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.

Using T˜-Transformation for Solving Tank and Heating System Equations

In this article, a fuzzy Tarig evolve (T-n-transform) is implemented. Similar theorems and properties have been proven. To explain the technique of this fuzzy transform in differential equations, examples in real life are presented. This study shows the applicability of this interesting fuzzy transform for solving differential equations with constant coefficients also for its computational power. It is desirable to use it as a new technique, to not only solve “nonlinear fractional differential equations", and to analyze prelocal system information. Moreover, significant theorems are presented to explain the properties of T˜-transform as well as a suggested method is validated with two reality examples.

A classification algorithm based on multi-dimensional fuzzy transforms

We present a new classification algorithm for machine learning numerical data based on direct and inverse fuzzy transforms. In our previous work fuzzy transforms were used for numerical attribute dependency in data analysis: the multi-dimensional inverse fuzzy transform was used to approximate the regression function. Also here the classification method presented is based on this operator. Strictly speaking, we apply the K-fold cross-validation algorithm for controlling the presence of over-fitting and for estimating the accuracy of the classification model: for each training (resp., testing) subset an iteration process evaluates the best fuzzy partitions of the inputs. Finally, a weighted mean of the multi-dimensional inverse fuzzy transforms calculated for each training subset (resp., testing) is used for data classification. We compare this algorithm on well-known datasets with other five classification methods.

Attribute dependency data analysis for massive datasets by fuzzy transforms

We present a numerical attribute dependency method for massive datasets based on the concepts of direct and inverse fuzzy transform. In a previous work, we used these concepts for numerical attribute dependency in data analysis: Therein, the multi-dimensional inverse fuzzy transform was useful for approximating a regression function. Here we give an extension of this method in massive datasets because the previous method could not be applied due to the high memory size. Our method is proved on a large dataset formed from 402,678 census sections of the Italian regions provided by the Italian National Statistical Institute (ISTAT) in 2011. The results of comparative tests with the well-known methods of regression, called support vector regression and multilayer perceptron, show that the proposed algorithm has comparable performance with those obtained using these two methods. Moreover, the number of parameters requested in our method is minor with respect to those of the cited in the above two algorithms.

An ensemble approach based on transformation functions for natural gas price forecasting considering optimal time delays

Natural gas, known as the cleanest fossil fuel, plays a vital role in the economies of producing and consuming countries. Understanding and tracking the drivers of natural gas prices are of significant interest to the many economic sectors. Hence, accurately forecasting the price is very important not only for providing an effective factor for implementing energy policy but also for playing an extremely significant role in government strategic planning. The purpose of this study is to provide an approach to forecast the natural gas price. First, optimal time delays are identified by a new approach based on the Euclidean Distance between input and target vectors. Then, wavelet decomposition has been implemented to reduce noise. Moreover, fuzzy transform with different membership functions has been used for modeling uncertainty in time series. The wavelet decomposition and fuzzy transform have been integrated into the preprocessing stage. An ensemble method is used for integrating the outputs of various neural networks. The results depict that the proposed preprocessing methods used in this paper cause to improve the accuracy of natural gas price forecasting and consider uncertainty in time series.

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.

On the Similarity and Dependence of Time Series

In this paper, we undertake the problem of evaluating interrelation among time series. Interrelation is measured using a similarity index. In this paper, we suggest a new one based on the known fuzzy transform (F-transform), which has been proven to remove higher frequencies than a given threshold and reduce the random noise significantly. The F-transform also provides an estimation of the slope of time series in a given imprecisely delineated time. We prove some of the suggested index properties and show its ability to measure similarity (and thus the interrelation) on a selection of several real financial time series. The method is well interpretable and easy to adjust.