Search results for: fuzzy wavelet packet
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 1452

Search results for: fuzzy wavelet packet

1152 Hybrid Artificial Bee Colony and Least Squares Method for Rule-Based Systems Learning

Authors: Ahcene Habbi, Yassine Boudouaoui

Abstract:

This paper deals with the problem of automatic rule generation for fuzzy systems design. The proposed approach is based on hybrid artificial bee colony (ABC) optimization and weighted least squares (LS) method and aims to find the structure and parameters of fuzzy systems simultaneously. More precisely, two ABC based fuzzy modeling strategies are presented and compared. The first strategy uses global optimization to learn fuzzy models, the second one hybridizes ABC and weighted least squares estimate method. The performances of the proposed ABC and ABC-LS fuzzy modeling strategies are evaluated on complex modeling problems and compared to other advanced modeling methods.

Keywords: Automatic design, learning, fuzzy rules, hybrid, swarm optimization.

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1151 Proposal of Additional Fuzzy Membership Functions in Smoothing Transition Autoregressive Models

Authors: Ε. Giovanis

Abstract:

In this paper we present, propose and examine additional membership functions for the Smoothing Transition Autoregressive (STAR) models. More specifically, we present the tangent hyperbolic, Gaussian and Generalized bell functions. Because Smoothing Transition Autoregressive (STAR) models follow fuzzy logic approach, more fuzzy membership functions should be tested. Furthermore, fuzzy rules can be incorporated or other training or computational methods can be applied as the error backpropagation or genetic algorithm instead to nonlinear squares. We examine two macroeconomic variables of US economy, the inflation rate and the 6-monthly treasury bills interest rates.

Keywords: Forecast , Fuzzy membership functions, Smoothingtransition, Time-series

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1150 Intelligent Automatic Generation Control of Two Area Interconnected Power System using Hybrid Neuro Fuzzy Controller

Authors: Sathans, A. Swarup

Abstract:

This paper presents the development and application of an adaptive neuro fuzzy inference system (ANFIS) based intelligent hybrid neuro fuzzy controller for automatic generation control (AGC) of two-area interconnected thermal power system with reheat non linearity. The dynamic response of the system has been studied for 1% step load perturbation in area-1. The performance of the proposed neuro fuzzy controller is compared against conventional proportional-integral (PI) controller, state feedback linear quadratic regulator (LQR) controller and fuzzy gain scheduled proportionalintegral (FGSPI) controller. Comparative analysis demonstrates that the proposed intelligent neuro fuzzy controller is the most effective of all in improving the transients of frequency and tie-line power deviations against small step load disturbances. Simulations have been performed using Matlab®.

Keywords: Automatic generation control, ANFIS, LQR, Hybrid neuro fuzzy controller

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1149 Wavelet-Based Classification of Myocardial Ischemia, Arrhythmia, Congestive Heart Failure and Sleep Apnea

Authors: Santanu Chattopadhyay, Gautam Sarkar, Arabinda Das

Abstract:

This paper presents wavelet based classification of various heart diseases. Electrocardiogram signals of different heart patients have been studied. Statistical natures of electrocardiogram signals for different heart diseases have been compared with the statistical nature of electrocardiograms for normal persons. Under this study four different heart diseases have been considered as follows: Myocardial Ischemia (MI), Congestive Heart Failure (CHF), Arrhythmia and Sleep Apnea. Statistical nature of electrocardiograms for each case has been considered in terms of kurtosis values of two types of wavelet coefficients: approximate and detail. Nine wavelet decomposition levels have been considered in each case. Kurtosis corresponding to both approximate and detail coefficients has been considered for decomposition level one to decomposition level nine. Based on significant difference, few decomposition levels have been chosen and then used for classification.

Keywords: Arrhythmia, congestive heart failure, discrete wavelet transform, electrocardiogram, myocardial ischemia, sleep apnea.

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1148 An Empirical Analysis of Arabic WebPages Classification using Fuzzy Operators

Authors: Ahmad T. Al-Taani, Noor Aldeen K. Al-Awad

Abstract:

In this study, a fuzzy similarity approach for Arabic web pages classification is presented. The approach uses a fuzzy term-category relation by manipulating membership degree for the training data and the degree value for a test web page. Six measures are used and compared in this study. These measures include: Einstein, Algebraic, Hamacher, MinMax, Special case fuzzy and Bounded Difference approaches. These measures are applied and compared using 50 different Arabic web pages. Einstein measure was gave best performance among the other measures. An analysis of these measures and concluding remarks are drawn in this study.

