Search results for: Fuzzy maximal flow problem

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: Wahyudin P. Syam, Ibrahim M. Al-Harkan

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This study compares three meta heuristics to minimize makespan (Cmax) for Hybrid Flow Shop (HFS) Scheduling Problem with Parallel Machines. This problem is known to be NP-Hard. This study proposes three algorithms among improvement heuristic searches which are: Genetic Algorithm (GA), Simulated Annealing (SA), and Tabu Search (TS). SA and TS are known as deterministic improvement heuristic search. GA is known as stochastic improvement heuristic search. A comprehensive comparison from these three improvement heuristic searches is presented. The results for the experiments conducted show that TS is effective and efficient to solve HFS scheduling problems.

Keywords: Flow shop, genetic algorithm, simulated annealing, tabu search.

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Authors: A. I. Dounis, P. Tiropanis, D. Tseles, G. Nikolaou, G. P. Syrcos

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The prediction of meteorological parameters at a meteorological station is an interesting and open problem. A firstorder linear dynamic model GM(1,1) is the main component of the grey system theory. The grey model requires only a few previous data points in order to make a real-time forecast. In this paper, we consider the daily average ambient temperature as a time series and the grey model GM(1,1) applied to local prediction (short-term prediction) of the temperature. In the same case study we use a fuzzy predictive model for global prediction. We conclude the paper with a comparison between local and global prediction schemes.

Keywords: Fuzzy predictive model, grey model, local andglobal prediction, meteorological forecasting, time series.

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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: 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: Ε. Giovanis

Abstract:

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

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

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Authors: Mohamed Amine Haraoubia, Abdelaziz Hamzaoui, Najib Essounbouli

Abstract:

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

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

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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: Vai Kuong Sin, Chon Kit Chio

Abstract:

This paper investigates the nature of the development of two-dimensional laminar flow of an incompressible fluid at the reversed stagnation-point. ". In this study, we revisit the problem of reversed stagnation-point flow over a flat plate. Proudman and Johnson (1962) first studied the flow and obtained an asymptotic solution by neglecting the viscous terms. This is no true in neglecting the viscous terms within the total flow field. In particular it is pointed out that for a plate impulsively accelerated from rest to a constant velocity V0 that a similarity solution to the self-similar ODE is obtained which is noteworthy completely analytical.

Keywords: reversed stagnation-point flow, similarity solutions, analytical solution, numerical solution

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Authors: Feng-Sheng Wang, Wu-Hsiung Wu, Kai-Cheng Hsu

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The optimization of biological systems, which is a branch of metabolic engineering, has generated a lot of industrial and academic interest for a long time. In the last decade, metabolic engineering approaches based on mathematical optimizations have been used extensively for the analysis and manipulation of metabolic networks. In practical optimization of metabolic reaction networks, designers have to manage the nature of uncertainty resulting from qualitative characters of metabolic reactions, e.g., the possibility of enzyme effects. A deterministic approach does not give an adequate representation for metabolic reaction networks with uncertain characters. Fuzzy optimization formulations can be applied to cope with this problem. A fuzzy multi-objective optimization problem can be introduced for finding the optimal engineering interventions on metabolic network systems considering the resilience phenomenon and cell viability constraints. The accuracy of optimization results depends heavily on the development of essential kinetic models of metabolic networks. Kinetic models can quantitatively capture the experimentally observed regulation data of metabolic systems and are often used to find the optimal manipulation of external inputs. To address the issues of optimizing the regulatory structure of metabolic networks, it is necessary to consider qualitative effects, e.g., the resilience phenomena and cell viability constraints. Combining the qualitative and quantitative descriptions for metabolic networks makes it possible to design a viable strain and accurately predict the maximum possible flux rates of desired products. Considering the resilience phenomena in metabolic networks can improve the predictions of gene intervention and maximum synthesis rates in metabolic engineering. Two case studies will present in the conference to illustrate the phenomena.

Keywords: Fuzzy multi-objective optimization problem, kinetic model, metabolic engineering.

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Authors: Liu-Chao Qiu

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The damage caused by surge waves generated in water bodies by flow-like landslides can be very high in terms of human lives and economic losses. The complicated phenomena occurred in this highly unsteady process are difficult to model because three interacting phases: air, water and sediment are involved. The problem therefore is challenging since the effects of non-Newtonian fluid describing the rheology of the flow-like landslides, multi-phase flow and free surface have to be included in the simulation. In this work, the commercial computational fluid dynamics (CFD) package FLUENT is used to model the surge waves due to flow-like landslides. The comparison between the numerical results and experimental data reported in the literature confirms the accuracy of the method.

Keywords: Flow-like landslide, surge wave, VOF, non-Newtonian fluids, multi-phase flows, free surface flow.

