Search results for: Fuzzy System

Authors: Agung Budi Muljono, I Made Ginarsa, I Made Ari Nrartha

Abstract:

A large-scale power system (LSPS) consists of two or more sub-systems connected by inter-connecting transmission. Loading pattern on an LSPS always changes from time to time and varies depend on consumer need. The serious instability problem is appeared in an LSPS due to load fluctuation in all of the bus. Adaptive neuro-fuzzy inference system (ANFIS)-based power system stabilizer (PSS) is presented to cover the stability problem and to enhance the stability of an LSPS. The ANFIS control is presented because the ANFIS control is more effective than Mamdani fuzzy control in the computation aspect. Simulation results show that the presented PSS is able to maintain the stability by decreasing peak overshoot to the value of −2.56 × 10−5 pu for rotor speed deviation Δω2−3. The presented PSS also makes the settling time to achieve at 3.78 s on local mode oscillation. Furthermore, the presented PSS is able to improve the peak overshoot and settling time of Δω3−9 to the value of −0.868 × 10−5 pu and at the time of 3.50 s for inter-area oscillation.

Keywords: ANFIS, large-scale, power system, PSS, stability enhancement.

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Authors: Ebrahim Abbasi, Amir Abouec

Abstract:

In this research, the researchers have managed to design a model to investigate the current trend of stock price of the "IRAN KHODRO corporation" at Tehran Stock Exchange by utilizing an Adaptive Neuro - Fuzzy Inference system. For the Longterm Period, a Neuro-Fuzzy with two Triangular membership functions and four independent Variables including trade volume, Dividend Per Share (DPS), Price to Earning Ratio (P/E), and also closing Price and Stock Price fluctuation as an dependent variable are selected as an optimal model. For the short-term Period, a neureo – fuzzy model with two triangular membership functions for the first quarter of a year, two trapezoidal membership functions for the Second quarter of a year, two Gaussian combination membership functions for the third quarter of a year and two trapezoidal membership functions for the fourth quarter of a year were selected as an optimal model for the stock price forecasting. In addition, three independent variables including trade volume, price to earning ratio, closing Stock Price and a dependent variable of stock price fluctuation were selected as an optimal model. The findings of the research demonstrate that the trend of stock price could be forecasted with the lower level of error.

Keywords: Stock Price forecast, membership functions, Adaptive Neuro-Fuzzy Inference System, trade volume, P/E, DPS.

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Authors: Changho Han, Jaemin Lee, Li Hua, Seokkwon Jeong

Abstract:

Design of membership function ranges in fuzzy logic control (FLC) is presented for robust control of a variable speed refrigeration system (VSRS). The criterion values of the membership function ranges can be carried out from the static experimental data, and two different values are offered to compare control performance. Some simulations and real experiments for the VSRS were conducted to verify the validity of the designed membership functions. The experimental results showed good agreement with the simulation results, and the error change rate and its sampling time strongly affected the control performance at transient state of the VSRS.

Keywords: Variable speed refrigeration system, Fuzzy logic control, membership function range, control performance.

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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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Authors: Ingu Kim, Shangmun Shin, Yongsun Choi, Nguyen Manh Thang, Edwin R. Ramos, Won-Joo Hwang

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Project selection problems on management information system (MIS) are often considered a multi-criteria decision-making (MCDM) for a solving method. These problems contain two aspects, such as interdependencies among criteria and candidate projects and qualitative and quantitative factors of projects. However, most existing methods reported in literature consider these aspects separately even though these two aspects are simultaneously incorporated. For this reason, we proposed a hybrid method using analytic network process (ANP) and fuzzy logic in order to represent both aspects. We then propose a goal programming model to conduct an optimization for the project selection problems interpreted by a hybrid concept. Finally, a numerical example is conducted as verification purposes.

Keywords: Analytic Network Process (ANP), Multi-Criteria Decision-Making (MCDM), Fuzzy Logic, Information System Project Selection, Goal Programming.

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Authors: M Nayeripour, H. Khorsand, A. Roosta, T. Niknam, E. Azad

Abstract:

Series compensators have been used for many years, to increase the stability and load ability of transmission line. They compensate retarded or advanced volt drop of transmission lines by placing advanced or retarded voltage in series with them to compensate the effective reactance, which cause to increase load ability of transmission lines. In this paper, two method of fuzzy controller, based on power reference tracking and impedance reference tracking have been developed on TCSC controller in order to increase load ability and improving power oscillation damping of system. In these methods, fire angle of thyristors are determined directly through the special Rule-bases with the error and change of error as the inputs. The simulation results of two area four- machines power system show the good performance of power oscillation damping in system. Comparison of this method with classical PI controller shows the increasing speed of system response in power oscillation damping.

