Fuzzy Fractal Dimension Research Articles

New version of Hyper-Fractal Analysis application for estimating the fuzzy fractal dimension of hyperspectral satellite ocean color images

In this work we present a new version of the Hyper-Fractal Analysis C# .Net application for estimating the fuzzy fractal dimension of hyperspectral images. As an example, we also present some initial results on 116D algal images obtained from the HYPSO-1 satellite. New version program summaryProgram Title: Hyper-Fractal Analysis v08.CPC Library link to program files:https://doi.org/10.17632/z9knmny56p.4.Licensing provisions: GPLv2.Programming language: C# 7.3 /.Net Framework 4.8.Journal reference of previous version: Computer Physics Communications 276 (2022) 108335.Does the new version supersede the previous version?: Yes.Nature of problem: Estimating the fuzzy fractal dimension of Hyperspectral images.Solution method: Optimized algorithm for Hyperspectral images stored in a specific csv file format.Reasons for the new version: Develop a set of tools for facilitating fuzzy fractal analysis of Hyperspectral images (more than 100 dimensions).

Predicting Essential Proteins Based on Integration of Local Fuzzy Fractal Dimension and Subcellular Location Information

Essential proteins are indispensable to cells’ survival and development. Prediction and analysis of essential proteins are crucial for uncovering the mechanisms of cells. With the help of computer science and high-throughput technologies, forecasting essential proteins by protein–protein interaction (PPI) networks has become more efficient than traditional approaches (expensive experimental methods are generally used). Many computational algorithms were employed to predict the essential proteins; however, they have various restrictions. To improve the prediction accuracy, by introducing the Local Fuzzy Fractal Dimension (LFFD) of complex networks into the analysis of the PPI network, we propose a novel algorithm named LDS, which combines the LFFD of the PPI network with the protein subcellular location information. By testing the proposed LDS algorithm on three different yeast PPI networks, the experimental results show that LDS outperforms some state-of-the-art essential protein-prediction techniques.

Migration of hyper-fractal analysis from visual basic 6 to C# .Net

In Grossu et al. (Comput. Phys. Commun. 184 (2013) 1812–1813) we presented Hyper-Fractal Analysis, a visual tool for estimating the fuzzy fractal dimension of images and 4D objects. As Visual Basic 6 could be considered an outdated language, with limited Object-Oriented Programming capabilities, migrating the application to C# .Net was treated in high priority. Following the goal of creating a highly reusable fractal analysis library, the code was also refactored to SOLID. Together with various improvements, the.Net version is also providing new tools for iso-fractal areas identification. The project success was confirmed by a comparative old/new version study. On the other hand, the most relevant functionalities were covered by unit tests. New version program summaryProgram Title: Hyper-Fractal Analysis v05CPC Library link to program files:https://doi.org/10.17632/z9knmny56p.1Licensing provisions: GPLv2Programming language: C# 7.3 /.Net Framework 4.7.1Journal reference of previous version: Computer Physics Communications 184, Issue 7 (2013) 1812–1813Does the new version supersede the previous version?: YesNature of problem: Estimating the fractal dimension of images and multi-dimensional objects.Solution method: Optimized version of the fuzzy box-counting algorithm.Reasons for the new version: Migration from VB6 to C# .Net, adding new tools for iso-fractal areas identification.Summary of revisions:•The main goal of this work was creating a highly reusable fractal analysis library. Following this purpose Hyper-Fractal Analysis v04 [1] was migrated from VB6 (an outdated language, with limited OOP capabilities) to C# .Net [2]. This opportunity was also used for refactoring the code to SOLID [3].•The box-counting algorithm [4] implemented in the previous version is limited to 4D objects. In current version the number of dimensions is limited only by the available resources.•The previous fuzzy [5,6] box-counting implementation is accepting only 0-255 shades of gray windows. The new version allows defining parametrizable fuzzy band-pass filters.•An important attention was also paid on developing new tools for identification of iso-fractal areas (the sets of points characterized by the same local fractal dimension [7]). This functionality is expected to be of particular interest in medical image analysis [7-13].•The Windows Forms GUI (Fig. 1) was completely reconsidered on top of the Model View Presenter pattern [14].•For an increased reliability and for minimizing the regression risks during future developments the most relevant functionalities were covered by unit tests [15].