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Authors: Shreyash Sinai Kunde, Siddhang Tendulkar, Shiv Prakash Gupta, Gaurav Kumar, Suresh Mikkili

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One of the major power quality concerns in modern times is the problem of current harmonics. The current harmonics is caused due to the increase in non-linear loads which is largely dominated by power electronics devices. The Shunt active filtering is one of the best solutions for mitigating current harmonics. This paper describes a fuzzy logic controller based (FLC) based three Phase Shunt active Filter to achieve low current harmonic distortion (THD) and Reactive power compensation. The performance of fuzzy logic controller is analysed under both balanced sinusoidal and unbalanced sinusoidal source condition. The above controller serves the purpose of maintaining DC Capacitor Voltage constant. The proposed shunt active filter uses hysteresis current controller for current control of IGBT based PWM inverter. The simulation results of model in Simulink MATLAB reveals satisfying results.

Keywords: Shunt active filter, Current harmonics, Fuzzy logic controller, Hysteresis current controller.

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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: Remica Aggarwal, Sanjeet Singh

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The decision to recruit manpower in an organization requires clear identification of the criteria (attributes) that distinguish successful from unsuccessful performance. The choice of appropriate attributes or criteria in different levels of hierarchy in an organization is a multi-criteria decision problem and therefore multi-criteria decision making (MCDM) techniques can be used for prioritization of such attributes. Analytic Hierarchy Process (AHP) is one such technique that is widely used for deciding among the complex criteria structure in different levels. In real applications, conventional AHP still cannot reflect the human thinking style as precise data concerning human attributes are quite hard to be extracted. Fuzzy logic offers a systematic base in dealing with situations, which are ambiguous or not well defined. This study aims at defining a methodology to improve the quality of prioritization of an employee-s performance measurement attributes under fuzziness. To do so, a methodology based on the Extent Fuzzy Analytic Hierarchy Process is proposed. Within the model, four main attributes such as Subject knowledge and achievements, Research aptitude, Personal qualities and strengths and Management skills with their subattributes are defined. The two approaches conventional AHP approach and the Extent Fuzzy Analytic Hierarchy Process approach have been compared on the same hierarchy structure and criteria set.

Keywords: AHP, Extent analysis method, Fuzzy AHP, Prioritization.

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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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Authors: Arkady Bolotin

Abstract:

Dichotomization of the outcome by a single cut-off point is an important part of various medical studies. Usually the relationship between the resulted dichotomized dependent variable and explanatory variables is analyzed with linear regression, probit regression or logistic regression. However, in many real-life situations, a certain cut-off point dividing the outcome into two groups is unknown and can be specified only approximately, i.e. surrounded by some (small) uncertainty. It means that in order to have any practical meaning the regression model must be robust to this uncertainty. In this paper, we show that neither the beta in the linear regression model, nor its significance level is robust to the small variations in the dichotomization cut-off point. As an alternative robust approach to the problem of uncertain medical categories, we propose to use the linear regression model with the fuzzy membership function as a dependent variable. This fuzzy membership function denotes to what degree the value of the underlying (continuous) outcome falls below or above the dichotomization cut-off point. In the paper, we demonstrate that the linear regression model of the fuzzy dependent variable can be insensitive against the uncertainty in the cut-off point location. In the paper we present the modeling results from the real study of low hemoglobin levels in infants. We systematically test the robustness of the binomial regression model and the linear regression model with the fuzzy dependent variable by changing the boundary for the category Anemia and show that the behavior of the latter model persists over a quite wide interval.

Keywords: Categorization, Uncertain medical categories, Binomial regression model, Fuzzy dependent variable, Robustness.

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Authors: Hirofumi Miyajima, Kazuya Kishida, Noritaka Shigei, Hiromi Miyajima

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Most of self-tuning fuzzy systems, which are automatically constructed from learning data, are based on the steepest descent method (SDM). However, this approach often requires a large convergence time and gets stuck into a shallow local minimum. One of its solutions is to use fuzzy rule modules with a small number of inputs such as DIRMs (Double-Input Rule Modules) and SIRMs (Single-Input Rule Modules). In this paper, we consider a (generalized) DIRMs model composed of double and single-input rule modules. Further, in order to reduce the redundant modules for the (generalized) DIRMs model, pruning and generative learning algorithms for the model are suggested. In order to show the effectiveness of them, numerical simulations for function approximation, Box-Jenkins and obstacle avoidance problems are performed.

Keywords: Box-Jenkins’s problem, Double-input rule module, Fuzzy inference model, Obstacle avoidance, Single-input rule module.

