Search results for: Fuzzy Hierarchical Clustering
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 1459

Search results for: Fuzzy Hierarchical Clustering

1189 Design and Implementation a New Energy Efficient Clustering Algorithm using Genetic Algorithm for Wireless Sensor Networks

Authors: Moslem Afrashteh Mehr

Abstract:

Wireless Sensor Networks consist of small battery powered devices with limited energy resources. once deployed, the small sensor nodes are usually inaccessible to the user, and thus replacement of the energy source is not feasible. Hence, One of the most important issues that needs to be enhanced in order to improve the life span of the network is energy efficiency. to overcome this demerit many research have been done. The clustering is the one of the representative approaches. in the clustering, the cluster heads gather data from nodes and sending them to the base station. In this paper, we introduce a dynamic clustering algorithm using genetic algorithm. This algorithm takes different parameters into consideration to increase the network lifetime. To prove efficiency of proposed algorithm, we simulated the proposed algorithm compared with LEACH algorithm using the matlab

Keywords: Wireless Sensor Networks, Clustering, Geneticalgorithm, Energy Consumption

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1188 Half-Circle Fuzzy Number Threshold Determination via Swarm Intelligence Method

Authors: P.-W. Tsai, J.-W. Chen, C.-W. Chen, C.-Y. Chen

Abstract:

In recent years, many researchers are involved in the field of fuzzy theory. However, there are still a lot of issues to be resolved. Especially on topics related to controller design such as the field of robot, artificial intelligence, and nonlinear systems etc. Besides fuzzy theory, algorithms in swarm intelligence are also a popular field for the researchers. In this paper, a concept of utilizing one of the swarm intelligence method, which is called Bacterial-GA Foraging, to find the stabilized common P matrix for the fuzzy controller system is proposed. An example is given in in the paper, as well.

Keywords: Half-circle fuzzy numbers, predictions, swarm intelligence, Lyapunov method.

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1187 Fuzzy Control of Macroeconomic Models

Authors: Andre A. Keller

Abstract:

The optimal control is one of the possible controllers for a dynamic system, having a linear quadratic regulator and using the Pontryagin-s principle or the dynamic programming method . Stochastic disturbances may affect the coefficients (multiplicative disturbances) or the equations (additive disturbances), provided that the shocks are not too great . Nevertheless, this approach encounters difficulties when uncertainties are very important or when the probability calculus is of no help with very imprecise data. The fuzzy logic contributes to a pragmatic solution of such a problem since it operates on fuzzy numbers. A fuzzy controller acts as an artificial decision maker that operates in a closed-loop system in real time. This contribution seeks to explore the tracking problem and control of dynamic macroeconomic models using a fuzzy learning algorithm. A two inputs - single output (TISO) fuzzy model is applied to the linear fluctuation model of Phillips and to the nonlinear growth model of Goodwin.

Keywords: fuzzy control, macroeconomic model, multiplier - accelerator, nonlinear accelerator, stabilization policy.

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1186 Fuzzy Logic PID Control of Automatic Voltage Regulator System

Authors: Aye Aye Mon

Abstract:

The application of a simple microcontroller to deal with a three variable input and a single output fuzzy logic controller, with Proportional – Integral – Derivative (PID) response control built-in has been tested for an automatic voltage regulator. The fuzzifiers are based on fixed range of the variables of output voltage. The control output is used to control the wiper motor of the auto transformer to adjust the voltage, using fuzzy logic principles, so that the voltage is stabilized. In this report, the author will demonstrate how fuzzy logic might provide elegant and efficient solutions in the design of multivariable control based on experimental results rather than on mathematical models.

Keywords: Fuzzy logic system, PID Controller, control systems, controlled A V R

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1185 Best Co-approximation and Best Simultaneous Co-approximation in Fuzzy Normed Spaces

Authors: J. Kavikumar, N. S. Manian, M.B.K. Moorthy

Abstract:

The main purpose of this paper is to consider the t-best co-approximation and t-best simultaneous co-approximation in fuzzy normed spaces. We develop the theory of t-best co-approximation and t-best simultaneous co-approximation in quotient spaces. This new concept is employed us to improve various characterisations of t-co-proximinal and t-co-Chebyshev sets.

Keywords: Fuzzy best co-approximation, fuzzy quotient spaces, proximinality, Chebyshevity, best simultaneous co-approximation.