Real Time Cognitive State Prediction Analysis using Brain Wave Signal

The teaching-learning process is seeing a big transformation in this digital age. It involves digital classrooms with various accessories of online tools such as video conferencing, digital materials, and other platforms for learning and assessment with options for both real-time and self-paced work in addition to the availability of teachers over video conferencing, text, phone, email, etc. To improve the online learning efficiency, assessing the cognitive state during the learning phase is highly required for the success of these developments. This work focused on cognitive state analysis during different learning tasks is determined by EEG brain signals that are captured using 128 channels Emotive Epoch headset device. Artifacts prominent in raw signals are filtered by linear filtering. Feature extraction for determination of concentration levels is done by applying fuzzy fractal dimension measures and Discrete Wavelet Transform (DWT) on the processed signals. The classification of extracted parameters into concentration levels is done by using deep learning algorithms like Enhanced Convolutional Neural Network (ECNN). This ECNN deep learning classification is highly accurate amongst all other remaining classifiers and is used as a feedback model to regulate this cognitive state.

Conversion based fuzzy fractal dimension integrating self-similarity and porosity, via DFS and FIS (Mamdani and Sugeno systems)

Abstract Fuzzy logic via Fractal geometry is a novel mathematical combination. Using Conversion Based Fuzzy Fractal Geometry (cbFFG), researchers can approach to fractal geometry with the utilization of Direct Fuzzy Sets DFS and Fuzzy Inference Systems FIS 1 in their immense fields of studies. It is proposed a new fuzzy fractal dimension FFD using membership functions instead of conventional log-log linear regression processes which needed more time and calculations. The results are derived from IP 2 by developing the defined FIS via Fuzzy Analyses and/or for the defined direct membership function. As that of FD, the cbFFD range is [0, 3] for solid geometry and is [0, 2] for plane geometry with discrimination that the output results are upon fuzzy inference and so identifiable and interpretable. Here, cbFFDs are computed by two main inputs: 1) Porosity Conversion Based Factor and 2) Self-Similarity Conversion Based Factor. The outputs of the cbFFD process can be both interpreted by linguistic terms and graduated by the fuzzy numbers. The cbFFD makes the geometric dimensioning more understandable. The final values of cbFFDs can accurately be ranged between geometric and arithmetic means of the proposed cbFFDs or logically computed by prepared FISs.

Evaluating Topological Vulnerability Based on Fuzzy Fractal Dimension

Complex networks have been widely applied in many complex systems existed in nature and society because of its rapid development. Many methods have been proposed to evaluate the vulnerability of the complex networks because of the high security requirements of the network. In this paper, a novel method is proposed to evaluate network’s vulnerability, which is based on fuzzy fractal dimension and average edge betweenness. Fuzzy fractal dimension can reflect the dynamic structure and topological structure of complex network, which is important to the vulnerability of complex network. So this proposed method can overcome the shortcomings of previous works by replacing the key coefficient p by fuzzy fractal dimension. In order to show this proposed method’s accuracy and effectiveness, six USAir networks in different years are applied in this paper. Three common methods are used to compare the results with this proposed method, and the RB attack strategy is used to analyze the vulnerability of dynamic characteristic. The fuzzy fractal dimension of randomly selecting largest connected subset which is close to the initial fuzzy fractal dimension shows the reliability and stability of this proposed method. The vulnerability order obtained by this proposed method is more realistic, because the Pearson correlation coefficient r about this method equals to 0.9805, which shows a extremely strong correlation with the reality.

The Structure of Glutinous-Lime Mortar: A Fuzzy Fractal System

The glutinous rice-lime mortar (M_GRL) is a high performance organic-inorganic composite, which has been commonly used as a building material since ancient times in China. However, the knowledge of nonlinear structure of M_GRL is limited. In this work, the nonlinear structure of traditional M_GRL was investigated. The particle size distribution (PSD) of fine and micro-aggregate were evaluated by fuzzy fractal set. The microstructure of M_GRL were tested by electron backscattered diffraction (EBSD) and field emission scanning electron microscope (FESEM) analysis. Results shown that the structure of M_GRL is a fuzzy fractal system. And the fuzzy fractal dimension of the system is correlated to the fracture resistance of M_GRL.

