Search results for: Fuzzy estimation

Authors: Yi Liu, Yang Xu

Abstract:

Applying the idea of soft set theory to lattice implication algebras, the novel concept of (implicative) filteristic soft lattice implication algebras which related to (implicative) filter(for short, (IF-)F-soft lattice implication algebras) are introduced. Basic properties of (IF-)F-soft lattice implication algebras are derived. Two kinds of fuzzy filters (i.e.(2, 2 _qk)((2, 2 _ qk))-fuzzy (implicative) filter) of L are introduced, which are generalizations of fuzzy (implicative) filters. Some characterizations for a soft set to be a (IF-)F-soft lattice implication algebra are provided. Analogously, this idea can be used in other types of filteristic lattice implication algebras (such as fantastic (positive implicative) filteristic soft lattice implication algebras).

Keywords: Soft set, (implicative) filteristic lattice implication algebras, fuzzy (implicative) filters, ((2, 2 _qk)) (2, 2 _ qk)-fuzzy(implicative) filters.

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Authors: Mehrdad N. Khajavi, Vahid Abdollahi

Abstract:

The purpose of suspension system in automobiles is to improve the ride comfort and road handling. In this research the ride and handling performance of a specific automobile with passive suspension system is compared to a proposed fuzzy logic semi active suspension system designed for that automobile. The bodysuspension- wheel system is modeled as a two degree of freedom quarter car model. MATLAB/SIMULINK [1] was used for simulation and controller design. The fuzzy logic controller is based on two inputs namely suspension velocity and body velocity. The output of the fuzzy controller is the damping coefficient of the variable damper. The result shows improvement over passive suspension method.

Keywords: Suspension System, Ride Comfort, Fuzzy Logic Controller, Passive and Semi Active System.

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Authors: Jianfeng Li, Feng Jin, Xiaoyu Yang

Abstract:

This paper applies fuzzy clustering algorithm in classifying real estate companies in China according to some general financial indexes, such as income per share, share accumulation fund, net profit margins, weighted net assets yield and shareholders' equity. By constructing and normalizing initial partition matrix, getting fuzzy similar matrix with Minkowski metric and gaining the transitive closure, the dynamic fuzzy clustering analysis for real estate companies is shown clearly that different clustered result change gradually with the threshold reducing, and then, it-s shown there is the similar relationship with the prices of those companies in stock market. In this way, it-s great valuable in contrasting the real estate companies- financial condition in order to grasp some good chances of investment, and so on.

Keywords: Fuzzy clustering algorithm, data mining, real estate company, financial analysis.

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Authors: Ali Haroonabadi, Mohammad Teshnehlab

Abstract:

None of the processing models in the software development has explained the software systems performance evaluation and modeling; likewise, there exist uncertainty in the information systems because of the natural essence of requirements, and this may cause other challenges in the processing of software development. By definition an extended version of UML (Fuzzy- UML), the functional requirements of the software defined uncertainly would be supported. In this study, the behavioral description of uncertain information systems by the aid of fuzzy-state diagram is crucial; moreover, the introduction of behavioral diagrams role in F-UML is investigated in software performance modeling process. To get the aim, a fuzzy sub-profile is used.

Keywords: Fuzzy System, Software Development Model, Software Performance Evaluation, UML

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Authors: C. Ardil

Abstract:

This paper investigates the application of the determinate fuzzy preference programming method for a more nuanced and comprehensive evaluation of stealth aircraft. Traditional methods often struggle to incorporate subjective factors and uncertainties inherent in complex systems like stealth aircraft. Determinate fuzzy preference programming addresses this limitation by leveraging the strengths of determinate fuzzy sets. The proposed novel multiple criteria decision-making algorithm integrates these concepts to consider aspects and criteria influencing aircraft performance. This approach aims to provide a more holistic assessment by enabling decision-makers to observe positive and negative outranking flows simultaneously. By demonstrating the validity and effectiveness of this approach through a practical example of selecting a stealth aircraft, this paper aims to establish the determinate fuzzy preference programming method as a valuable tool for informed decision-making in this critical domain.