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1184 A Fuzzy Approach to Liver Tumor Segmentation with Zernike Moments

Authors: Abder-Rahman Ali, Antoine Vacavant, Manuel Grand-Brochier, Adélaïde Albouy-Kissi, Jean-Yves Boire

Abstract:

In this paper, we present a new segmentation approach for liver lesions in regions of interest within MRI (Magnetic Resonance Imaging). This approach, based on a two-cluster Fuzzy CMeans methodology, considers the parameter variable compactness to handle uncertainty. Fine boundaries are detected by a local recursive merging of ambiguous pixels with a sequential forward floating selection with Zernike moments. The method has been tested on both synthetic and real images. When applied on synthetic images, the proposed approach provides good performance, segmentations obtained are accurate, their shape is consistent with the ground truth, and the extracted information is reliable. The results obtained on MR images confirm such observations. Our approach allows, even for difficult cases of MR images, to extract a segmentation with good performance in terms of accuracy and shape, which implies that the geometry of the tumor is preserved for further clinical activities (such as automatic extraction of pharmaco-kinetics properties, lesion characterization, etc.).

Keywords: Defuzzification, floating search, fuzzy clustering, Zernike moments.

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1183 Robust Fuzzy Control of Nonlinear Fuzzy Impulsive Singular Perturbed Systems with Time-varying Delay

Authors: Caigen Zhou, Haibo Jiang

Abstract:

The problem of robust fuzzy control for a class of nonlinear fuzzy impulsive singular perturbed systems with time-varying delay is investigated by employing Lyapunov functions. The nonlinear delay system is built based on the well-known T–S fuzzy model. The so-called parallel distributed compensation idea is employed to design the state feedback controller. Sufficient conditions for global exponential stability of the closed-loop system are derived in terms of linear matrix inequalities (LMIs), which can be easily solved by LMI technique. Some simulations illustrate the effectiveness of the proposed method.

Keywords: T–S fuzzy model, singular perturbed systems, time-varying delay, robust control.

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1182 Improved K-Modes for Categorical Clustering Using Weighted Dissimilarity Measure

Authors: S.Aranganayagi, K.Thangavel

Abstract:

K-Modes is an extension of K-Means clustering algorithm, developed to cluster the categorical data, where the mean is replaced by the mode. The similarity measure proposed by Huang is the simple matching or mismatching measure. Weight of attribute values contribute much in clustering; thus in this paper we propose a new weighted dissimilarity measure for K-Modes, based on the ratio of frequency of attribute values in the cluster and in the data set. The new weighted measure is experimented with the data sets obtained from the UCI data repository. The results are compared with K-Modes and K-representative, which show that the new measure generates clusters with high purity.

Keywords: Clustering, categorical data, K-Modes, weighted dissimilarity measure

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1181 Adomian Method for Second-order Fuzzy Differential Equation

Authors: Lei Wang, Sizong Guo

Abstract:

In this paper, we study the numerical method for solving second-order fuzzy differential equations using Adomian method under strongly generalized differentiability. And, we present an example with initial condition having four different solutions to illustrate the efficiency of the proposed method under strongly generalized differentiability.

Keywords: Fuzzy-valued function, fuzzy initial value problem, strongly generalized differentiability, adomian decomposition method.

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1180 Processing Web-Cam Images by a Neuro-Fuzzy Approach for Vehicular Traffic Monitoring

Authors: A. Faro, D. Giordano, C. Spampinato

Abstract:

Traffic management in an urban area is highly facilitated by the knowledge of the traffic conditions in every street or highway involved in the vehicular mobility system. Aim of the paper is to propose a neuro-fuzzy approach able to compute the main parameters of a traffic system, i.e., car density, velocity and flow, by using the images collected by the web-cams located at the crossroads of the traffic network. The performances of this approach encourage its application when the traffic system is far from the saturation. A fuzzy model is also outlined to evaluate when it is suitable to use more accurate, even if more time consuming, algorithms for measuring traffic conditions near to saturation.

Keywords: Neuro-fuzzy networks, computer vision, Fuzzy systems, intelligent transportation system.

