Search results for: Fuzzy Theory
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 2407

Search results for: Fuzzy Theory

2167 A Method for Solving a Bi-Objective Transportation Problem under Fuzzy Environment

Authors: Sukhveer Singh, Sandeep Singh

Abstract:

A bi-objective fuzzy transportation problem with the objectives to minimize the total fuzzy cost and fuzzy time of transportation without according priorities to them is considered. To the best of our knowledge, there is no method in the literature to find efficient solutions of the bi-objective transportation problem under uncertainty. In this paper, a bi-objective transportation problem in an uncertain environment has been formulated. An algorithm has been proposed to find efficient solutions of the bi-objective transportation problem under uncertainty. The proposed algorithm avoids the degeneracy and gives the optimal solution faster than other existing algorithms for the given uncertain transportation problem.

Keywords: Transportation problem, efficient solution, ranking function, fuzzy transportation problem.

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2166 Evolving a Fuzzy Rule-Base for Image Segmentation

Authors: A. Borji, M. Hamidi

Abstract:

A new method for color image segmentation using fuzzy logic is proposed in this paper. Our aim here is to automatically produce a fuzzy system for color classification and image segmentation with least number of rules and minimum error rate. Particle swarm optimization is a sub class of evolutionary algorithms that has been inspired from social behavior of fishes, bees, birds, etc, that live together in colonies. We use comprehensive learning particle swarm optimization (CLPSO) technique to find optimal fuzzy rules and membership functions because it discourages premature convergence. Here each particle of the swarm codes a set of fuzzy rules. During evolution, a population member tries to maximize a fitness criterion which is here high classification rate and small number of rules. Finally, particle with the highest fitness value is selected as the best set of fuzzy rules for image segmentation. Our results, using this method for soccer field image segmentation in Robocop contests shows 89% performance. Less computational load is needed when using this method compared with other methods like ANFIS, because it generates a smaller number of fuzzy rules. Large train dataset and its variety, makes the proposed method invariant to illumination noise

Keywords: Comprehensive learning Particle Swarmoptimization, fuzzy classification.

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2165 Use of Fuzzy Edge Image in Block Truncation Coding for Image Compression

Authors: Amarunnishad T.M., Govindan V.K., Abraham T. Mathew

Abstract:

An image compression method has been developed using fuzzy edge image utilizing the basic Block Truncation Coding (BTC) algorithm. The fuzzy edge image has been validated with classical edge detectors on the basis of the results of the well-known Canny edge detector prior to applying to the proposed method. The bit plane generated by the conventional BTC method is replaced with the fuzzy bit plane generated by the logical OR operation between the fuzzy edge image and the corresponding conventional BTC bit plane. The input image is encoded with the block mean and standard deviation and the fuzzy bit plane. The proposed method has been tested with test images of 8 bits/pixel and size 512×512 and found to be superior with better Peak Signal to Noise Ratio (PSNR) when compared to the conventional BTC, and adaptive bit plane selection BTC (ABTC) methods. The raggedness and jagged appearance, and the ringing artifacts at sharp edges are greatly reduced in reconstructed images by the proposed method with the fuzzy bit plane.

Keywords: Image compression, Edge detection, Ground truth image, Peak signal to noise ratio

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2164 A Comparative Analysis of Fuzzy, Neuro-Fuzzy and Fuzzy-GA Based Approaches for Software Reusability Evaluation

Authors: Parvinder Singh Sandhu, Dalwinder Singh Salaria, Hardeep Singh

Abstract:

Software Reusability is primary attribute of software quality. There are metrics for identifying the quality of reusable components but the function that makes use of these metrics to find reusability of software components is still not clear. These metrics if identified in the design phase or even in the coding phase can help us to reduce the rework by improving quality of reuse of the component and hence improve the productivity due to probabilistic increase in the reuse level. In this paper, we have devised the framework of metrics that uses McCabe-s Cyclometric Complexity Measure for Complexity measurement, Regularity Metric, Halstead Software Science Indicator for Volume indication, Reuse Frequency metric and Coupling Metric values of the software component as input attributes and calculated reusability of the software component. Here, comparative analysis of the fuzzy, Neuro-fuzzy and Fuzzy-GA approaches is performed to evaluate the reusability of software components and Fuzzy-GA results outperform the other used approaches. The developed reusability model has produced high precision results as expected by the human experts.

