Search results for: Fuzzy neural networks

Authors: Margaret F. Shipley

Abstract:

Fuzzy logic can be used when knowledge is incomplete or when ambiguity of data exists. The purpose of this paper is to propose a proactive fuzzy set- based model for reacting to the risk inherent in investment activities relative to a complete view of portfolio management. Fuzzy rules are given where, depending on the antecedents, the portfolio size may be slightly or significantly decreased or increased. The decision maker considers acceptable bounds on the proportion of acceptable risk and return. The Fuzzy Controller model allows learning to be achieved as 1) the firing strength of each rule is measured, 2) fuzzy output allows rules to be updated, and 3) new actions are recommended as the system continues to loop. An extension is given to the fuzzy controller that evaluates potential financial loss before adjusting the portfolio. An application is presented that illustrates the algorithm and extension developed in the paper.

Keywords: Portfolio Management, Financial Market Monitoring, Fuzzy Controller, Fuzzy Logic,

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Authors: Fan-Yong Meng

Abstract:

In this paper, a generalized form of the Banzhaf-Owen value for cooperative fuzzy games with a coalition structure is proposed. Its axiomatic system is given by extending crisp case. In order to better understand the Banzhaf-Owen value for fuzzy games with a coalition structure, we briefly introduce the Banzhaf-Owen values for two special kinds of fuzzy games with a coalition structure, and give their explicit forms.

Keywords: Cooperative fuzzy game, Banzhaf-Owen value, multi linear extension, Choquet integral.

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Authors: Sara A.Yones, Ahmed S. Moussa

Abstract:

Quantitative measurements of tumor in general and tumor volume in particular, become more realistic with the use of Magnetic Resonance imaging, especially when the tumor morphological changes become irregular and difficult to assess by clinical examination. However, tumor volume estimation strongly depends on the image segmentation, which is fuzzy by nature. In this paper a fuzzy approach is presented for tumor volume segmentation based on the fuzzy connectedness algorithm. The fuzzy affinity matrix resulting from segmentation is then used to estimate a fuzzy volume based on a certainty parameter, an Alpha Cut, defined by the user. The proposed method was shown to highly affect treatment decisions. A statistical analysis was performed in this study to validate the results based on a manual method for volume estimation and the importance of using the Alpha Cut is further explained.

Keywords: Alpha Cut, Fuzzy Connectedness, Magnetic Resonance Imaging, Tumor volume estimation.

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Authors: Sanae Attioui, Said Najah

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The Earth's surface is constantly changing through forces of nature and human activities. Reliable, accurate, and timely change detection is critical to environmental monitoring, resource management, and planning activities. Recently, interest in deep learning algorithms, especially convolutional neural networks, has increased in the field of image change detection due to their powerful ability to extract multi-level image features automatically. However, these networks are prone to drawbacks that limit their applications, which reside in their inability to capture spatial relationships between image instances, as this necessitates a large amount of training data. As an alternative, Capsule Network has been proposed to overcome these shortcomings. Although its effectiveness in remote sensing image analysis has been experimentally verified, its application in change detection tasks remains very sparse. Motivated by its greater robustness towards improved hierarchical object representation, this study aims to apply a capsule network for PolSAR image Change Detection. The experimental results demonstrate that the proposed change detection method can yield a significantly higher detection rate compared to methods based on convolutional neural networks.

Keywords: Change detection, capsule network, deep network, Convolutional Neural Networks, polarimetric synthetic aperture radar images, PolSAR images.

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Authors: F. Smach, M. Atri, J. Mitéran, M. Abid

Abstract:

Face detection and recognition has many applications in a variety of fields such as security system, videoconferencing and identification. Face classification is currently implemented in software. A hardware implementation allows real-time processing, but has higher cost and time to-market. The objective of this work is to implement a classifier based on neural networks MLP (Multi-layer Perceptron) for face detection. The MLP is used to classify face and non-face patterns. The systm is described using C language on a P4 (2.4 Ghz) to extract weight values. Then a Hardware implementation is achieved using VHDL based Methodology. We target Xilinx FPGA as the implementation support.

Keywords: Classification, Face Detection, FPGA Hardware description, MLP.