Keywords: Text classification, HTML documents, Web pages, Machine learning, Fuzzy logic, Arabic Web pages.

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1147 Ranking Fuzzy Numbers Based on Lexicographical Ordering

Authors: B. Farhadinia

Abstract:

Although so far, many methods for ranking fuzzy numbers have been discussed broadly, most of them contained some shortcomings, such as requirement of complicated calculations, inconsistency with human intuition and indiscrimination. The motivation of this study is to develop a model for ranking fuzzy numbers based on the lexicographical ordering which provides decision-makers with a simple and efficient algorithm to generate an ordering founded on a precedence. The main emphasis here is put on the ease of use and reliability. The effectiveness of the proposed method is finally demonstrated by including a comprehensive comparing different ranking methods with the present one.

Keywords: Ranking fuzzy numbers, Lexicographical ordering.

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1146 Energy Distribution of EEG Signals: EEG Signal Wavelet-Neural Network Classifier

Authors: I. Omerhodzic, S. Avdakovic, A. Nuhanovic, K. Dizdarevic

Abstract:

In this paper, a wavelet-based neural network (WNN) classifier for recognizing EEG signals is implemented and tested under three sets EEG signals (healthy subjects, patients with epilepsy and patients with epileptic syndrome during the seizure). First, the Discrete Wavelet Transform (DWT) with the Multi-Resolution Analysis (MRA) is applied to decompose EEG signal at resolution levels of the components of the EEG signal (δ, θ, α, β and γ) and the Parseval-s theorem are employed to extract the percentage distribution of energy features of the EEG signal at different resolution levels. Second, the neural network (NN) classifies these extracted features to identify the EEGs type according to the percentage distribution of energy features. The performance of the proposed algorithm has been evaluated using in total 300 EEG signals. The results showed that the proposed classifier has the ability of recognizing and classifying EEG signals efficiently.

Keywords: Epilepsy, EEG, Wavelet transform, Energydistribution, Neural Network, Classification.

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1145 Jacobi-Based Methods in Solving Fuzzy Linear Systems

Authors: Lazim Abdullah, Nurhakimah Ab. Rahman

Abstract:

Linear systems are widely used in many fields of science and engineering. In many applications, at least some of the parameters of the system are represented by fuzzy rather than crisp numbers. Therefore it is important to perform numerical algorithms or procedures that would treat general fuzzy linear systems and solve them using iterative methods. This paper aims are to solve fuzzy linear systems using four types of Jacobi based iterative methods. Four iterative methods based on Jacobi are used for solving a general n × n fuzzy system of linear equations of the form Ax = b , where A is a crisp matrix and b an arbitrary fuzzy vector. The Jacobi, Jacobi Over-Relaxation, Refinement of Jacobi and Refinement of Jacobi Over-Relaxation methods was tested to a five by five fuzzy linear system. It is found that all the tested methods were iterated differently. Due to the effect of extrapolation parameters and the refinement, the Refinement of Jacobi Over-Relaxation method was outperformed the other three methods.

Keywords: Fuzzy linear systems, Jacobi, Jacobi Over- Relaxation, Refinement of Jacobi, Refinement of Jacobi Over- Relaxation.

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1144 Time-Frequency Modeling and Analysis of Faulty Rotor

Authors: B. X. Tchomeni, A. A. Alugongo, T. B. Tengen

Abstract:

In this paper, de Laval rotor system has been characterized by a hinge model and its transient response numerically treated for a dynamic solution. The effect of the ensuing non-linear disturbances namely rub and breathing crack is numerically simulated. Subsequently, three analysis methods: Orbit Analysis, Fast Fourier Transform (FFT), and Wavelet Transform (WT) are employed to extract features of the vibration signal of the faulty system. An analysis of the system response orbits clearly indicates the perturbations due to the rotor-to-stator contact. The sensitivities of WT to the variation in system speed have been investigated by Continuous Wavelet Transform (CWT). The analysis reveals that features of crack, rubs and unbalance in vibration response can be useful for condition monitoring. WT reveals its ability to detect nonlinear signal, and obtained results provide a useful tool method for detecting machinery faults.