Keywords: Software Reusability, Software Metrics, Neural Networks, Genetic Algorithm, Fuzzy Logic.

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2163 Processing the Medical Sensors Signals Using Fuzzy Inference System

Authors: S. Bouharati, I. Bouharati, C. Benzidane, F. Alleg, M. Belmahdi

Abstract:

Sensors possess several properties of physical measures. Whether devices that convert a sensed signal into an electrical signal, chemical sensors and biosensors, thus all these sensors can be considered as an interface between the physical and electrical equipment. The problem is the analysis of the multitudes of saved settings as input variables. However, they do not all have the same level of influence on the outputs. In order to identify the most sensitive parameters, those that can guide users in gathering information on the ground and in the process of model calibration and sensitivity analysis for the effect of each change made. Mathematical models used for processing become very complex. In this paper a fuzzy rule-based system is proposed as a solution for this problem. The system collects the available signals information from sensors. Moreover, the system allows the study of the influence of the various factors that take part in the decision system. Since its inception fuzzy set theory has been regarded as a formalism suitable to deal with the imprecision intrinsic to many problems. At the same time, fuzzy sets allow to use symbolic models. In this study an example was applied for resolving variety of physiological parameters that define human health state. The application system was done for medical diagnosis help. The inputs are the signals expressed the cardiovascular system parameters, blood pressure, Respiratory system paramsystem was done, it will be able to predict the state of patient according any input values.

Keywords: Sensors, Sensivity, fuzzy logic, analysis, physiological parameters, medical diagnosis.

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2162 Prediction of Compressive Strength of Self- Compacting Concrete with Fuzzy Logic

Authors: Paratibha Aggarwal, Yogesh Aggarwal

Abstract:

The paper presents the potential of fuzzy logic (FL-I) and neural network techniques (ANN-I) for predicting the compressive strength, for SCC mixtures. Six input parameters that is contents of cement, sand, coarse aggregate, fly ash, superplasticizer percentage and water-to-binder ratio and an output parameter i.e. 28- day compressive strength for ANN-I and FL-I are used for modeling. The fuzzy logic model showed better performance than neural network model.

Keywords: Self compacting concrete, compressive strength, prediction, neural network, Fuzzy logic.

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2161 Fuzzy Logic Control for Flexible Joint Manipulator: An Experimental Implementation

Authors: Sophia Fry, Mahir Irtiza, Alexa Hoffman, Yousef Sardahi

Abstract:

This study presents an intelligent control algorithm for a flexible robotic arm. Fuzzy control is used to control the motion of the arm to maintain the arm tip at the desired position while reducing vibration and increasing the system speed of response. The Fuzzy controller (FC) is based on adding the tip angular position to the arm deflection angle and using their sum as a feedback signal to the control algorithm. This reduces the complexity of the FC in terms of the input variables, number of membership functions, fuzzy rules, and control structure. Also, the design of the fuzzy controller is model-free and uses only our knowledge about the system. To show the efficacy of the FC, the control algorithm is implemented on the flexible joint manipulator (FJM) developed by Quanser. The results show that the proposed control method is effective in terms of response time, overshoot, and vibration amplitude.

Keywords: Fuzzy logic control, model-free control, flexible joint manipulators, nonlinear control.

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2160 Fuzzy Trust for Peer-to-Peer Based Systems

Authors: Farag Azzedin, Ahmad Ridha, Ali Rizvi

Abstract:

Trust management is one of the drawbacks in Peer-to-Peer (P2P) system. Lack of centralized control makes it difficult to control the behavior of the peers. Reputation system is one approach to provide trust assessment in P2P system. In this paper, we use fuzzy logic to model trust in a P2P environment. Our trust model combines first-hand (direct experience) and second-hand (reputation)information to allow peers to represent and reason with uncertainty regarding other peers' trustworthiness. Fuzzy logic can help in handling the imprecise nature and uncertainty of trust. Linguistic labels are used to enable peers assign a trust level intuitively. Our fuzzy trust model is flexible such that inference rules are used to weight first-hand and second-hand accordingly.