Keywords: Determinate fuzzy set, stealth aircraft selection, distance function, decision making, uncertainty, preference programming. MCDM

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Authors: Joseph C. Chen, Venkata Mohan Kudapa

Abstract:

Development of two real-time surface roughness (Ra) prediction systems for milling operations was attempted. The systems used not only cutting parameters, such as feed rate and spindle speed, but also the cutting current generated and corrected by a clamp type energy sensor. Two different approaches were developed. First, a fuzzy inference system (FIS), in which the fuzzy logic rules are generated by experts in the milling processes, was used to conduct prediction modeling using current cutting data. Second, a neuro-fuzzy system (ANFIS) was explored. Neuro-fuzzy systems are adaptive techniques in which data are collected on the network, processed, and rules are generated by the system. The inference system then uses these rules to predict Ra as the output. Experimental results showed that the parameters of spindle speed, feed rate, depth of cut, and input current variation could predict Ra. These two systems enable the prediction of Ra during the milling operation with an average of 91.83% and 94.48% accuracy by FIS and ANFIS systems, respectively. Statistically, the ANFIS system provided better prediction accuracy than that of the FIS system.

Keywords: Surface roughness, input current, fuzzy logic, neuro-fuzzy, milling operations.

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Authors: Vassilis S. Kodogiannis, John N. Lygouras

Abstract:

In this research study, an intelligent detection system to support medical diagnosis and detection of abnormal lesions by processing endoscopic images is presented. The images used in this study have been obtained using the M2A Swallowable Imaging Capsule - a patented, video color-imaging disposable capsule. Schemes have been developed to extract texture features from the fuzzy texture spectra in the chromatic and achromatic domains for a selected region of interest from each color component histogram of endoscopic images. The implementation of an advanced fuzzy inference neural network which combines fuzzy systems and artificial neural networks and the concept of fusion of multiple classifiers dedicated to specific feature parameters have been also adopted in this paper. The achieved high detection accuracy of the proposed system has provided thus an indication that such intelligent schemes could be used as a supplementary diagnostic tool in endoscopy.

Keywords: Medical imaging, Computer aided diagnosis, Endoscopy, Neuro-fuzzy networks, Fuzzy integral.

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Authors: S. Areerachakul

Abstract:

Nowadays, several techniques such as; Fuzzy Inference System (FIS) and Neural Network (NN) are employed for developing of the predictive models to estimate parameters of water quality. The main objective of this study is to compare between the predictive ability of the Adaptive Neuro-Fuzzy Inference System (ANFIS) model and Artificial Neural Network (ANN) model to estimate the Biochemical Oxygen Demand (BOD) on data from 11 sampling sites of Saen Saep canal in Bangkok, Thailand. The data is obtained from the Department of Drainage and Sewerage, Bangkok Metropolitan Administration, during 2004-2011. The five parameters of water quality namely Dissolved Oxygen (DO), Chemical Oxygen Demand (COD), Ammonia Nitrogen (NH3N), Nitrate Nitrogen (NO3N), and Total Coliform bacteria (T-coliform) are used as the input of the models. These water quality indices affect the biochemical oxygen demand. The experimental results indicate that the ANN model provides a higher correlation coefficient (R=0.73) and a lower root mean square error (RMSE=4.53) than the corresponding ANFIS model.

Keywords: adaptive neuro-fuzzy inference system, artificial neural network, biochemical oxygen demand, surface water.

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Authors: C. Ardil

Abstract:

This article presents a new 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). In the proposed approach, fuzzy decision information related to the aircraft selection problem is taken into account in ranking the alternatives and selecting the best one. The basic procedural step is to transform the fuzzy decision matrices into matrices of alternatives evaluated according to all decision criteria. A numerical example illustrates the proposed approach for the military combat aircraft selection problem.

Keywords: trapezoidal fuzzy numbers, multiple criteria decision making analysis, decision making, aircraft selection, MCDMA, fuzzy TOPSIS

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Authors: František Včelař, Zuzana Pátíková

Abstract:

Recently a new type of very general relational structures, the so called (L-)complete propelattices, was introduced. These significantly generalize complete lattices and completely lattice L-ordered sets, because they do not assume the technically very strong property of transitivity. For these structures also the main part of the original Tarski’s fixed point theorem holds for (L-fuzzy) isotone maps, i.e., the part which concerns the existence of fixed points and the structure of their set. In this paper, fundamental properties of (L-)complete propelattices are recalled and the so called L-fuzzy relatively isotone maps are introduced. For these maps it is proved that they also have fixed points in L-complete propelattices, even if their set does not have to be of an awaited analogous structure of a complete propelattice.

Keywords: Fixed point, L-complete propelattice, L-fuzzy (relatively) isotone map, residuated lattice, transitivity.