Keywords: TCSC, Two area network, Fuzzy controller, Power oscillation damping.

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Authors: Y. J. Huang, C. H. Chang

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In this paper, an intelligent automatic parking control method is proposed. First, the dynamical equation of the rear parking control is derived. Then a fuzzy logic control is proposed to perform the parking planning process. Further, a rear neural network is proposed for the steering control. Through the simulations and experiments, the intelligent auto-parking mode controllers have been shown to achieve the demanded goals with satisfactory control performance and to guarantee the system robustness under parametric variations and external disturbances. To improve some shortcomings and limitations in conventional parking mode control and further to reduce consumption time and prime cost.

Keywords: Auto-parking system, Fuzzy control, Neural network, Robust

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Authors: Takashi Mitsuishi, Kiyoshi Sawada, Yasunari Shidama

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

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

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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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Authors: M. G. Papoutsidakis, G. Chamilothoris, F. Dailami, N. Larsen, A Pipe

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Due to their high power-to-weight ratio and low cost, pneumatic actuators are attractive for robotics and automation applications; however, achieving fast and accurate control of their position have been known as a complex control problem. A methodology for obtaining high position accuracy with a linear pneumatic actuator is presented. During experimentation with a number of PID classical control approaches over many operations of the pneumatic system, the need for frequent manual re-tuning of the controller could not be eliminated. The reason for this problem is thermal and energy losses inside the cylinder body due to the complex friction forces developed by the piston displacements. Although PD controllers performed very well over short periods, it was necessary in our research project to introduce some form of automatic gain-scheduling to achieve good long-term performance. We chose a fuzzy logic system to do this, which proved to be an easily designed and robust approach. Since the PD approach showed very good behaviour in terms of position accuracy and settling time, it was incorporated into a modified form of the 1st order Tagaki- Sugeno fuzzy method to build an overall controller. This fuzzy gainscheduler uses an input variable which automatically changes the PD gain values of the controller according to the frequency of repeated system operations. Performance of the new controller was significantly improved and the need for manual re-tuning was eliminated without a decrease in performance. The performance of the controller operating with the above method is going to be tested through a high-speed web network (GRID) for research purposes.

Keywords: Fuzzy logic, gain scheduling, leaky integrator, pneumatic actuator.

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Authors: S. Khosravi, A. Afshar, F. Barazandeh

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In this study we propose a novel monitor hydraulic automatic gauge control (HAGC) system based on fuzzy feedforward controller. This is used in the development of cold rolling mill automation system to improve the quality of cold strip. According to features/ properties of entry steel strip like its average yield stress, width of strip, and desired exit thickness, this controller realizes the compensation for the exit thickness error. The traditional methods of adjusting the roller position, can-t tolerate the variance in the entry steel strip. The proposed method uses a mathematical model of the system together with the expert knowledge to perform this adjustment while minimizing the effect of the stated problem. In order to improve the speed of the controller in rejecting disturbances introduced by entry strip thickness variations, expert knowledge is added as a feed-forward term to the HAGC system. Simulation results for the application of the proposed controller to a real cold mill show that the exit strip quality is highly improved.

Keywords: Fuzzy feed-forward controller, monitor HAGC system, dynamic mathematical model, entry strip thickness deviation compensation

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

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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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Authors: Erika Martinez Ramirez, Rene V. Mayorga

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Nowadays, more engineering systems are using some kind of Artificial Intelligence (AI) for the development of their processes. Some well-known AI techniques include artificial neural nets, fuzzy inference systems, and neuro-fuzzy inference systems among others. Furthermore, many decision-making applications base their intelligent processes on Fuzzy Logic; due to the Fuzzy Inference Systems (FIS) capability to deal with problems that are based on user knowledge and experience. Also, knowing that users have a wide variety of distinctiveness, and generally, provide uncertain data, this information can be used and properly processed by a FIS. To properly consider uncertainty and inexact system input values, FIS normally use Membership Functions (MF) that represent a degree of user satisfaction on certain conditions and/or constraints. In order to define the parameters of the MFs, the knowledge from experts in the field is very important. This knowledge defines the MF shape to process the user inputs and through fuzzy reasoning and inference mechanisms, the FIS can provide an “appropriate" output. However an important issue immediately arises: How can it be assured that the obtained output is the optimum solution? How can it be guaranteed that each MF has an optimum shape? A viable solution to these questions is through the MFs parameter optimization. In this Paper a novel parameter optimization process is presented. The process for FIS parameter optimization consists of the five simple steps that can be easily realized off-line. Here the proposed process of FIS parameter optimization it is demonstrated by its implementation on an Intelligent Interface section dealing with the on-line customization / personalization of internet portals applied to E-commerce.