Keywords: P2P Systems; Trust, Reputation, Fuzzy Logic.

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2159 Classification of Radio Communication Signals using Fuzzy Logic

Authors: Zuzana Dideková, Beata Mikovičová

Abstract:

Characterization of radio communication signals aims at automatic recognition of different characteristics of radio signals in order to detect their modulation type, the central frequency, and the level. Our purpose is to apply techniques used in image processing in order to extract pertinent characteristics. To the single analysis, we add several rules for checking the consistency of hypotheses using fuzzy logic. This allows taking into account ambiguity and uncertainty that may remain after the extraction of individual characteristics. The aim is to improve the process of radio communications characterization.

Keywords: fuzzy classification, fuzzy inference system, radio communication signals, telecommunications

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2158 Hybrid GA Tuned RBF Based Neuro-Fuzzy Controller for Robotic Manipulator

Authors: Sufian Ashraf Mazhari, Surendra Kumar

Abstract:

In this paper performance of Puma 560 manipulator is being compared for hybrid gradient descent and least square method learning based ANFIS controller with hybrid Genetic Algorithm and Generalized Pattern Search tuned radial basis function based Neuro-Fuzzy controller. ANFIS which is based on Takagi Sugeno type Fuzzy controller needs prior knowledge of rule base while in radial basis function based Neuro-Fuzzy rule base knowledge is not required. Hybrid Genetic Algorithm with generalized Pattern Search is used for tuning weights of radial basis function based Neuro- fuzzy controller. All the controllers are checked for butterfly trajectory tracking and results in the form of Cartesian and joint space errors are being compared. ANFIS based controller is showing better performance compared to Radial Basis Function based Neuro-Fuzzy Controller but rule base independency of RBF based Neuro-Fuzzy gives it an edge over ANFIS

Keywords: Neuro-Fuzzy, Robotic Control, RBFNF, ANFIS, Hybrid GA.

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2157 Fuzzy Neuro Approach to Busbar Protection; Design and Implementation

Authors: M. R. Aghaebrahimi, H. Khorashadi Zadeh

Abstract:

This paper presents a new approach for busbar protection with stable operation of current transformer during saturation, using fuzzy neuro and symmetrical components theory. This technique uses symmetrical components of current signals to learn the hidden relationship existing in the input patterns. Simulation studies are preformed and the influence of changing system parameters such as inception fault and source impedance is studied. Details of the design procedure and the results of performance studies with the proposed relay are given in the paper. An analysis of the performance of the proposed technique during ct saturation conditions is presented. The performance of the technique was investigated for a variety of operating conditions and for several busbar configurations. Data generated by EMTDC simulations of model power systems were used in the investigations. The results indicate that the proposed technique is stable during ct saturation conditions.

Keywords: Busbar protection, fuzzy neuro, Ct saturation.

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2156 Fuzzy Based Stabilizer Control System for Quad-Rotor

Authors: B. G. Sampath, K. C. R. Perera, W. A. S. I. Wijesuriya, V. P. C. Dassanayake

Abstract:

In this paper the design, development and testing of a stabilizer control system for a Quad-rotor is presented which is focused on the maneuverability. The mechanical design is performed along with the design of the controlling algorithm which is devised using fuzzy logic controller. The inputs for the system are the angular positions and angular rates of the Quad-rotor relative to three axes. Then the output data is filtered from an accelerometer and a gyroscope through a Kalman filter. In the development of the stability controlling system Mandani fuzzy model is incorporated. The results prove that the fuzzy based stabilizer control system is superior in high dynamic disturbances compared to the traditional systems which use PID integrated stabilizer control systems.

Keywords: Fuzzy stabilizer, maneuverability, PID, Quad-rotor.

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2155 A New Objective Weight on Interval Type-2 Fuzzy Sets

Authors: Nurnadiah Z., Lazim A.