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Authors: Prasan Pitiranggon, Nunthika Benjathepanun, Somsri Banditvilai, Veera Boonjing

Abstract:

Our study proposes an alternative method in building Fuzzy Rule-Based System (FRB) from Support Vector Machine (SVM). The first set of fuzzy IF-THEN rules is obtained through an equivalence of the SVM decision network and the zero-ordered Sugeno FRB type of the Adaptive Network Fuzzy Inference System (ANFIS). The second set of rules is generated by combining the first set based on strength of firing signals of support vectors using Gaussian kernel. The final set of rules is then obtained from the second set through input scatter partitioning. A distinctive advantage of our method is the guarantee that the number of final fuzzy IFTHEN rules is not more than the number of support vectors in the trained SVM. The final FRB system obtained is capable of performing classification with results comparable to its SVM counterpart, but it has an advantage over the black-boxed SVM in that it may reveal human comprehensible patterns.

Keywords: Fuzzy Rule Base, Rule Extraction, Rule Generation, Support Vector Machine.

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Authors: Keun-Chang Kwak

Abstract:

This paper is concerned with motion recognition based fuzzy WP(Wavelet Packet) feature extraction approach from Vicon physical data sets. For this purpose, we use an efficient fuzzy mutual-information-based WP transform for feature extraction. This method estimates the required mutual information using a novel approach based on fuzzy membership function. The physical action data set includes 10 normal and 10 aggressive physical actions that measure the human activity. The data have been collected from 10 subjects using the Vicon 3D tracker. The experiments consist of running, seating, and walking as physical activity motion among various activities. The experimental results revealed that the presented feature extraction approach showed good recognition performance.

Keywords: Motion recognition, fuzzy wavelet packet, Vicon physical data.

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Authors: Po-Chun Lin, Jyh-Cherng Gu

Abstract:

This study adopted previous fault patterns, results of detection analysis, historical records and data, and experts- experiences to establish fuzzy principles and estimate the failure probability index of components of a power transformer. Considering that actual parameters and limiting conditions of parameters may differ, this study used the standard data of IEC, IEEE, and CIGRE as condition parameters. According to the characteristics of each condition parameter, relative degradation was introduced to reflect the degree of influence of the factors on the transformer condition. The method of fuzzy mathematics was adopted to determine the subordinate function of the transformer condition. The calculation used the Matlab Fuzzy Tool Box to select the condition parameters of coil winding, iron core, bushing, OLTC, insulating oil and other auxiliary components and factors (e.g., load records, performance history, and maintenance records) of the transformer to establish the fuzzy principles. Examples were presented to support the rationality and effectiveness of the evaluation method of power transformer performance conditions, as based on fuzzy comprehensive evaluation.

Keywords: Fuzzy, relative degradation degree, condition-basedmaintenance, power transformer

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Authors: Ahmad Aljaafreh

Abstract:

Safer driver behavior promoting is the main goal of this paper. It is a fact that drivers behavior is relatively safer when being monitored. Thus, in this paper, we propose a monitoring system to report specific driving event as well as the potentially aggressive events for estimation of the driving performance. Our driving monitoring system is composed of two parts. The first part is the in-vehicle embedded system which is composed of a GPS receiver, a two-axis accelerometer, radar sensor, OBD interface, and GPRS modem. The design considerations that led to this architecture is described in this paper. The second part is a web server where an adaptive hierarchical fuzzy system is proposed to classify the driving performance based on the data that is sent by the in-vehicle embedded system and the data that is provided by the geographical information system (GIS). Our system is robust, inexpensive and small enough to fit inside a vehicle without distracting the driver.

Keywords: Driving monitoring system, In-vehicle embedded system, Hierarchical fuzzy system.

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Authors: C. Ardil

Abstract:

Fuzzy set and intuitionistic fuzzy set are dealing with the imprecision and uncertainty inherent in a complex decision problem. However, sometimes these theories are not sufficient to model indeterminate and inconsistent information encountered in real-life problems. To overcome this insufficiency, the neutrosophic set, which is useful in practical applications, is proposed, triangular neutrosophic numbers and trapezoidal neutrosophic numbers are examined, their definitions and applications are discussed. In this study, a decision making algorithm is developed using neutrosophic set processes and an application is given in fighter aircraft selection as an example of a decision making problem. The estimation of the fighter aircraft selection with the neutrosophic multiple criteria decision analysis method is examined.  