Keywords: Continuous wavelet, crack, discrete wavelet, high acceleration, low acceleration, nonlinear, rotor-stator, rub.

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1143 Classification of Fuzzy Petri Nets, and Their Applications

Authors: M.H.Aziz, Erik L.J.Bohez, Manukid Parnichkun, Chanchal Saha

Abstract:

Petri Net (PN) has proven to be effective graphical, mathematical, simulation, and control tool for Discrete Event Systems (DES). But, with the growth in the complexity of modern industrial, and communication systems, PN found themselves inadequate to address the problems of uncertainty, and imprecision in data. This gave rise to amalgamation of Fuzzy logic with Petri nets and a new tool emerged with the name of Fuzzy Petri Nets (FPN). Although there had been a lot of research done on FPN and a number of their applications have been anticipated, but their basic types and structure are still ambiguous. Therefore, in this research, an effort is made to categorize FPN according to their structure and algorithms Further, literature review of the applications of FPN in the light of their classifications has been done.

Keywords: Discrete event systems, Fuzzy logic, Fuzzy Petri nets, and Petri nets.

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1142 Economic Dispatch Fuzzy Linear Regression and Optimization

Authors: A. K. Al-Othman

Abstract:

This study presents a new approach based on Tanaka's fuzzy linear regression (FLP) algorithm to solve well-known power system economic load dispatch problem (ELD). Tanaka's fuzzy linear regression (FLP) formulation will be employed to compute the optimal solution of optimization problem after linearization. The unknowns are expressed as fuzzy numbers with a triangular membership function that has middle and spread value reflected on the unknowns. The proposed fuzzy model is formulated as a linear optimization problem, where the objective is to minimize the sum of the spread of the unknowns, subject to double inequality constraints. Linear programming technique is employed to obtain the middle and the symmetric spread for every unknown (power generation level). Simulation results of the proposed approach will be compared with those reported in literature.

Keywords: Economic Dispatch, Fuzzy Linear Regression (FLP)and Optimization.

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1141 Improving Ride Comfort of a Bus Using Fuzzy Logic Controlled Suspension

Authors: Mujde Turkkan, Nurkan Yagiz

Abstract:

In this study an active controller is presented for vibration suppression of a full-bus model. The bus is modeled having seven degrees of freedom. Using the achieved model via Lagrange Equations the system equations of motion are derived. The suspensions of the bus model include air springs with two auxiliary chambers are used. Fuzzy logic controller is used to improve the ride comfort. The numerical results, verifies that the presented fuzzy logic controller improves the ride comfort.

Keywords: Ride comfort, air spring, bus, fuzzy logic controller.

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1140 On the Solution of Fully Fuzzy Linear Systems

Authors: Hsuan-Ku Liu

Abstract:

A linear system is called a fully fuzzy linear system (FFLS) if quantities in this system are all fuzzy numbers. For the FFLS, we investigate its solution and develop a new approximate method for solving the FFLS. Observing the numerical results, we find that our method is accurate than the iterative Jacobi and Gauss- Seidel methods on approximating the solution of FFLS.

Keywords: Fully fuzzy linear equations, iterative method, homotopy perturbation method, approximate solutions.

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1139 Computationally Efficient Signal Quality Improvement Method for VoIP System

Authors: H. P. Singh, S. Singh

Abstract:

The voice signal in Voice over Internet protocol (VoIP) system is processed through the best effort policy based IP network, which leads to the network degradations including delay, packet loss jitter. The work in this paper presents the implementation of finite impulse response (FIR) filter for voice quality improvement in the VoIP system through distributed arithmetic (DA) algorithm. The VoIP simulations are conducted with AMR-NB 6.70 kbps and G.729a speech coders at different packet loss rates and the performance of the enhanced VoIP signal is evaluated using the perceptual evaluation of speech quality (PESQ) measurement for narrowband signal. The results show reduction in the computational complexity in the system and significant improvement in the quality of the VoIP voice signal.

Keywords: VoIP, Signal Quality, Distributed Arithmetic, Packet Loss, Speech Coder.

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1138 Continuity of Defuzzification and Its Application to Fuzzy Control

Authors: Takashi Mitsuishi, Kiyoshi Sawada, Yasunari Shidama

Abstract:

The mathematical framework for studying of a fuzzy approximate reasoning is presented in this paper. Two important defuzzification methods (Area defuzzification and Height defuzzification) besides the center of gravity method which is the best well known defuzzification method are described. The continuity of the defuzzification methods and its application to a fuzzy feedback control are discussed.