Abstract:

The design of weight is one of the important parts in fuzzy decision making, as it would have a deep effect on the evaluation results. Entropy is one of the weight measure based on objective evaluation. Non--probabilistic-type entropy measures for fuzzy set and interval type-2 fuzzy sets (IT2FS) have been developed and applied to weight measure. Since the entropy for (IT2FS) for decision making yet to be explored, this paper proposes a new objective weight method by using entropy weight method for multiple attribute decision making (MADM). This paper utilizes the nature of IT2FS concept in the evaluation process to assess the attribute weight based on the credibility of data. An example was presented to demonstrate the feasibility of the new method in decision making. The entropy measure of interval type-2 fuzzy sets yield flexible judgment and could be applied in decision making environment.

Keywords: Objective weight, entropy weight, multiple attributedecision making, type-2 fuzzy sets, interval type-2 fuzzy sets

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2154 Improving Load Frequency Control of Multi-Area Power System by Considering Uncertainty by Using Optimized Type 2 Fuzzy Pid Controller with the Harmony Search Algorithm

Authors: Mehrdad Mahmudizad, Roya Ahmadi Ahangar

Abstract:

This paper presents the method of designing the type 2 fuzzy PID controllers in order to solve the problem of Load Frequency Control (LFC). The Harmony Search (HS) algorithm is used to regulate the measurement factors and the effect of uncertainty of membership functions of Interval Type 2 Fuzzy Proportional Integral Differential (IT2FPID) controllers in order to reduce the frequency deviation resulted from the load oscillations. The simulation results implicitly show that the performance of the proposed IT2FPID LFC in terms of error, settling time and resistance against different load oscillations is more appropriate and preferred than PID and Type 1 Fuzzy Proportional Integral Differential (T1FPID) controllers.

Keywords: Load Frequency Control, Fuzzy-PID controller, Type 2 fuzzy system, Harmony Search algorithm.

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2153 Optimizing of Fuzzy C-Means Clustering Algorithm Using GA

Authors: Mohanad Alata, Mohammad Molhim, Abdullah Ramini

Abstract:

Fuzzy C-means Clustering algorithm (FCM) is a method that is frequently used in pattern recognition. It has the advantage of giving good modeling results in many cases, although, it is not capable of specifying the number of clusters by itself. In FCM algorithm most researchers fix weighting exponent (m) to a conventional value of 2 which might not be the appropriate for all applications. Consequently, the main objective of this paper is to use the subtractive clustering algorithm to provide the optimal number of clusters needed by FCM algorithm by optimizing the parameters of the subtractive clustering algorithm by an iterative search approach and then to find an optimal weighting exponent (m) for the FCM algorithm. In order to get an optimal number of clusters, the iterative search approach is used to find the optimal single-output Sugenotype Fuzzy Inference System (FIS) model by optimizing the parameters of the subtractive clustering algorithm that give minimum least square error between the actual data and the Sugeno fuzzy model. Once the number of clusters is optimized, then two approaches are proposed to optimize the weighting exponent (m) in the FCM algorithm, namely, the iterative search approach and the genetic algorithms. The above mentioned approach is tested on the generated data from the original function and optimal fuzzy models are obtained with minimum error between the real data and the obtained fuzzy models.

Keywords: Fuzzy clustering, Fuzzy C-Means, Genetic Algorithm, Sugeno fuzzy systems.

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2152 Best Coapproximation in Fuzzy Anti-n-Normed Spaces

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

Abstract:

The main purpose of this paper is to consider the new kind of approximation which is called as t-best coapproximation in fuzzy n-normed spaces. The set of all t-best coapproximation define the t-coproximinal, t-co-Chebyshev and F-best coapproximation and then prove several theorems pertaining to this sets. 