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Authors: Amin Sedighfar, M. R. Moniri

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Determination of state of charge (SOC) in today’s world becomes an increasingly important issue in all the applications that include a battery. In fact, estimation of the SOC is a fundamental need for the battery, which is the most important energy storage in Hybrid Electric Vehicles (HEVs), smart grid systems, drones, UPS and so on. Regarding those applications, the SOC estimation algorithm is expected to be precise and easy to implement. This paper presents an online method for the estimation of the SOC of Valve-Regulated Lead Acid (VRLA) batteries. The proposed method uses the well-known Kalman Filter (KF), and Neural Networks (NNs) and all of the simulations have been done with MATLAB software. The NN is trained offline using the data collected from the battery discharging process. A generic cell model is used, and the underlying dynamic behavior of the model has used two capacitors (bulk and surface) and three resistors (terminal, surface, and end), where the SOC determined from the voltage represents the bulk capacitor. The aim of this work is to compare the performance of conventional integration-based SOC estimation methods with a mixed algorithm. Moreover, by containing the effect of temperature, the final result becomes more accurate. 

Keywords: Kalman filter, neural networks, state-of-charge, VRLA battery.

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Authors: Atiqul Islam, Shamim Akhter, Tumnun E. Mursalin

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Least Development Countries (LDC) like Bangladesh, whose 25% revenue earning is achieved from Textile export, requires producing less defective textile for minimizing production cost and time. Inspection processes done on these industries are mostly manual and time consuming. To reduce error on identifying fabric defects requires more automotive and accurate inspection process. Considering this lacking, this research implements a Textile Defect Recognizer which uses computer vision methodology with the combination of multi-layer neural networks to identify four classifications of textile defects. The recognizer, suitable for LDC countries, identifies the fabric defects within economical cost and produces less error prone inspection system in real time. In order to generate input set for the neural network, primarily the recognizer captures digital fabric images by image acquisition device and converts the RGB images into binary images by restoration process and local threshold techniques. Later, the output of the processed image, the area of the faulty portion, the number of objects of the image and the sharp factor of the image, are feed backed as an input layer to the neural network which uses back propagation algorithm to compute the weighted factors and generates the desired classifications of defects as an output.

Keywords: Computer vision, image acquisition device, machine vision, multi-layer neural networks.

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Authors: A. Mirzaaghazadeh, H. Motameni, M. Karshenas, H. Nematzadeh

Abstract:

Learning the gradient of neuron's activity function like the weight of links causes a new specification which is flexibility. In flexible neural networks because of supervising and controlling the operation of neurons, all the burden of the learning is not dedicated to the weight of links, therefore in each period of learning of each neuron, in fact the gradient of their activity function, cooperate in order to achieve the goal of learning thus the number of learning will be decreased considerably. Furthermore, learning neurons parameters immunes them against changing in their inputs and factors which cause such changing. Likewise initial selecting of weights, type of activity function, selecting the initial gradient of activity function and selecting a fixed amount which is multiplied by gradient of error to calculate the weight changes and gradient of activity function, has a direct affect in convergence of network for learning.

Keywords: Back propagation, Flexible, Gradient, Learning, Neural network, Pattern recognition.

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Authors: Ben Khayut, Lina Fabri, Maya Avikhana

Abstract:

The modern Artificial Narrow Intelligence (ANI) models cannot: a) independently, situationally, and continuously function without of human intelligence, used for retraining and reprogramming the ANI’s models, and b) think, understand, be conscious, and cognize under uncertainty and changing of the environmental objects. To eliminate these shortcomings and build a new generation of Artificial Intelligence systems, the paper proposes a Conception, Model, and Method of Computational Psycholinguistic Cognitive Situational-Fuzzy Self-Controlled Brain and Mind System (CPCSFSCBMSUU). This system uses a neural network as its computational memory, and activates functions of the perception, identification of real objects, fuzzy situational control, and forming images of these objects. These images and objects are used for modeling their psychological, linguistic, cognitive, and neural values of properties and features, the meanings of which are identified, interpreted, generated, and formed taking into account the identified subject area, using the data, information, knowledge, accumulated in the Memory. The functioning of the CPCSFSCBMSUU is carried out by its subsystems of the: fuzzy situational control of all processes, computational perception, identifying of reactions and actions, Psycholinguistic Cognitive Fuzzy Logical Inference, Decision Making, Reasoning, Systems Thinking, Planning, Awareness, Consciousness, Cognition, Intuition, and Wisdom. In doing so are performed analysis and processing of the psycholinguistic, subject, visual, signal, sound and other objects, accumulation and using the data, information and knowledge of the Memory, communication, and interaction with other computing systems, robots and humans in order of solving the joint tasks. To investigate the functional processes of the proposed system, the principles of situational control, fuzzy logic, psycholinguistics, informatics, and modern possibilities of data science were applied. The proposed self-controlled system of brain and mind is oriented on use as a plug-in in multilingual subject applications.

