F-transform and integral operators is used to introduce a data-driven F-transform, which encodes intrinsic information (e.g., structure, geometry, and sampling density) about the input data. In this way, we avoid coarse fuzzy partitions, which group data into large clusters that do not adapt to their local behavior, or a too dense fuzzy partition, which generally has cells that are not covered by the data, thus being redundant and resulting in a higher computational cost. To this end, the data-driven membership functions are defined by properly filtering the spectrum of the Laplace–Beltrami operator associated with the input data. Finally, we introduce the space of continuous F-transforms, which is useful for the comparison of different continuous F-transforms and for their efficient computation.

A Summary of F-Transform Techniques in Data Analysis

Fuzzy transform is a technique applied to approximate a function of one or more variables applied by researchers in various image and data analysis. In this work we present a summary of a fuzzy transform method proposed in recent years in different data mining disciplines, such as the detection of relationships between features and the extraction of association rules, time series analysis, data classification. After having given the definition of the concept of Fuzzy Transform in one or more dimensions in which the constraint of sufficient data density with respect to fuzzy partitions is also explored, the data analysis approaches recently proposed in the literature based on the use of the Fuzzy Transform are analyzed. In particular, the strategies adopted in these approaches for managing the constraint of sufficient data density and the performance results obtained, compared with those measured by adopting other methods in the literature, are explored. The last section is dedicated to final considerations and future scenarios for using the Fuzzy Transform for the analysis of massive and high-dimensional data.

Degraded Image Enhancement Using Dual-Domain-Adaptive Wavelet and Improved Fuzzy Transform

A novel enhancement algorithm for degraded image using dual-domain-adaptive wavelet and improved fuzzy transform is proposed, aiming at the problem of surveillance videos degradation caused by the complex lighting conditions underground coal mine. Firstly, the dual-domain filtering (DDF) is used to decompose the image into base image and detail image, and the contrast limited adaptive histogram enhancement (CLAHE) is adopted to adjust the overall brightness and contrast of the base image. Then, the discrete wavelet transform (DWT) is utilized to obtain the low frequency sub-band (LFS) and high frequency sub-band (HFS). Next, the wavelet shrinkage threshold is applied to calculate the wavelet threshold corresponding to the HFS at different scales. Meanwhile, a new Garrate threshold function that introduces adjustment factor and enhancement coefficient is designed to adaptively de-noise and enhance the HFS coefficients, and the Gamma function is employed to correct the LFS coefficients. Finally, the PAL fuzzy enhancement operator is improved and used to perform contrast enhancement and highlight area suppression on the reconstructed image to obtain an enhanced image. Experimental results show that the proposed algorithm can not only significantly improve the overall brightness and contrast of the degraded image but also suppresses the noise of dust and spray and enhances the image details. Compared with the similar algorithms of STFE, GTFE, CLAHE, SSR, MSR, DGR, and MSWT algorithms, the indicator values of comprehensive performance of the proposed algorithm are increased by 205%, 195%, 200%, 185%, 185%, 85%, 140%, and 215%, respectively. Moreover, compared with the other seven algorithms, the proposed algorithm has strong robustness and is more suitable for image enhancement in different mine environments.

Bitcoin Analysis and Forecasting through Fuzzy Transform

Sentiment analysis to characterize the properties of Bitcoin prices and their forecasting is here developed thanks to the capability of the Fuzzy Transform (F-transform for short) to capture stylized facts and mutual connections between time series with different natures. The recently proposed Lp-norm F-transform is a powerful and flexible methodology for data analysis, non-parametric smoothing and for fitting and forecasting. Its capabilities are illustrated by empirical analyses concerning Bitcoin prices and Google Trend scores (six years of daily data): we apply the (inverse) F-transform to both time series and, using clustering techniques, we identify stylized facts for Bitcoin prices, based on (local) smoothing and fitting F-transform, and we study their time evolution in terms of a transition matrix. Finally, we examine the dependence of Bitcoin prices on Google Trend scores and we estimate short-term forecasting models; the Diebold–Mariano (DM) test statistics, applied for their significance, shows that sentiment analysis is useful in short-term forecasting of Bitcoin cryptocurrency.

Applications of modified Mickens-type NSFD schemes to Lane–Emden equations

If there is a jump discontinuity present in the forcing term of a boundary value problem (BVP), the nonstandard finite difference (NSFD) and finite difference (FD) methods do not approximate the solutions very well. Here we use fuzzy transforms (FTs) and derive fuzzy transformed NSFD schemes that are referred to as non-standard fuzzy transform methods (NFTMs). The convergence of the derived NFTMs is established. Numerical solutions of Lane–Emden type equations are obtained using NFTMs. We show that NFTMs provide better results than NSFD and FD methods when the forcing term has a jump discontinuity. Even for large jumps, the NFTMs provide more accurate results than the other methods.

Trend‐cycle Estimation Using Fuzzy Transform and Its Application for Identifying Bull and Bear Phases in Markets

SummaryThis paper is focused on one of the fundamental problems in financial time‐series analysis; namely, the identification of the historical bull and bear phases. We start with the proof that the trend‐cycle can be well estimated using the technique of a higher degree fuzzy transform. Then, we suggest a mathematical definition of the bull and bear phases and provide a novel technique for their identification. As a consequence, the turning points (i.e. the points where the market changes its phase) are detected. We illustrate our methodology on several examples.