Keywords: Fuzzy-n-normed space, best coapproximation, co-proximinal, co-Chebyshev, F-best coapproximation, orthogonality

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2151 Fuzzy Adjacency Matrix in Graphs

Authors: Mahdi Taheri, Mehrana Niroumand

Abstract:

In this paper a new definition of adjacency matrix in the simple graphs is presented that is called fuzzy adjacency matrix, so that elements of it are in the form of 0 and n N n 1 , ∈ that are in the interval [0, 1], and then some charactristics of this matrix are presented with the related examples . This form matrix has complete of information of a graph.

Keywords: Graph, adjacency matrix, fuzzy numbers

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2150 Block Homotopy Perturbation Method for Solving Fuzzy Linear Systems

Authors: Shu-Xin Miao

Abstract:

In this paper, we present an efficient numerical algorithm, namely block homotopy perturbation method, for solving fuzzy linear systems based on homotopy perturbation method. Some numerical examples are given to show the efficiency of the algorithm.

Keywords: Homotopy perturbation method, fuzzy linear systems, block linear system, fuzzy solution, embedding parameter.

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2149 Determinate Fuzzy Set Ranking Analysis for Combat Aircraft Selection with Multiple Criteria Group Decision Making

Authors: C. Ardil

Abstract:

Using the aid of Hausdorff distance function and Minkowski distance function, this study proposes a novel method for selecting combat aircraft for Air Force. In order to do this, the proximity measure method was developed with determinate fuzzy degrees based on the relationship between attributes and combat aircraft alternatives. The combat aircraft selection attributes were identified as payloadability, maneuverability, speedability, stealthability, and survivability. Determinate fuzzy data from the combat aircraft attributes was then aggregated using the determinate fuzzy weighted arithmetic average operator. For the selection of combat aircraft, correlation analysis of the ranking order patterns of options was also examined. A numerical example from military aviation is used to demonstrate the applicability and effectiveness of the proposed method.

Keywords: Combat aircraft selection, multiple criteria decision making, fuzzy sets, determinate fuzzy sets, intuitionistic fuzzy sets, proximity measure method, Hausdorff distance function, Minkowski distance function, PMM, MCDM

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2148 Genetic Algorithm Based Design of Fuzzy Logic Power System Stabilizers in Multimachine Power System

Authors: Manisha Dubey, Aalok Dubey

Abstract:

This paper presents an approach for the design of fuzzy logic power system stabilizers using genetic algorithms. In the proposed fuzzy expert system, speed deviation and its derivative have been selected as fuzzy inputs. In this approach the parameters of the fuzzy logic controllers have been tuned using genetic algorithm. Incorporation of GA in the design of fuzzy logic power system stabilizer will add an intelligent dimension to the stabilizer and significantly reduces computational time in the design process. It is shown in this paper that the system dynamic performance can be improved significantly by incorporating a genetic-based searching mechanism. To demonstrate the robustness of the genetic based fuzzy logic power system stabilizer (GFLPSS), simulation studies on multimachine system subjected to small perturbation and three-phase fault have been carried out. Simulation results show the superiority and robustness of GA based power system stabilizer as compare to conventionally tuned controller to enhance system dynamic performance over a wide range of operating conditions.

Keywords: Dynamic stability, Fuzzy logic power systemstabilizer, Genetic Algorithms, Genetic based power systemstabilizer

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2147 Fuzzy Expert System Design for Determining Wearing Properties of Nitrided and Non Nitrided Steel

Authors: Serafettin Ekinci, Kursat Zuhtuogullari

Abstract:

This paper proposes a Fuzzy Expert System design to determine the wearing properties of nitrided and non nitrided steel. The proposed Fuzzy Expert System approach helps the user and the manufacturer to forecast the wearing properties of nitrided and non nitrided steel under specified laboratory conditions. Surfaces of the engineering components are often nitrided for improving wear, corosion, fatigue specifications. A major property of nitriding process is reducing distortion and wearing of the metalic alloys. A Fuzzy Expert System was developed for determining the wearing and durability properties of nitrided and non nitrided steels that were tested under different loads and different sliding speeds in the laboratory conditions.