Keywords: Fuzzy approximate reasoning, defuzzification, area method, height method.

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1137 A Generator from Cascade Markov Model for Packet Loss and Subsequent Bit Error Description

Authors: Jaroslav Polec, Viliam Hirner, Michal Martinovič, Kvetoslava Kotuliaková

Abstract:

In this paper we present a novel error model for packet loss and subsequent error description. The proposed model simulates the error performance of wireless communication link. The model is designed as two independent Markov chains, where the first one is used for packet generation and the second one generates correctly and incorrectly transmitted bits for received packets from the first chain. The statistical analyses of real communication on the wireless link are used for determination of model-s parameters. Using the obtained parameters and the implementation of the generator, we collected generated traffic. The obtained results generated by proposed model are compared with the real data collection.

Keywords: Wireless channel, error model, Markov chain, Elliot model, Gilbert model, generator, IEEE 802.11.

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1136 Fuzzy Error Recovery in Feedback Control for Three Wheel Omnidirectional Soccer Robot

Authors: Vahid Rostami, Omid sojodishijani , Saeed Ebrahimijam, Ali MohsenizanjaniNejad

Abstract:

This paper is described one of the intelligent control method in Autonomous systems, which is called fuzzy control to correct the three wheel omnidirectional robot movement while it make mistake to catch the target. Fuzzy logic is especially advantageous for problems that can not be easily represented by mathematical modeling because data is either unavailable, incomplete or the process is too complex. Such systems can be easily up grated by adding new rules to improve performance or add new features. In many cases , fuzzy control can be used to improve existing traditional controller systems by adding an extra layer of intelligence to the current control method. The fuzzy controller designed here is more accurate and flexible than the traditional controllers. The project is done at MRL middle size soccer robot team.

Keywords: Robocup , omnidirectional , fuzzy control, soccer robot , intelligent control.

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1135 A Comparative Study of Web-pages Classification Methods using Fuzzy Operators Applied to Arabic Web-pages

Authors: Ahmad T. Al-Taani, Noor Aldeen K. Al-Awad

Abstract:

In this study, a fuzzy similarity approach for Arabic web pages classification is presented. The approach uses a fuzzy term-category relation by manipulating membership degree for the training data and the degree value for a test web page. Six measures are used and compared in this study. These measures include: Einstein, Algebraic, Hamacher, MinMax, Special case fuzzy and Bounded Difference approaches. These measures are applied and compared using 50 different Arabic web-pages. Einstein measure was gave best performance among the other measures. An analysis of these measures and concluding remarks are drawn in this study.

Keywords: Text classification, HTML, web pages, machine learning, fuzzy logic, Arabic web pages.

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1134 Single Valued Neutrosophic Hesitant Fuzzy Rough Set and Its Application

Authors: K. M. Alsager, N. O. Alshehri

Abstract:

In this paper, we proposed the notion of single valued neutrosophic hesitant fuzzy rough set, by combining single valued neutrosophic hesitant fuzzy set and rough set. The combination of single valued neutrosophic hesitant fuzzy set and rough set is a powerful tool for dealing with uncertainty, granularity and incompleteness of knowledge in information systems. We presented both definition and some basic properties of the proposed model. Finally, we gave a general approach which is applied to a decision making problem in disease diagnoses, and demonstrated the effectiveness of the approach by a numerical example.

Keywords: Single valued neutrosophic hesitant set, single valued neutrosophic hesitant relation, single valued neutrosophic hesitant fuzzy rough set, decision making method.

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1133 Modified Fuzzy ARTMAP and Supervised Fuzzy ART: Comparative Study with Multispectral Classification

Authors: F.Alilat, S.Loumi, H.Merrad, B.Sansal

Abstract:

In this article a modification of the algorithm of the fuzzy ART network, aiming at returning it supervised is carried out. It consists of the search for the comparison, training and vigilance parameters giving the minimum quadratic distances between the output of the training base and those obtained by the network. The same process is applied for the determination of the parameters of the fuzzy ARTMAP giving the most powerful network. The modification consist in making learn the fuzzy ARTMAP a base of examples not only once as it is of use, but as many time as its architecture is in evolution or than the objective error is not reached . In this way, we don-t worry about the values to impose on the eight (08) parameters of the network. To evaluate each one of these three networks modified, a comparison of their performances is carried out. As application we carried out a classification of the image of Algiers-s bay taken by SPOT XS. We use as criterion of evaluation the training duration, the mean square error (MSE) in step control and the rate of good classification per class. The results of this study presented as curves, tables and images show that modified fuzzy ARTMAP presents the best compromise quality/computing time.