Keywords: Artificial Intelligence, Fuzzy Logic, Fuzzy InferenceSystems, Nonlinear Optimization.

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Authors: Seo Young Kim, Tai Myong Choi

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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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Authors: K. Muthukannan, P. Latha

Abstract:

In addition to environmental parameters like rain, temperature diseases on crop is a major factor which affects production quality & quantity of crop yield. Hence disease management is a key issue in agriculture. For the management of disease, it needs to be detected at early stage. So, treat it properly & control spread of the disease. Now a day, it is possible to use the images of diseased leaf to detect the type of disease by using image processing techniques. This can be achieved by extracting features from the images which can be further used with classification algorithms or content based image retrieval systems. In this paper, color image is used to extract the features such as mean and standard deviation after the process of region cropping. The selected features are taken from the cropped image with different image size samples. Then, the extracted features are taken in to the account for classification using Fuzzy Inference System (FIS).

Keywords: Image Cropping, Classification, Color, Fuzzy Rule, Feature Extraction.

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Authors: Mohamed Amine Haraoubia, Abdelaziz Hamzaoui, Najib Essounbouli

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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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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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Authors: Marco Soares dos Santos, Jorge Augusto Ferreira, Camila Nicola Boeri, Fernando Neto da Silva

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The present paper proposes high performance nonlinear force controllers for a servopneumatic real-time fatigue test machine. A CompactRIO® controller was used, being fully programmed using LabVIEW language. Fuzzy logic control algorithms were evaluated to tune the integral and derivative components in the development of hybrid controllers, namely a FLC P and a hybrid FLC PID real-time-based controllers. Their behaviours were described by using state diagrams. The main contribution is to ensure a smooth transition between control states, avoiding discrete transitions in controller outputs. Steady-state errors lower than 1.5 N were reached, without retuning the controllers. Good results were also obtained for sinusoidal tracking tasks from 1/¤Ç to 8/¤Ç Hz.

Keywords: Hybrid Fuzzy Selecting, Control, Range Controllers, Servopneumatic Fatigue System.

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Authors: Andrés C. Cuervo Pinilla, Christian G. Quintero M., Chinthaka Premachandra

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This paper considers people’s driving skills diagnosis under real driving conditions. In that sense, this research presents an approach that uses GPS signals which have a direct correlation with driving maneuvers. Besides, it is presented a novel expert-driving-criteria approximation using fuzzy logic which seeks to analyze GPS signals in order to issue an intelligent driving diagnosis. Based on above, this works presents in the first section the intelligent driving diagnosis system approach in terms of its own characteristics properties, explaining in detail significant considerations about how an expert-driving-criteria approximation must be developed. In the next section, the implementation of our developed system based on the proposed fuzzy logic approach is explained. Here, a proposed set of rules which corresponds to a quantitative abstraction of some traffics laws and driving secure techniques seeking to approach an expert-driving- criteria approximation is presented. Experimental testing has been performed in real driving conditions. The testing results show that the intelligent driving diagnosis system qualifies driver’s performance quantitatively with a high degree of reliability.

Keywords: Driver support systems, intelligent transportation systems, fuzzy logic, real time data processing.

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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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Authors: Pankaj Dutta, Debjani Chakraborty

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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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Authors: V. S. Meenakshi, G. Padmavathi

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Biometric techniques are gaining importance for personal authentication and identification as compared to the traditional authentication methods. Biometric templates are vulnerable to variety of attacks due to their inherent nature. When a person-s biometric is compromised his identity is lost. In contrast to password, biometric is not revocable. Therefore, providing security to the stored biometric template is very crucial. Crypto biometric systems are authentication systems, which blends the idea of cryptography and biometrics. Fuzzy vault is a proven crypto biometric construct which is used to secure the biometric templates. However fuzzy vault suffer from certain limitations like nonrevocability, cross matching. Security of the fuzzy vault is affected by the non-uniform nature of the biometric data. Fuzzy vault when hardened with password overcomes these limitations. Password provides an additional layer of security and enhances user privacy. Retina has certain advantages over other biometric traits. Retinal scans are used in high-end security applications like access control to areas or rooms in military installations, power plants, and other high risk security areas. This work applies the idea of fuzzy vault for retinal biometric template. Multimodal biometric system performance is well compared to single modal biometric systems. The proposed multi modal biometric fuzzy vault includes combined feature points from retina and fingerprint. The combined vault is hardened with user password for achieving high level of security. The security of the combined vault is measured using min-entropy. The proposed password hardened multi biometric fuzzy vault is robust towards stored biometric template attacks.