Keywords: Fuzzy Expert System Design, Rule Based Systems, Fatigue, Corrosion

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2146 Neuro-Fuzzy Algorithm for a Biped Robotic System

Authors: Hataitep Wongsuwarn, Djitt Laowattana

Abstract:

This paper summaries basic principles and concepts of intelligent controls, implemented in humanoid robotics as well as recent algorithms being devised for advanced control of humanoid robots. Secondly, this paper presents a new approach neuro-fuzzy system. We have included some simulating results from our computational intelligence technique that will be applied to our humanoid robot. Subsequently, we determine a relationship between joint trajectories and located forces on robot-s foot through a proposed neuro-fuzzy technique.

Keywords: Biped Robot, Computational Intelligence, Static and Dynamic Walking, Gait Synthesis, Neuro-Fuzzy System.

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2145 Neuro-Fuzzy Networks for Identification of Mathematical Model Parameters of Geofield

Authors: A. Pashayev, R. Sadiqov, C. Ardil, F. Ildiz , H. Karabork

Abstract:

The new technology of fuzzy neural networks for identification of parameters for mathematical models of geofields is proposed and checked. The effectiveness of that soft computing technology is demonstrated, especially in the early stage of modeling, when the information is uncertain and limited.

Keywords: Identification, interpolation methods, neuro-fuzzy networks, geofield.

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2144 Big Bang – Big Crunch Learning Method for Fuzzy Cognitive Maps

Authors: Engin Yesil, Leon Urbas

Abstract:

Modeling of complex dynamic systems, which are very complicated to establish mathematical models, requires new and modern methodologies that will exploit the existing expert knowledge, human experience and historical data. Fuzzy cognitive maps are very suitable, simple, and powerful tools for simulation and analysis of these kinds of dynamic systems. However, human experts are subjective and can handle only relatively simple fuzzy cognitive maps; therefore, there is a need of developing new approaches for an automated generation of fuzzy cognitive maps using historical data. In this study, a new learning algorithm, which is called Big Bang-Big Crunch, is proposed for the first time in literature for an automated generation of fuzzy cognitive maps from data. Two real-world examples; namely a process control system and radiation therapy process, and one synthetic model are used to emphasize the effectiveness and usefulness of the proposed methodology.

Keywords: Big Bang-Big Crunch optimization, Dynamic Systems, Fuzzy Cognitive Maps, Learning.

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2143 Mamdani Model based Adaptive Neural Fuzzy Inference System and its Application

Authors: Yuanyuan Chai, Limin Jia, Zundong Zhang

Abstract:

Hybrid algorithm is the hot issue in Computational Intelligence (CI) study. From in-depth discussion on Simulation Mechanism Based (SMB) classification method and composite patterns, this paper presents the Mamdani model based Adaptive Neural Fuzzy Inference System (M-ANFIS) and weight updating formula in consideration with qualitative representation of inference consequent parts in fuzzy neural networks. M-ANFIS model adopts Mamdani fuzzy inference system which has advantages in consequent part. Experiment results of applying M-ANFIS to evaluate traffic Level of service show that M-ANFIS, as a new hybrid algorithm in computational intelligence, has great advantages in non-linear modeling, membership functions in consequent parts, scale of training data and amount of adjusted parameters.

Keywords: Fuzzy neural networks, Mamdani fuzzy inference, M-ANFIS

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2142 Design and Implementation of a Hybrid Fuzzy Controller for a High-Performance Induction

Authors: M. Zerikat, S. Chekroun

Abstract:

This paper proposes an effective algorithm approach to hybrid control systems combining fuzzy logic and conventional control techniques of controlling the speed of induction motor assumed to operate in high-performance drives environment. The introducing of fuzzy logic in the control systems helps to achieve good dynamical response, disturbance rejection and low sensibility to parameter variations and external influences. Some fundamentals of the fuzzy logic control are preliminary illustrated. The developed control algorithm is robust, efficient and simple. It also assures precise trajectory tracking with the prescribed dynamics. Experimental results have shown excellent tracking performance of the proposed control system, and have convincingly demonstrated the validity and the usefulness of the hybrid fuzzy controller in high-performance drives with parameter and load uncertainties. Satisfactory performance was observed for most reference tracks.