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1179 A Growing Natural Gas Approach for Evaluating Quality of Software Modules

Authors: Parvinder S. Sandhu, Sandeep Khimta, Kiranpreet Kaur

Abstract:

The prediction of Software quality during development life cycle of software project helps the development organization to make efficient use of available resource to produce the product of highest quality. “Whether a module is faulty or not" approach can be used to predict quality of a software module. There are numbers of software quality prediction models described in the literature based upon genetic algorithms, artificial neural network and other data mining algorithms. One of the promising aspects for quality prediction is based on clustering techniques. Most quality prediction models that are based on clustering techniques make use of K-means, Mixture-of-Guassians, Self-Organizing Map, Neural Gas and fuzzy K-means algorithm for prediction. In all these techniques a predefined structure is required that is number of neurons or clusters should be known before we start clustering process. But in case of Growing Neural Gas there is no need of predetermining the quantity of neurons and the topology of the structure to be used and it starts with a minimal neurons structure that is incremented during training until it reaches a maximum number user defined limits for clusters. Hence, in this work we have used Growing Neural Gas as underlying cluster algorithm that produces the initial set of labeled cluster from training data set and thereafter this set of clusters is used to predict the quality of test data set of software modules. The best testing results shows 80% accuracy in evaluating the quality of software modules. Hence, the proposed technique can be used by programmers in evaluating the quality of modules during software development.

Keywords: Growing Neural Gas, data clustering, fault prediction.

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1178 Self – Tuning Method of Fuzzy System: An Application on Greenhouse Process

Authors: M. Massour El Aoud, M. Franceschi, M. Maher

Abstract:

The approach proposed here is oriented in the direction of fuzzy system for the analysis and the synthesis of intelligent climate controllers, the simulation of the internal climate of the greenhouse is achieved by a linear model whose coefficients are obtained by identification. The use of fuzzy logic controllers for the regulation of climate variables represents a powerful way to minimize the energy cost. Strategies of reduction and optimization are adopted to facilitate the tuning and to reduce the complexity of the controller.

Keywords: Greenhouse, fuzzy logic, optimization, gradient descent.

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1177 Solving Fully Fuzzy Linear Systems by use of a Certain Decomposition of the Coefficient Matrix

Authors: S. H. Nasseri, M. Sohrabi, E. Ardil

Abstract:

In this paper, we give a certain decomposition of the coefficient matrix of the fully fuzzy linear system (FFLS) to obtain a simple algorithm for solving these systems. The new algorithm can solve FFLS in a smaller computing process. We will illustrate our method by solving some examples.

Keywords: Fully fuzzy linear system, Fuzzy number, LUdecomposition.

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1176 A Fuzzy Dynamic Load Balancing Algorithm for Homogenous Distributed Systems

Authors: Ali M. Alakeel

Abstract:

Load balancing in distributed computer systems is the process of redistributing the work load among processors in the system to improve system performance. Most of previous research in using fuzzy logic for the purpose of load balancing has only concentrated in utilizing fuzzy logic concepts in describing processors load and tasks execution length. The responsibility of the fuzzy-based load balancing process itself, however, has not been discussed and in most reported work is assumed to be performed in a distributed fashion by all nodes in the network. This paper proposes a new fuzzy dynamic load balancing algorithm for homogenous distributed systems. The proposed algorithm utilizes fuzzy logic in dealing with inaccurate load information, making load distribution decisions, and maintaining overall system stability. In terms of control, we propose a new approach that specifies how, when, and by which node the load balancing is implemented. Our approach is called Centralized-But-Distributed (CBD).

Keywords: Dynamic load balancing, fuzzy logic, distributed systems, algorithm.

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1175 Hybrid Modeling Algorithm for Continuous Tamil Speech Recognition

Authors: M. Kalamani, S. Valarmathy, M. Krishnamoorthi

Abstract:

In this paper, Fuzzy C-Means clustering with Expectation Maximization-Gaussian Mixture Model based hybrid modeling algorithm is proposed for Continuous Tamil Speech Recognition. The speech sentences from various speakers are used for training and testing phase and objective measures are between the proposed and existing Continuous Speech Recognition algorithms. From the simulated results, it is observed that the proposed algorithm improves the recognition accuracy and F-measure up to 3% as compared to that of the existing algorithms for the speech signal from various speakers. In addition, it reduces the Word Error Rate, Error Rate and Error up to 4% as compared to that of the existing algorithms. In all aspects, the proposed hybrid modeling for Tamil speech recognition provides the significant improvements for speechto- text conversion in various applications.

Keywords: Speech Segmentation, Feature Extraction, Clustering, HMM, EM-GMM, CSR.