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Authors: Lina Yan, Shiheng Wang, Ke Wang

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A preconditioned Jacobi (PJ) method is provided for solving fuzzy linear systems whose coefficient matrices are crisp Mmatrices and the right-hand side columns are arbitrary fuzzy number vectors. The iterative algorithm is given for the preconditioned Jacobi method. The convergence is analyzed with convergence theorems. Numerical examples are given to illustrate the procedure and show the effectiveness and efficiency of the method.

Keywords: preconditioning, M-matrix, Jacobi method, fuzzy linear system (FLS).

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Authors: Radim Farana, Bogdan Walek, Michal Janosek, Jaroslav Zacek

Abstract:

This paper presents the advantages of fuzzy control use in technological processes control. The paper presents a real application of the Linguistic Fuzzy-Logic Control, developed at the University of Ostrava for the control of physical models in the Intelligent Systems Laboratory. The paper presents an example of a sensitive non-linear model, such as a magnetic levitation model and obtained results which show how modern information technologies can help to solve actual technical problems. A special method based on the LFLC controller with partial components is presented in this paper followed by the method of automatic context change, which is very helpful to achieve more accurate control results. The main advantage of the used system is its robustness in changing conditions demonstrated by comparing with conventional PID controller. This technology and real models are also used as a background for problem-oriented teaching, realized at the department for master students and their collaborative as well as individual final projects.

Keywords: Control, fuzzy logic, sensitive system, technological proves.

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Authors: Muhammad M. A. S. Mahmoud

Abstract:

Natural gas sweetening process is a controlled process that must be done at maximum efficiency and with the highest quality. In this work, due to complexity and non-linearity of the process, the H2S gas separation and the intelligent fuzzy controller, which is used to enhance the process, are simulated in MATLAB – Simulink. New design of fuzzy control for Gas Separator is discussed in this paper. The design is based on the utilization of linear state-estimation to generate the internal knowledge-base that stores input-output pairs. The obtained input/output pairs are then used to design a feedback fuzzy controller. The proposed closed-loop fuzzy control system maintains the system asymptotically-stability while it enhances the system time response to achieve better control of the concentration of the output gas from the tower. Simulation studies are carried out to illustrate the Gas Separator system performance.

Keywords: Gas separator, gas sweetening, intelligent controller, fuzzy control.

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Authors: Udomsak Thongkrajay, Padej Pao-La-Or, Thanatchai Kulworawanichpong

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Installation of power compensation equipment in some cases places additional buses into the system. Therefore, a total number of power flow equations and voltage unknowns increase due to additional locations of installed devices. In this circumstance, power flow calculation is more complicated. It may result in a computational convergence problem. This paper presents a power flow calculation by using Newton-Raphson iterative method together with the proposed load transfer technique. This concept is to eliminate additional buses by transferring installed loads at the new buses to existing two adjacent buses. Thus, the total number of power flow equations is not changed. The overall computational speed is expectedly shorter than that of solving the problem without applying the load transfer technique. A 15-bus test system is employed for test to evaluate the effectiveness of the proposed load transfer technique. As a result, the total number of iteration required and execution time is significantly reduced.

Keywords: Load transfer technique, Newton-Raphson power flow, ill-condition

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Authors: Chien-Hua Wang, Wei-Hsuan Lee, Chin-Tzong Pang

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In data mining, the association rules are used to find for the associations between the different items of the transactions database. As the data collected and stored, rules of value can be found through association rules, which can be applied to help managers execute marketing strategies and establish sound market frameworks. This paper aims to use Fuzzy Frequent Pattern growth (FFP-growth) to derive from fuzzy association rules. At first, we apply fuzzy partition methods and decide a membership function of quantitative value for each transaction item. Next, we implement FFP-growth to deal with the process of data mining. In addition, in order to understand the impact of Apriori algorithm and FFP-growth algorithm on the execution time and the number of generated association rules, the experiment will be performed by using different sizes of databases and thresholds. Lastly, the experiment results show FFPgrowth algorithm is more efficient than other existing methods.

Keywords: Data mining, association rule, fuzzy frequent patterngrowth.

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Authors: Ermanu A. Hakim, Adi Soeprijanto, Mauridhi H.P

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This paper presents PSS (Power system stabilizer) design based on optimal fuzzy PID (OFPID). OFPID based PSS design is considered for single-machine power systems. The main motivation for this design is to stabilize or to control low-frequency oscillation on power systems. Firstly, describing the linear PID control then to combine this PID control with fuzzy logic control mechanism. Finally, Fuzzy PID parameters (Kp. Kd, KI, Kupd, Kui) are tuned by Genetic Algorthm (GA) to reach optimal global stability. The effectiveness of the proposed PSS in increasing the damping of system electromechanical oscillation is demonstrated in a one-machine-infinite-bus system

Keywords: Fuzzy PID, Genetic Algorithm, power system stabilizer.