Keywords: Fuzzy controller, high-performance, inductionmotor, intelligent control, robustness.

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2141 Optimized Fuzzy Control by Particle Swarm Optimization Technique for Control of CSTR

Authors: Saeed Vaneshani, Hooshang Jazayeri-Rad

Abstract:

Fuzzy logic control (FLC) systems have been tested in many technical and industrial applications as a useful modeling tool that can handle the uncertainties and nonlinearities of modern control systems. The main drawback of the FLC methodologies in the industrial environment is challenging for selecting the number of optimum tuning parameters. In this paper, a method has been proposed for finding the optimum membership functions of a fuzzy system using particle swarm optimization (PSO) algorithm. A synthetic algorithm combined from fuzzy logic control and PSO algorithm is used to design a controller for a continuous stirred tank reactor (CSTR) with the aim of achieving the accurate and acceptable desired results. To exhibit the effectiveness of proposed algorithm, it is used to optimize the Gaussian membership functions of the fuzzy model of a nonlinear CSTR system as a case study. It is clearly proved that the optimized membership functions (MFs) provided better performance than a fuzzy model for the same system, when the MFs were heuristically defined.

Keywords: continuous stirred tank reactor (CSTR), fuzzy logiccontrol (FLC), membership function(MF), particle swarmoptimization (PSO)

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2140 IFS on the Multi-Fuzzy Fractal Space

Authors: Nadia M. G. AL-Sa'idi, Muhammad Rushdan Md. Sd., Adil M. Ahmed

Abstract:

The IFS is a scheme for describing and manipulating complex fractal attractors using simple mathematical models. More precisely, the most popular “fractal –based" algorithms for both representation and compression of computer images have involved some implementation of the method of Iterated Function Systems (IFS) on complete metric spaces. In this paper a new generalized space called Multi-Fuzzy Fractal Space was constructed. On these spases a distance function is defined, and its completeness is proved. The completeness property of this space ensures the existence of a fixed-point theorem for the family of continuous mappings. This theorem is the fundamental result on which the IFS methods are based and the fractals are built. The defined mappings are proved to satisfy some generalizations of the contraction condition.

Keywords: Fuzzy metric space, Fuzzy fractal space, Multi fuzzy fractal space.

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2139 A New Concept for Deriving the Expected Value of Fuzzy Random Variables

Authors: Liang-Hsuan Chen, Chia-Jung Chang

Abstract:

Fuzzy random variables have been introduced as an imprecise concept of numeric values for characterizing the imprecise knowledge. The descriptive parameters can be used to describe the primary features of a set of fuzzy random observations. In fuzzy environments, the expected values are usually represented as fuzzy-valued, interval-valued or numeric-valued descriptive parameters using various metrics. Instead of the concept of area metric that is usually adopted in the relevant studies, the numeric expected value is proposed by the concept of distance metric in this study based on two characters (fuzziness and randomness) of FRVs. Comparing with the existing measures, although the results show that the proposed numeric expected value is same with those using the different metric, if only triangular membership functions are used. However, the proposed approach has the advantages of intuitiveness and computational efficiency, when the membership functions are not triangular types. An example with three datasets is provided for verifying the proposed approach.

Keywords: Fuzzy random variables, Distance measure, Expected value.

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2138 Trajectory Control of a Robotic Manipulator Utilizing an Adaptive Fuzzy Sliding Mode

Authors: T. C. Kuo

Abstract:

In this paper, a novel adaptive fuzzy sliding mode control method is proposed for the robust tracking control of robotic manipulators. The proposed controller possesses the advantages of adaptive control, fuzzy control, and sliding mode control. First, system stability and robustness are guaranteed based on the sliding mode control. Further, fuzzy rules are developed incorporating with adaptation law to alleviate the input chattering effectively. Stability of the control system is proven by using the Lyapunov method. An application to a three-degree-of-freedom robotic manipulator is carried out. Accurate trajectory tracking as well as robustness is achieved. Input chattering is greatly eliminated.

Keywords: Fuzzy control, sliding mode control, roboticmanipulator, adaptive control.

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