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1174 Analyzing The Effect of Variable Round Time for Clustering Approach in Wireless Sensor Networks

Authors: Vipin Pal, Girdhari Singh, R P Yadav

Abstract:

As wireless sensor networks are energy constraint networks so energy efficiency of sensor nodes is the main design issue. Clustering of nodes is an energy efficient approach. It prolongs the lifetime of wireless sensor networks by avoiding long distance communication. Clustering algorithms operate in rounds. Performance of clustering algorithm depends upon the round time. A large round time consumes more energy of cluster heads while a small round time causes frequent re-clustering. So existing clustering algorithms apply a trade off to round time and calculate it from the initial parameters of networks. But it is not appropriate to use initial parameters based round time value throughout the network lifetime because wireless sensor networks are dynamic in nature (nodes can be added to the network or some nodes go out of energy). In this paper a variable round time approach is proposed that calculates round time depending upon the number of active nodes remaining in the field. The proposed approach makes the clustering algorithm adaptive to network dynamics. For simulation the approach is implemented with LEACH in NS-2 and the results show that there is 6% increase in network lifetime, 7% increase in 50% node death time and 5% improvement over the data units gathered at the base station.

Keywords: Wireless Sensor Network, Clustering, Energy Efficiency, Round Time.

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1173 Constructing a Fuzzy Net Present Value Method to Evaluating the BOT Sport Facilities

Authors: Huei-Fu Lu

Abstract:

This paper is to develop a fuzzy net present value (FNPV) method by taking vague cash flow and imprecise required rate of return into account for evaluating the value of the Build-Operate-Transfer (BOT) sport facilities. In order to clearly manifest a more realistic capital budgeting model based on the classical net present value (NPV) method, some uncertain financial elements in NPV formula will be fuzzified as triangular fuzzy numbers. Through the conscientious manipulation of fuzzy set theory, we will find that the proposed FNPV model is a more explicit extension of classical (crisp) model and could be more practicable for the financial managers to capture the essence of capital budgeting of sport facilities than non-fuzzy model.

Keywords: Fuzzy sets; Capital budgeting, Sport facility, Net present value (NPV), Build-Operate-Transfer (BOT) scheme

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1172 Neural Network Tuned Fuzzy Controller for MIMO System

Authors: Seema Chopra, R. Mitra, Vijay Kumar

Abstract:

In this paper, a neural network tuned fuzzy controller is proposed for controlling Multi-Input Multi-Output (MIMO) systems. For the convenience of analysis, the structure of MIMO fuzzy controller is divided into single input single-output (SISO) controllers for controlling each degree of freedom. Secondly, according to the characteristics of the system-s dynamics coupling, an appropriate coupling fuzzy controller is incorporated to improve the performance. The simulation analysis on a two-level mass–spring MIMO vibration system is carried out and results show the effectiveness of the proposed fuzzy controller. The performance though improved, the computational time and memory used is comparatively higher, because it has four fuzzy reasoning blocks and number may increase in case of other MIMO system. Then a fuzzy neural network is designed from a set of input-output training data to reduce the computing burden during implementation. This control strategy can not only simplify the implementation problem of fuzzy control, but also reduce computational time and consume less memory.

Keywords: Fuzzy Control, Neural Network, MIMO System, Optimization of Membership functions.

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1171 Speed Control of Permanent Magnet Synchronous Motor Using Evolutionary Fuzzy PID Controller

Authors: M. Umabharathi, S. Vijayabaskar

Abstract:

Evolutionary Fuzzy PID Speed Controller for Permanent Magnet Synchronous Motor (PMSM) is developed to achieve the Speed control of PMSM in Closed Loop operation and to deal with the existence of transients. Consider a Fuzzy PID control design problem, based on common control Engineering Knowledge. If the transient error is big, that Good transient performance can be obtained by increasing the P and I gains and decreasing the D gains. To autotune the control parameters of the Fuzzy PID controller, the Evolutionary Algorithms (EA) are developed. EA based Fuzzy PID controller provides better speed control and guarantees the closed loop stability. The Evolutionary Fuzzy PID controller can be implemented in real time Applications without any concern about instabilities that leads to system failure or damage.

Keywords: Evolutionary Algorithm (EA), Fuzzy system, Genetic Algorithm (GA), Membership, Permanent Magnet Synchronous Motor (PMSM).