Fuzzy fractal dimension of complex networks

Complex networks are widely used to describe the structure of many complex systems in nature and society. The box-covering algorithm is widely applied to calculate the fractal dimension, which plays an important role in complex networks. However, there are two open issues in the existing box-covering algorithms. On the one hand, to identify the minimum boxes for any given size belongs to a family of Non-deterministic Polynomial-time hard problems. On the other hand, there exists randomness. In this paper, a fuzzy fractal dimension model of complex networks with fuzzy sets is proposed. The results are illustrated to show that the proposed model is efficient and less time consuming.

Fuzzy fractal dimension based on escape time algorithm

Fractal dimension is a mathematical concept used to measure the geometrical complexity of fractal set. It is defined for fractal geometric images, and considered as global features for them. There are many methods to estimate the fractal dimension of an object. The box counting dimension is an easier and a widely used one, while the escape time dimension is another method used to estimate the dimension of fractals generated using escape time algorithm. These methods are used to calculate the dimension for monochrome images (2Dimages). The necessity to generalize these concepts to be applicable for real world application ( e.g. gray scale image, or colored images) has motivating us to introducing the concepts of fuzzy sets. Fuzzy fractal dimension is proposed as the fractal feature for n-dimensional image. In this paper, a new approach to determine fractal dimension is proposed and a new local fuzzy fractal dimension based on this approach is proposed also. It will help to extend this feature to be used in many real world applications that cannot be served based on traditional fractal dimension. By this new approach, the FD is estimated with a reduced number of computational processes. This will helps to improve the complexity of the escape time algorithm that is considered as an NP-Hard problem, and with high precision results.

CLASSIFICATION OF AIRCRAFT TARGETS WITH SURVEILLANCE RADARS BASED ON FUZZY FRACTAL FEATURES

The fuzzy fractal characteristics of return signals from aircraft targets in conventional radars ofier a description of dynamic features which induce the echo structure of targets, therefore they can provide a new way for aircraft target classiflcation and recognition with low-resolution surveillance radars. On basis of introducing fuzzy fractal theory, the paper analyzes the fuzzy fractal characteristics of return signals from aircraft targets in a VHF-band surveillance radar by means of the fuzzy fractal analysis, and puts forward a fuzzy- fractal-feature-based classiflcation method for aircraft targets with a low-resolution radar from the viewpoint of pattern recognition. The analysis shows that the fuzzy fractal characteristic parameters such as the local fuzzy fractal dimension (LFFD) and local degree of fractality (LGF) can be used as efiective features for aircraft target classiflcation and recognition. The results of classiflcation experiments validate the proposed method.

Local fuzzy fractal dimension and its application in medical image processing

The local fuzzy fractal dimension (LFFD) is proposed to extract local fractal feature of medical images. The definition of LFFD is an extension of the pixel-covering method by incorporating the fuzzy set. Multi-feature edge detection is implemented with the LFFD and the Sobel operator. The LFFD can also serve as a characteristic of motion in medical image sequences. The experimental results show that the LFFD is an important feature of edge areas in medical images and can provide information for segmentation of echocardiogram image sequences.

Hybrid intelligent systems for time series prediction using neural networks, fuzzy logic, and fractal theory

In this paper, we describe a new method for the estimation of the fractal dimension of a geometrical object using fuzzy logic techniques. The fractal dimension is a mathematical concept, which measures the geometrical complexity of an object. The algorithms for estimating the fractal dimension calculate a numerical value using as data a time series for the specific problem. This numerical (crisp) value gives an idea of the complexity of the geometrical object (or time series). However, there is an underlying uncertainty in the estimation of the fractal dimension because we use only a sample of points of the object, and also because the numerical algorithms for the fractal dimension are not completely accurate. For this reason, we have proposed a new definition of the fractal dimension that incorporates the concept of a fuzzy set. This new definition can be considered a weaker definition (but more realistic) of the fractal dimension, and we have named this the "fuzzy fractal dimension." We can apply this new definition of the fractal dimension in conjunction with soft computing techniques for the problem of time series prediction. We have developed hybrid intelligent systems combining neural networks, fuzzy logic, and the fractal dimension, for the problem of time series prediction, and we have achieved very good results.