Keywords: Computational psycholinguistic cognitive brain and mind system, situational fuzzy control, uncertainty, AI.

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Authors: Shaoquan Sun, Chunxiang Liu

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The aim of this paper is to introduce the concepts of the (λ, μ)-intuitionistic fuzzy subgroups and (λ, μ)-intuitionistic fuzzy normal subgroups of groups with operators, and to investigate their properties and characterizations based on M-group homomorphism.

Keywords: Intuitionistic fuzzy group, (λ, μ)-intuitionistic fuzzy subgroup of groups with operators, (λ, μ)-intuitionistic fuzzy normal subgroup of groups with operators, M-group homomorphism.

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Authors: A. Denker, U. Akıncıoğlu

Abstract:

In this paper a neural adaptive control method has been developed and applied to robot control. Simulation results are presented to verify the effectiveness of the controller. These results show that the performance by using this controller is better than those which just use either direct inverse control or predictive control. In addition, they show that the resulting is a useful method which combines the advantages of both direct inverse control and predictive control.

Keywords: Neural networks, robotics, direct inverse control, predictive control.

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Authors: A. Greco, N. Mammone, F.C. Morabito, M.Versaci

Abstract:

This paper is mainly concerned with the application of a novel technique of data interpretation for classifying measurements of plasma columns in Tokamak reactors for nuclear fusion applications. The proposed method exploits several concepts derived from soft computing theory. In particular, Artificial Neural Networks and Multi-Class Support Vector Machines have been exploited to classify magnetic variables useful to determine shape and position of the plasma with a reduced computational complexity. The proposed technique is used to analyze simulated databases of plasma equilibria based on ITER geometry configuration. As well as demonstrating the successful recovery of scalar equilibrium parameters, we show that the technique can yield practical advantages compared with earlier methods.

Keywords: Tokamak, Classification, Artificial Neural Network, Support Vector Machines.

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Authors: Mogari I. Rapoo, Diteboho Xaba

Abstract:

This paper examines the forecasting performance of Autoregressive Integrated Moving Average (ARIMA) and Artificial Neural Networks (ANN) models with the published exchange rate obtained from South African Reserve Bank (SARB). ARIMA is one of the popular linear models in time series forecasting for the past decades. ARIMA and ANN models are often compared and literature revealed mixed results in terms of forecasting performance. The study used the MSE and MAE to measure the forecasting performance of the models. The empirical results obtained reveal the superiority of ARIMA model over ANN model. The findings further resolve and clarify the contradiction reported in literature over the superiority of ARIMA and ANN models.

Keywords: ARIMA, artificial neural networks models, error metrics, exchange rates.

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Authors: Qianqian Li, Shaoquan Sun

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The aim of this paper is to introduce the notion of intuitionistic fuzzy positive implicative ideals with thresholds (λ, μ) of BCI-algebras and to investigate its properties and characterizations.

Keywords: BCI-algebra, intuitionistic fuzzy set, intuitionistic fuzzy ideal with thresholds (λ, μ), intuitionistic fuzzy positive implicative ideal with thresholds (λ, μ).

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Authors: A. J. Al-Shareef, E. A. Mohamed, E. Al-Judaibi

Abstract:

Load forecasting has become in recent years one of the major areas of research in electrical engineering. Most traditional forecasting models and artificial intelligence neural network techniques have been tried out in this task. Artificial neural networks (ANN) have lately received much attention, and a great number of papers have reported successful experiments and practical tests. This article presents the development of an ANN-based short-term load forecasting model with improved generalization technique for the Regional Power Control Center of Saudi Electricity Company, Western Operation Area (SEC-WOA). The proposed ANN is trained with weather-related data and historical electric load-related data using the data from the calendar years 2001, 2002, 2003, and 2004 for training. The model tested for one week at five different seasons, typically, winter, spring, summer, Ramadan and fall seasons, and the mean absolute average error for one hour-ahead load forecasting found 1.12%.