A Fuzzy Transform Method for Numerical Solution of Fractional Volterra Integral Equations

Many researchers have used the numerical methods for the purpose of solving Volterra integral equations. In this research work, we have shown that it is possible to use fuzzy transform method ($$ F\text {-transform} $$) to tackle with the fractional Volterra integral equation. The core idea of the technique of F-transforms is a fuzzy partition of a universe into fuzzy subsets. A function can be associated with a mapping from a set of fuzzy subsets to the set of its thus obtained average values. In numerical method, in order to approximate a function on a particular interval, only a restricted number of points have been employed. However, what makes the $$ F\text {-transform} $$ preferable to other methods is that it makes use of all points in this interval. Thus, a number of clear and specific examples have been enumerated for the purpose of illustrating the simplicity and the efficiency of the suggested method.

Detection of Brain Tumor by Medical Image Processing

Medical image processing is the most inspiring and developing field today. This paper labels the method of discovery & removal of brain tumor from patient’s MRI scan images of the brain. In this paper, a technique for separation of brain tumor has been developed on 2D-MRI facts which allow the documentation of tumor tissue with great accuracy and reproducibility compared to manual techniques. The first step of discovery of brain tumor is to patterned the symmetric and asymmetric Form of brain which will define the irregularity After this step the next step is segmentation which is built on two techniques 1) F-Transform (Fuzzy Transform) 2) Morphological operation. These two techniques are used to project the image in MRI. Now by this help of project we can sense the boundaries of brain tumor and calculate the real area of tumor.
 Keywords: Brain tumor, medical image processing, MRI.

Discrete Complex Fuzzy Transform based Face Image Recognition Method

Discrete Complex Fuzzy Transform based Face Image Recognition Method

Image Contrast Enhancement by Homomorphic Filtering based Parametric Fuzzy Transform

In this paper, a new image contrast enhancement technique by taking the advantages of Homomorphic decomposition and fuzzy transform is been employed. For increasing the clarity of the image generally, histogram or Retinex theory based algorithms were used. These procedures worked on enhancing the reflectance layer by ignoring illumination, which is not a better strategy and leads to poor results. Fuzzy based image enhancement approach makes use of illumination by omitting reflectance. In our proposed algorithm, Homomorphic decomposition is used for getting the exact illumination image from the value layer of HSV (Hue, Saturation, Value) image. Next, the parametric fuzzy transform is employed to enhance the image by updating its membership functions and thereby smoothing the luminance layer. Finally, a weighted image is generated by pixel neighborhood property for preserving the image details. The results show the profoundness of the algorithm in terms of its clarity and complexity even for nonuniform illumination images.

Design of fuzzy radial basis function neural network classifier based on information data preprocessing for recycling black plastic wastes: comparative studies of ATR FT-IR and Raman spectroscopy

As large amounts of plastics are widely used in diverse areas of industry, the amount of plastic waste, including black plastics, continues to increase. In this situation, the necessity of useful recycling having limited resources gradually increases. The design of plastic classification systems for plastics recycling becomes more important to effectively address recycling activities. Until now, conventional sorting systems based on the near infrared ray technology have been used to classify plastic wastes. However, the classification of black plastic waste still remains a challenge because such materials do not reflect sufficient signals due to the absorption of laser light coming from the NIR spectrometer. In order to solve such problems, this research is focused on an efficient way to identify black plastics. Attenuated Total Reflectance (ATR) Fourier Transform Infrared Radiation (FT-IR) and a Raman spectrometer are used to carry out qualitative and quantitative analysis for the effective as well as efficient classification of black plastic wastes. In this study, to effectively classify the black plastic waste, data processing and Fuzzy Transform (F-Transform) as well as PCA-based Fuzzy Radial Basis Function Neural Networks (FRBFNNs) classifier is proposed. Input variables extracted on a basis of chemical characteristic peaks as well as interval range positioned near the chemical characteristic peaks were exploited as a way to improve the classification performance of the FRBFNN classifier. In order to evaluate the performance of the classifier, a suite of techniques including F-Transform-based as well as Principal Component Analysis (PCA)-based FRBFNNs classifier designed with the aid of Particle Swam Optimization are developed to analyze and classify black plastics.

New Approximation Methods Based on Fuzzy Transform for Solving SODEs: II

In this research, three approximation methods are used in the new generalized uniform fuzzy partition to solve the system of differential equations (SODEs) based on fuzzy transform (FzT). New representations of basic functions are proposed based on the new types of a uniform fuzzy partition and a subnormal generating function. The main properties of a new uniform fuzzy partition are examined. Further, the simpler form of the fuzzy transform is given alongside some of its fundamental results. New theorems and lemmas are proved. In accordance with the three conventional numerical methods: Trapezoidal rule (one step) and Adams Moulton method (two and three step modifications), new iterative methods (NIM) based on the fuzzy transform are proposed. These new fuzzy approximation methods yield more accurate results in comparison with the above-mentioned conventional methods.