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Authors: Chih-Jer Lin, Chun-Ying Lee, Ying Liu, Chiang-Ho Cheng

Abstract:

The main objective of this article is to present the semi-active vibration control using an electro-rheological fluid embedded sandwich structure for a cantilever beam. ER fluid is a smart material, which cause the suspended particles polarize and connect each other to form chain. The stiffness and damping coefficients of the ER fluid can be changed in 10 micro seconds; therefore, ERF is suitable to become the material embedded in the tunable vibration absorber to become a smart absorber. For the ERF smart material embedded structure, the fuzzy control law depends on the experimental expert database and the proposed self-tuning strategy. The electric field is controlled by a CRIO embedded system to implement the real application. This study investigates the different performances using the Type-1 fuzzy and interval Type-2 fuzzy controllers. The Interval type-2 fuzzy control is used to improve the modeling uncertainties for this ERF embedded shock absorber. The self-tuning vibration controllers using Type-1 and Interval Type-2 fuzzy law are implemented to the shock absorber system. Based on the resulting performance, Internal Type-2 fuzzy is better than the traditional Type-1 fuzzy control for this vibration control system.

 

Keywords: Electro-Rheological Fluid, Semi-active vibration control, shock absorber, type 2 fuzzy control.

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Authors: S. Leghmizi, S. Liu, F. Naeim

Abstract:

This paper presents a fuzzy control system for a three degree of freedom (3-DOF) stabilized platform with explicit decoupling scheme. The system under consideration is a system with strong interactions between three channels. By using the concept of decentralized control, a control structure is developed that is composed of three control loops, each of which is associated with a single-variable fuzzy controller and a decoupling unit. Takagi-Sugeno (TS) fuzzy control algorithm is used to implement the fuzzy controller. The decoupling units design is based on the adaptive theory reasoning. Simulation tests were established using Simulink of Matlab. The obtained results have demonstrated the feasibility and effectiveness of the proposed approach. Simulation results are represented in this paper.

Keywords: 3-DOF platform of a ship carried antenna, the concept of decentralized control, Takagi-Sugeno (TS) fuzzy control algorithm, Simulink.

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Authors: Aqeel S. Jaber, Abu Zaharin Ahmad, Ahmed N. Abdalla

Abstract:

The artificial intelligent controller in power system plays as most important rule for many applications such as system operation and its control specially Load Frequency Controller (LFC). The main objective of LFC is to keep the frequency and tie-line power close to their decidable bounds in case of disturbance. In this paper, parallel fuzzy PI adaptive with conventional PD technique for Load Frequency Control system was proposed. PSO optimization method used to optimize both of scale fuzzy PI and tuning of PD. Two equal interconnected power system areas were used as a test system. Simulation results show the effectiveness of the proposed controller compared with different PID and classical fuzzy PI controllers in terms of speed response and damping frequency.

Keywords: Load frequency control, PSO, fuzzy control.

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Authors: R. Tur, A. Yardımcı

Abstract:

Imperfect knowledge cannot be avoided all the time. Imperfections may have several forms; uncertainties, imprecision and incompleteness. When we look to classification of methods for the management of imperfect knowledge we see fuzzy set-based techniques. The choice of a method to process data is linked to the choice of knowledge representation, which can be numerical, symbolic, logical or semantic and it depends on the nature of the problem to be solved for example decision support, which will be mentioned in our study. Fuzzy Logic is used for its ability to manage imprecise knowledge, but it can take advantage of the ability of neural networks to learn coefficients or functions. Such an association of methods is typical of so-called soft computing. In this study a new method was used for the management of imprecision for collected knowledge which related to economic analysis of construction industry in Turkey. Because of sudden changes occurring in economic factors decrease competition strength of construction companies. The better evaluation of these changes in economical factors in view of construction industry will made positive influence on company-s decisions which are dealing construction.

Keywords: Fuzzy logic, decision support systems, construction industry.

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Authors: Faisal Alshuwaier, Ali Areshey

Abstract:

Text mining techniques are generally applied for classifying the text, finding fuzzy relations and structures in data sets. This research provides plenty text mining capabilities. One common application is text classification and event extraction, which encompass deducing specific knowledge concerning incidents referred to in texts. The main contribution of this paper is the clarification of a concept graph generation mechanism, which is based on a text classification and optimal fuzzy relationship extraction. Furthermore, the work presented in this paper explains the application of fuzzy relationship extraction and branch and bound (BB) method to simplify the texts.

Keywords: Extraction, Max-Prod, Fuzzy Relations, Text Mining, Memberships, Classification.

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