Keywords: Artificial neural networks, short-term load forecasting, back propagation.

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Authors: Magdi M. Nabi, Ding-Li Yu

Abstract:

Control of a semi-batch polymerization reactor using an adaptive radial basis function (RBF) neural network method is investigated in this paper. A neural network inverse model is used to estimate the valve position of the reactor; this method can identify the controlled system with the RBF neural network identifier. The weights of the adaptive PID controller are timely adjusted based on the identification of the plant and self-learning capability of RBFNN. A PID controller is used in the feedback control to regulate the actual temperature by compensating the neural network inverse model output. Simulation results show that the proposed control has strong adaptability, robustness and satisfactory control performance and the nonlinear system is achieved.

Keywords: Chylla-Haase polymerization reactor, RBF neural networks, feed-forward and feedback control.

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Authors: Chaitanya Chawla, Divya Panwar, Gurneesh Singh Anand, M. P. S Bhatia

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This paper presents a deep-learning mechanism for classifying computer generated images and photographic images. The proposed method accounts for a convolutional layer capable of automatically learning correlation between neighbouring pixels. In the current form, Convolutional Neural Network (CNN) will learn features based on an image's content instead of the structural features of the image. The layer is particularly designed to subdue an image's content and robustly learn the sensor pattern noise features (usually inherited from image processing in a camera) as well as the statistical properties of images. The paper was assessed on latest natural and computer generated images, and it was concluded that it performs better than the current state of the art methods.

Keywords: Image forensics, computer graphics, classification, deep learning, convolutional neural networks.

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Authors: Ulas Vural, M. Ergun Okay, E. Mesut Yildiz

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Telecommunication service providers demand accurate and precise prediction of customer churn probabilities to increase the effectiveness of their customer relation services. The large amount of customer data owned by the service providers is suitable for analysis by machine learning methods. In this study, expenditure data of customers are analyzed by using an artificial neural network (ANN). The ANN model is applied to the data of customers with different billing duration. The proposed model successfully predicts the churn probabilities at 83% accuracy for only three months expenditure data and the prediction accuracy increases up to 89% when the nine month data is used. The experiments also show that the accuracy of ANN model increases on an extended feature set with information of the changes on the bill amounts.

Keywords: Customer relationship management, churn prediction, telecom industry, deep learning, Artificial Neural Networks, ANN.

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Authors: N. Subramanian, U. K. Misra, M. S. Panda

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In this paper the concept of strongly (λM)p - Ces'aro summability of a sequence of fuzzy numbers and strongly λM- statistically convergent sequences of fuzzy numbers is introduced.

Keywords: Fuzzy numbers, statistical convergence, Orlicz space, entire sequence.

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Authors: Fazıl Gökgöz, Fahrettin Filiz

Abstract:

Electricity prices have sophisticated features such as high volatility, nonlinearity and high frequency that make forecasting quite difficult. Electricity price has a volatile and non-random character so that, it is possible to identify the patterns based on the historical data. Intelligent decision-making requires accurate price forecasting for market traders, retailers, and generation companies. So far, many shallow-ANN (artificial neural networks) models have been published in the literature and showed adequate forecasting results. During the last years, neural networks with many hidden layers, which are referred to as DNN (deep neural networks) have been using in the machine learning community. The goal of this study is to investigate electricity price forecasting performance of the shallow-ANN and DNN models for the Turkish day-ahead electricity market. The forecasting accuracy of the models has been evaluated with publicly available data from the Turkish day-ahead electricity market. Both shallow-ANN and DNN approach would give successful result in forecasting problems. Historical load, price and weather temperature data are used as the input variables for the models. The data set includes power consumption measurements gathered between January 2016 and December 2017 with one-hour resolution. In this regard, forecasting studies have been carried out comparatively with shallow-ANN and DNN models for Turkish electricity markets in the related time period. The main contribution of this study is the investigation of different shallow-ANN and DNN models in the field of electricity price forecast. All models are compared regarding their MAE (Mean Absolute Error) and MSE (Mean Square) results. DNN models give better forecasting performance compare to shallow-ANN. Best five MAE results for DNN models are 0.346, 0.372, 0.392, 0,402 and 0.409.

Keywords: Deep learning, artificial neural networks, energy price forecasting, Turkey.