Keywords: Neural Networks, fuzzy ART, fuzzy ARTMAP, Remote sensing, multispectral Classification.

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1132 Wavelet Based Residual Method of Detecting GSM Signal Strength Fading

Authors: Danladi Ali, Onah Festus Iloabuchi

Abstract:

In this paper, GSM signal strength was measured in order to detect the type of the signal fading phenomenon using onedimensional multilevel wavelet residual method and neural network clustering to determine the average GSM signal strength received in the study area. The wavelet residual method predicted that the GSM signal experienced slow fading and attenuated with MSE of 3.875dB. The neural network clustering revealed that mostly -75dB, -85dB and -95dB were received. This means that the signal strength received in the study is a weak signal.

Keywords: One-dimensional multilevel wavelets, path loss, GSM signal strength, propagation and urban environment.

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1131 Fuzzy Types Clustering for Microarray Data

Authors: Seo Young Kim, Tai Myong Choi

Abstract:

The main goal of microarray experiments is to quantify the expression of every object on a slide as precisely as possible, with a further goal of clustering the objects. Recently, many studies have discussed clustering issues involving similar patterns of gene expression. This paper presents an application of fuzzy-type methods for clustering DNA microarray data that can be applied to typical comparisons. Clustering and analyses were performed on microarray and simulated data. The results show that fuzzy-possibility c-means clustering substantially improves the findings obtained by others.

Keywords: Clustering, microarray data, Fuzzy-type clustering, Validation

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1130 A Study of Neuro-Fuzzy Inference System for Gross Domestic Product Growth Forecasting

Authors: Ε. Giovanis

Abstract:

In this paper we present a Adaptive Neuro-Fuzzy System (ANFIS) with inputs the lagged dependent variable for the prediction of Gross domestic Product growth rate in six countries. We compare the results with those of Autoregressive (AR) model. We conclude that the forecasting performance of neuro-fuzzy-system in the out-of-sample period is much more superior and can be a very useful alternative tool used by the national statistical services and the banking and finance industry.

Keywords: Autoregressive model, Forecasting, Gross DomesticProduct, Neuro-Fuzzy

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1129 Comparative Study of Fault Identification and Classification on EHV Lines Using Discrete Wavelet Transform and Fourier Transform Based ANN

Authors: K.Gayathri, N. Kumarappan

Abstract:

An appropriate method for fault identification and classification on extra high voltage transmission line using discrete wavelet transform is proposed in this paper. The sharp variations of the generated short circuit transient signals which are recorded at the sending end of the transmission line are adopted to identify the fault. The threshold values involve fault classification and these are done on the basis of the multiresolution analysis. A comparative study of the performance is also presented for Discrete Fourier Transform (DFT) based Artificial Neural Network (ANN) and Discrete Wavelet Transform (DWT). The results prove that the proposed method is an effective and efficient one in obtaining the accurate result within short duration of time by using Daubechies 4 and 9. Simulation of the power system is done using MATLAB.

Keywords: EHV transmission line, Fault identification and classification, Discrete wavelet transform, Multiresolution analysis, Artificial neural network

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1128 Maximum Power Point Tracking Using FLC Tuned with GA

Authors: Mohamed Amine Haraoubia, Abdelaziz Hamzaoui, Najib Essounbouli

Abstract:

The pursuit of the MPPT has led to the development of many kinds of controllers, one of which is the Fuzzy Logic controller, which has proven its worth. To further tune this controller this paper will discuss and analyze the use of Genetic Algorithms to tune the Fuzzy Logic Controller. It will provide an introduction to both systems, and test their compatibility and performance.

Keywords: Fuzzy logic controller (FLC), fuzzy logic (FL), genetic algorithm (GA), maximum power point (MPP), maximum power point tracking (MPPT).