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1170 Comparison of Mamdani and Sugeno Fuzzy Interference Systems for the Breast Cancer Risk

Authors: Alshalaa A. Shleeg, Issmail M. Ellabib

Abstract:

Breast cancer is a major health burden worldwide being a major cause of death amongst women. In this paper, Fuzzy Inference Systems (FIS) are developed for the evaluation of breast cancer risk using Mamdani-type and Sugeno-type models. The paper outlines the basic difference between Mamdani-type FIS and Sugeno-type FIS. The results demonstrated the performance comparison of the two systems and the advantages of using Sugeno- type over Mamdani-type.

Keywords: Breast cancer diagnosis, Fuzzy Inference System (FIS), Fuzzy Logic, fuzzy intelligent technique.

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1169 A New Evolutionary Algorithm for Cluster Analysis

Authors: B.Bahmani Firouzi, T. Niknam, M. Nayeripour

Abstract:

Clustering is a very well known technique in data mining. One of the most widely used clustering techniques is the kmeans algorithm. Solutions obtained from this technique depend on the initialization of cluster centers and the final solution converges to local minima. In order to overcome K-means algorithm shortcomings, this paper proposes a hybrid evolutionary algorithm based on the combination of PSO, SA and K-means algorithms, called PSO-SA-K, which can find better cluster partition. The performance is evaluated through several benchmark data sets. The simulation results show that the proposed algorithm outperforms previous approaches, such as PSO, SA and K-means for partitional clustering problem.

Keywords: Data clustering, Hybrid evolutionary optimization algorithm, K-means algorithm, Simulated Annealing (SA), Particle Swarm Optimization (PSO).

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1168 A New Algorithm for Cluster Initialization

Authors: Moth'd Belal. Al-Daoud

Abstract:

Clustering is a very well known technique in data mining. One of the most widely used clustering techniques is the k-means algorithm. Solutions obtained from this technique are dependent on the initialization of cluster centers. In this article we propose a new algorithm to initialize the clusters. The proposed algorithm is based on finding a set of medians extracted from a dimension with maximum variance. The algorithm has been applied to different data sets and good results are obtained.

Keywords: clustering, k-means, data mining.

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1167 A Serial Hierarchical Support Vector Machine and 2D Feature Sets Act for Brain DTI Segmentation

Authors: Mohammad Javadi

Abstract:

Serial hierarchical support vector machine (SHSVM) is proposed to discriminate three brain tissues which are white matter (WM), gray matter (GM), and cerebrospinal fluid (CSF). SHSVM has novel classification approach by repeating the hierarchical classification on data set iteratively. It used Radial Basis Function (rbf) Kernel with different tuning to obtain accurate results. Also as the second approach, segmentation performed with DAGSVM method. In this article eight univariate features from the raw DTI data are extracted and all the possible 2D feature sets are examined within the segmentation process. SHSVM succeed to obtain DSI values higher than 0.95 accuracy for all the three tissues, which are higher than DAGSVM results.

Keywords: Brain segmentation, DTI, hierarchical, SVM.

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1166 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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1165 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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1164 On the Hierarchical Ergodicity Coefficient

Authors: Yilun Shang

Abstract:

In this paper, we deal with the fundamental concepts and properties of ergodicity coefficients in a hierarchical sense by making use of partition. Moreover, we establish a hierarchial Hajnal’s inequality improving some previous results.

Keywords: Stochastic matrix, ergodicity coefficient, partition.

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1163 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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1162 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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1161 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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1160 Density Clustering Based On Radius of Data (DCBRD)

Authors: A.M. Fahim, A. M. Salem, F. A. Torkey, M. A. Ramadan

Abstract:

Clustering algorithms are attractive for the task of class identification in spatial databases. However, the application to large spatial databases rises the following requirements for clustering algorithms: minimal requirements of domain knowledge to determine the input parameters, discovery of clusters with arbitrary shape and good efficiency on large databases. The well-known clustering algorithms offer no solution to the combination of these requirements. In this paper, a density based clustering algorithm (DCBRD) is presented, relying on a knowledge acquired from the data by dividing the data space into overlapped regions. The proposed algorithm discovers arbitrary shaped clusters, requires no input parameters and uses the same definitions of DBSCAN algorithm. We performed an experimental evaluation of the effectiveness and efficiency of it, and compared this results with that of DBSCAN. The results of our experiments demonstrate that the proposed algorithm is significantly efficient in discovering clusters of arbitrary shape and size.

Keywords: Clustering Algorithms, Arbitrary Shape of clusters, cluster Analysis.

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