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Authors: J-P. Skön, M. Johansson, M. Raatikainen, K. Leiviskä, M. Kolehmainen

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The use of neural networks is popular in various building applications such as prediction of heating load, ventilation rate and indoor temperature. Significant is, that only few papers deal with indoor carbon dioxide (CO2) prediction which is a very good indicator of indoor air quality (IAQ). In this study, a data-driven modelling method based on multilayer perceptron network for indoor air carbon dioxide in an apartment building is developed. Temperature and humidity measurements are used as input variables to the network. Motivation for this study derives from the following issues. First, measuring carbon dioxide is expensive and sensors power consumptions is high and secondly, this leads to short operating times of battery-powered sensors. The results show that predicting CO2 concentration based on relative humidity and temperature measurements, is difficult. Therefore, more additional information is needed.

Keywords: Indoor air quality, Modelling, Neural networks

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Authors: Seunghee Park, Junkyeong Kim, Eun-Seok Shin, Sang-Hun Han

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In this study, two kinds of nondestructive evaluation  (NDE) techniques (rebound hardness and ultrasonic pulse velocity  methods) are investigated for the effective maintenance of underwater  concrete structures. A new methodology to estimate the underwater  concrete strengths more effectively, named “artificial neural network  (ANN) – based concrete strength estimation with the combination of  rebound hardness and ultrasonic pulse velocity methods” is proposed  and verified throughout a series of experimental works.

 

Keywords: Underwater Concrete, Rebound Hardness, Schmidt hammer, Ultrasonic Pulse Velocity, Ultrasonic Sensor, Artificial Neural Networks, ANN.

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Authors: D. Triantakonstantis, D. Stathakis

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Urban areas have been expanded throughout the globe. Monitoring and modelling urban growth have become a necessity for a sustainable urban planning and decision making. Urban prediction models are important tools for analyzing the causes and consequences of urban land use dynamics. The objective of this research paper is to analyze and model the urban change, which has been occurred from 1990 to 2000 using CORINE land cover maps. The model was developed using drivers of urban changes (such as road distance, slope, etc.) under an Artificial Neural Network modelling approach. Validation was achieved using a prediction map for 2006 which was compared with a real map of Urban Atlas of 2006. The accuracy produced a Kappa index of agreement of 0,639 and a value of Cramer's V of 0,648. These encouraging results indicate the importance of the developed urban growth prediction model which using a set of available common biophysical drivers could serve as a management tool for the assessment of urban change.

Keywords: Artificial Neural Networks, CORINE, Urban Atlas, Urban Growth Prediction.

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Authors: Guojian Cheng, Tianshi Liu, Jiaxin Han, Zheng Wang

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The competitive learning is an adaptive process in which the neurons in a neural network gradually become sensitive to different input pattern clusters. The basic idea behind the Kohonen-s Self-Organizing Feature Maps (SOFM) is competitive learning. SOFM can generate mappings from high-dimensional signal spaces to lower dimensional topological structures. The main features of this kind of mappings are topology preserving, feature mappings and probability distribution approximation of input patterns. To overcome some limitations of SOFM, e.g., a fixed number of neural units and a topology of fixed dimensionality, Growing Self-Organizing Neural Network (GSONN) can be used. GSONN can change its topological structure during learning. It grows by learning and shrinks by forgetting. To speed up the training and convergence, a new variant of GSONN, twin growing cell structures (TGCS) is presented here. This paper first gives an introduction to competitive learning, SOFM and its variants. Then, we discuss some GSONN with fixed dimensionality, which include growing cell structures, its variants and the author-s model: TGCS. It is ended with some testing results comparison and conclusions.

Keywords: Artificial neural networks, Competitive learning, Growing cell structures, Self-organizing feature maps.

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Authors: P. Karimi, A. H. Khedmati Bazkiaei

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The main goal of this study is to test differential neural network as a controller of smart structure and is to enumerate its advantages and disadvantages in comparison with other controllers. In this study, the smart structure has been considered as a Euler Bernoulli cantilever beam and it has been tried that it be under control with the use of vibration neural network resulting from movement. Also, a linear observer has been considered as a reference controller and has been compared its results. The considered vibration charts and the controlled state have been recounted in the final part of this text. The obtained result show that neural observer has better performance in comparison to the implemented linear observer.