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1127 Unsupervised Segmentation using Fuzzy Logicbased Texture Spectrum for MRI Brain Images

Authors: G.Wiselin Jiji, L.Ganesan

Abstract:

Textures are replications, symmetries and combinations of various basic patterns, usually with some random variation one of the gray-level statistics. This article proposes a new approach to Segment texture images. The proposed approach proceeds in 2 stages. First, in this method, local texture information of a pixel is obtained by fuzzy texture unit and global texture information of an image is obtained by fuzzy texture spectrum. The purpose of this paper is to demonstrate the usefulness of fuzzy texture spectrum for texture Segmentation. The 2nd Stage of the method is devoted to a decision process, applying a global analysis followed by a fine segmentation, which is only focused on ambiguous points. The above Proposed approach was applied to brain image to identify the components of brain in turn, used to locate the brain tumor and its Growth rate.

Keywords: Fuzzy Texture Unit, Fuzzy Texture Spectrum, andPattern Recognition, segmentation.

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1126 Fault Zone Detection on Advanced Series Compensated Transmission Line using Discrete Wavelet Transform and SVM

Authors: Renju Gangadharan, G. N. Pillai, Indra Gupta

Abstract:

In this paper a novel method for finding the fault zone on a Thyristor Controlled Series Capacitor (TCSC) incorporated transmission line is presented. The method makes use of the Support Vector Machine (SVM), used in the classification mode to distinguish between the zones, before or after the TCSC. The use of Discrete Wavelet Transform is made to prepare the features which would be given as the input to the SVM. This method was tested on a 400 kV, 50 Hz, 300 Km transmission line and the results were highly accurate.

Keywords: Flexible ac transmission system (FACTS), thyristorcontrolled series-capacitor (TCSC), discrete wavelet transforms(DWT), support vector machine (SVM).

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1125 Fighter Aircraft Evaluation and Selection Process Based on Triangular Fuzzy Numbers in Multiple Criteria Decision Making Analysis Using the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS)

Authors: C. Ardil

Abstract:

This article presents a multiple criteria evaluation approach to uncertainty, vagueness, and imprecision analysis for ranking alternatives with fuzzy data for decision making using the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). The fighter aircraft evaluation and selection decision making problem is modeled in a fuzzy environment with triangular fuzzy numbers. The fuzzy decision information related to the fighter aircraft selection problem is taken into account in ordering the alternatives and selecting the best candidate. The basic fuzzy TOPSIS procedure steps transform fuzzy decision matrices into matrices of alternatives evaluated according to all decision criteria. A practical numerical example illustrates the proposed approach to the fighter aircraft selection problem.

Keywords: triangular fuzzy number (TFN), multiple criteria decision making analysis, decision making, aircraft selection, MCDMA, fuzzy TOPSIS

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1124 Object Tracking in Motion Blurred Images with Adaptive Mean Shift and Wavelet Feature

Authors: Iman Iraei, Mina Sharifi

Abstract:

A method for object tracking in motion blurred images is proposed in this article. This paper shows that object tracking could be improved with this approach. We use mean shift algorithm to track different objects as a main tracker. But, the problem is that mean shift could not track the selected object accurately in blurred scenes. So, for better tracking result, and increasing the accuracy of tracking, wavelet transform is used. We use a feature named as blur extent, which could help us to get better results in tracking. For calculating of this feature, we should use Harr wavelet. We can look at this matter from two different angles which lead to determine whether an image is blurred or not and to what extent an image is blur. In fact, this feature left an impact on the covariance matrix of mean shift algorithm and cause to better performance of tracking. This method has been concentrated mostly on motion blur parameter. transform. The results reveal the ability of our method in order to reach more accurately tracking.

Keywords: Mean shift, object tracking, blur extent, wavelet transform, motion blur.

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1123 A Study on Linking Upward Substitution and Fuzzy Demands in the Newsboy-Type Problem

Authors: Pankaj Dutta, Debjani Chakraborty

Abstract:

This paper investigates the effect of product substitution in the single-period 'newsboy-type' problem in a fuzzy environment. It is supposed that the single-period problem operates under uncertainty in customer demand, which is described by imprecise terms and modelled by fuzzy sets. To perform this analysis, we consider the fuzzy model for two-item with upward substitution. This upward substitutability is reasonable when the products can be stored according to certain attribute levels such as quality, brand or package size. We show that the explicit consideration of this substitution opportunity increase the average expected profit. Computational study is performed to observe the benefits of product's substitution.

Keywords: Fuzzy demand, Newsboy, Single-period problem, Substitution.

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