Keywords: Biometric Template Security, Crypto Biometric Systems, Hardening Fuzzy Vault, Min-Entropy.

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Authors: Abduladheem A. Ali, Easa A. Abd

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The robot is a repeated task plant. The control of such a plant under parameter variations and load disturbances is one of the important problems. The aim of this work is to design Geno-Fuzzy controller suitable for online applications to control single link rigid robot arm plant. The genetic-fuzzy online controller (indirect controller) has two genetic-fuzzy blocks, the first as controller, the second as identifier. The identification method is based on inverse identification technique. The proposed controller it tested in normal and load disturbance conditions.

Keywords: Fuzzy network, genetic algorithm, robot control, online genetic control, parameter identification.

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Authors: M.M. Zahedi, L. Torkzadeh

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In this note first we define the notions of intuitionistic fuzzy dual positive implicative hyper K-ideals of types 1,2,3,4 and intuitionistic fuzzy dual hyper K-ideals. Then we give some classifications about these notions according to the level subsets. Also by given some examples we show that these notions are not equivalent, however we prove some theorems which show that there are some relationships between these notions. Finally we define the notions of product and antiproduct of two fuzzy subsets and then give some theorems about the relationships between the intuitionistic fuzzy dual positive implicative hyper K-ideal of types 1,2,3,4 and their (anti-)products, in particular we give a main decomposition theorem.

Keywords: hyper K-algebra, intuitionistic fuzzy dual positive implicative hyper K-ideal.

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Authors: Hamid Reza Boveiri

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In this paper, a new proposed system for Persian printed numeral characters recognition with emphasis on representation and recognition stages is introduced. For the first time, in Persian optical character recognition, geometrical central moments as character image descriptor and fuzzy min-max neural network for Persian numeral character recognition has been used. Set of different experiments on binary images of regular, translated, rotated and scaled Persian numeral characters has been done and variety of results has been presented. The best result was 99.16% correct recognition demonstrating geometrical central moments and fuzzy min-max neural network are adequate for Persian printed numeral character recognition.

Keywords: Fuzzy min-max neural network, geometrical centralmoments, optical character recognition, Persian digits recognition, Persian printed numeral characters recognition.

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Authors: Nasser Mohamed Ramli, Mohamad Syafiq Mohamad

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Many types of controllers were applied on the continuous stirred tank reactor (CSTR) unit to control the temperature. In this research paper, Proportional-Integral-Derivative (PID) controller are compared with Fuzzy Logic controller for temperature control of CSTR. The control system for temperature non-isothermal of a CSTR will produce a stable response curve to its set point temperature. A mathematical model of a CSTR using the most general operating condition was developed through a set of differential equations into S-function using MATLAB. The reactor model and S-function are developed using m.file. After developing the S-function of CSTR model, User-Defined functions are used to link to SIMULINK file. Results that are obtained from simulation and temperature control were better when using Fuzzy logic control compared to PID control.

Keywords: CSTR, temperature, PID, fuzzy logic.

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Authors: S. Boonpoke, B. Marungsri

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This paper presents the effectiveness of artificial intelligent technique to apply for pattern recognition and classification of Partial Discharge (PD). Characteristics of PD signal for pattern recognition and classification are computed from the relation of the voltage phase angle, the discharge magnitude and the repeated existing of partial discharges by using statistical and fractal methods. The simplified fuzzy ARTMAP (SFAM) is used for pattern recognition and classification as artificial intelligent technique. PDs quantities, 13 parameters from statistical method and fractal method results, are inputted to Simplified Fuzzy ARTMAP to train system for pattern recognition and classification. The results confirm the effectiveness of purpose technique.

Keywords: Partial discharges, PD Pattern recognition, PDClassification, Artificial intelligent, Simplified Fuzzy ARTMAP

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Authors: M.A. Lazim, M.T.Abu Osman

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This paper deals with the application of a fuzzy set in measuring teachers- beliefs about mathematics. The vagueness of beliefs was transformed into standard mathematical values using a fuzzy preferences model. The study employed a fuzzy approach questionnaire which consists of six attributes for measuring mathematics teachers- beliefs about mathematics. The fuzzy conjoint analysis approach based on fuzzy set theory was used to analyze the data from twenty three mathematics teachers from four secondary schools in Terengganu, Malaysia. Teachers- beliefs were recorded in form of degrees of similarity and its levels of agreement. The attribute 'Drills and practice is one of the best ways of learning mathematics' scored the highest degree of similarity at 0. 79860 with level of 'strongly agree'. The results showed that the teachers- beliefs about mathematics were varied. This is shown by different levels of agreement and degrees of similarity of the measured attributes.

Keywords: belief, membership function, degree of similarity, conjoint analysis

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