Keywords: Smart material, on-line differential artificial neural network, active control, finite element method.

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Authors: Yurii Bloshko, Oksana Olar

Abstract:

This paper presents the analysis of six different classes of Petri nets: fuzzy Petri nets (FPN), generalized fuzzy Petri nets (GFPN), parameterized fuzzy Petri nets (PFPN), T2GFPN, flexible generalized fuzzy Petri nets (FGFPN), binary Petri nets (BPN). These classes were simulated in the special software PNeS® for the analysis of its pros and cons on the example of models which are dedicated to the decision-making process of passenger transport logistics. The paper includes the analysis of two approaches: when input values are filled with the experts’ knowledge; when fuzzy expectations represented by output values are added to the point. These approaches fulfill the possibilities of triples of functions which are replaced with different combinations of t-/s-norms.

Keywords: Fuzzy petri net, intelligent computational techniques, knowledge representation, triangular norms.

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Authors: Han Xiao, Xiaoyan Zhu

Abstract:

Margin-Based Principle has been proposed for a long time, it has been proved that this principle could reduce the structural risk and improve the performance in both theoretical and practical aspects. Meanwhile, feed-forward neural network is a traditional classifier, which is very hot at present with a deeper architecture. However, the training algorithm of feed-forward neural network is developed and generated from Widrow-Hoff Principle that means to minimize the squared error. In this paper, we propose a new training algorithm for feed-forward neural networks based on Margin-Based Principle, which could effectively promote the accuracy and generalization ability of neural network classifiers with less labelled samples and flexible network. We have conducted experiments on four UCI open datasets and achieved good results as expected. In conclusion, our model could handle more sparse labelled and more high-dimension dataset in a high accuracy while modification from old ANN method to our method is easy and almost free of work.

Keywords: Max-Margin Principle, Feed-Forward Neural Network, Classifier.

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Authors: Hazem M. El-Bakry

Abstract:

In this paper a new fast simplification method is presented. Such method realizes Karnough map with large number of variables. In order to accelerate the operation of the proposed method, a new approach for fast detection of group of ones is presented. Such approach implemented in the frequency domain. The search operation relies on performing cross correlation in the frequency domain rather than time one. It is proved mathematically and practically that the number of computation steps required for the presented method is less than that needed by conventional cross correlation. Simulation results using MATLAB confirm the theoretical computations. Furthermore, a powerful solution for realization of complex functions is given. The simplified functions are implemented by using a new desigen for neural networks. Neural networks are used because they are fault tolerance and as a result they can recognize signals even with noise or distortion. This is very useful for logic functions used in data and computer communications. Moreover, the implemented functions are realized with minimum amount of components. This is done by using modular neural nets (MNNs) that divide the input space into several homogenous regions. Such approach is applied to implement XOR function, 16 logic functions on one bit level, and 2-bit digital multiplier. Compared to previous non- modular designs, a clear reduction in the order of computations and hardware requirements is achieved.

Keywords: Boolean Functions, Simplification, KarnoughMap, Implementation of Logic Functions, Modular NeuralNetworks.

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Authors: Ersin Kaya, Bulent Oran, Ahmet Arslan

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In this study, fuzzy rule-based classifier is used for the diagnosis of congenital heart disease. Congenital heart diseases are defined as structural or functional heart disease. Medical data sets were obtained from Pediatric Cardiology Department at Selcuk University, from years 2000 to 2003. Firstly, fuzzy rules were generated by using medical data. Then the weights of fuzzy rules were calculated. Two different reasoning methods as “weighted vote method" and “singles winner method" were used in this study. The results of fuzzy classifiers were compared.

Keywords: Congenital heart disease, Fuzzy rule-basedclassifiers, Classification

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Authors: Qingqing Wang, Shouming Zhong

Abstract:

This paper is concerned with the stability problem with two additive time-varying delay components. By choosing one augmented Lyapunov-Krasovskii functional, using some new zero equalities, and combining linear matrix inequalities (LMI) techniques, two new sufficient criteria ensuring the global stability asymptotic stability of DNNs is obtained. These stability criteria are present in terms of linear matrix inequalities and can be easily checked. Finally, some examples are showed to demonstrate the effectiveness and less conservatism of the proposed method.

Keywords: Neural networks, Globally asymptotic stability, LMI approach, Additive time-varying delays.

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