Keywords: neutrosophic set, multiple criteria decision making analysis, fighter aircraft selection, MCDMA, neutrosophic numbers

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Authors: Kexin Jia, Youxin Lu

Abstract:

To make the modulation classification system more suitable for signals in a wide range of signal to noise rate (SNR), a novel method of designing combined classifier based on fuzzy neural network (FNN) is presented in this paper. The method employs fuzzy neural network classifiers and interclass distance (ICD) to improve recognition reliability. Experimental results show that the proposed combined classifier has high recognition rate with large variation range of SNR (success rates are over 99.9% when SNR is not lower than 5dB).

Keywords: Modulation classification, combined classifier, fuzzy neural network, interclass distance.

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Authors: Jagadish H. Pujar, S. F. Kodad

Abstract:

Recent developments in Soft computing techniques, power electronic switches and low-cost computational hardware have made it possible to design and implement sophisticated control strategies for sensorless speed control of AC motor drives. Such an attempt has been made in this work, for Sensorless Speed Control of Induction Motor (IM) by means of Direct Torque Fuzzy Control (DTFC), PI-type fuzzy speed regulator and MRAS speed estimator strategy, which is absolutely nonlinear in its nature. Direct torque control is known to produce quick and robust response in AC drive system. However, during steady state, torque, flux and current ripple occurs. So, the performance of conventional DTC with PI speed regulator can be improved by implementing fuzzy logic techniques. Certain important issues in design including the space vector modulated (SVM) 3-Ф voltage source inverter, DTFC design, generation of reference torque using PI-type fuzzy speed regulator and sensor less speed estimator have been resolved. The proposed scheme is validated through extensive numerical simulations on MATLAB. The simulated results indicate the sensor less speed control of IM with DTFC and PI-type fuzzy speed regulator provides satisfactory high dynamic and static performance compare to conventional DTC with PI speed regulator.

Keywords: Sensor-less Speed Estimator, Fuzzy Logic Control(FLC), SVM, DTC, DTFC, IM, fuzzy speed regulator.

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Authors: Abdelaziz Sahbani, Kamel Ben Saad, Mohamed Benrejeb

Abstract:

This paper proposes a Fuzzy Sliding Mode Control (FSMC) as a control strategy for Buck-Boost DC-DC converter. The proposed fuzzy controller specifies changes in the control signal based on the knowledge of the surface and the surface change to satisfy the sliding mode stability and attraction conditions. The performances of the proposed fuzzy sliding controller are compared to those obtained by a classical sliding mode controller. The satisfactory simulation results show the efficiency of the proposed control law which reduces the chattering phenomenon. Moreover, the obtained results prove the robustness of the proposed control law against variation of the load resistance and the input voltage of the studied converter.

Keywords: Buck Boost converter, Sliding Mode Control, Fuzzy Sliding Mode Control, robustness, chattering.

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Authors: Shabbar Naqvi, Jonathan M. Garibaldi

Abstract:

Breast cancer is one of the most frequent occurring cancers in women throughout the world including U.K. The grading of this cancer plays a vital role in the prognosis of the disease. In this paper we present an overview of the use of advanced computational method of fuzzy inference system as a tool for the automation of breast cancer grading. A new spectral data set obtained from Fourier Transform Infrared Spectroscopy (FTIR) of cancer patients has been used for this study. The future work outlines the potential areas of fuzzy systems that can be used for the automation of breast cancer grading.

Keywords: Breast cancer, FTIR, fuzzy inference system, principal component analysis

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Authors: Fayssal Amrane, Azeddine Chaiba

Abstract:

In this paper, type-2 fuzzy logic control (T2FLC) and neuro-fuzzy control (NFC) for a doubly fed induction generator (DFIG) based on direct power control (DPC) with a fixed switching frequency is proposed for wind generation application. First, a mathematical model of the doubly-fed induction generator implemented in d-q reference frame is achieved. Then, a DPC algorithm approach for controlling active and reactive power of DFIG via fixed switching frequency is incorporated using PID. The performance of T2FLC and NFC, which is based on the DPC algorithm, are investigated and compared to those obtained from the PID controller. Finally, simulation results demonstrate that the NFC is more robust, superior dynamic performance for wind power generation system applications.

Keywords: Doubly fed induction generetor, direct power control, space vector modulation, type-2 fuzzy logic control, neuro-fuzzy control, maximum power point tracking.

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Authors: Seema Chopra, R. Mitra, Vijay Kumar

Abstract:

A neurofuzzy approach for a given set of input-output training data is proposed in two phases. Firstly, the data set is partitioned automatically into a set of clusters. Then a fuzzy if-then rule is extracted from each cluster to form a fuzzy rule base. Secondly, a fuzzy neural network is constructed accordingly and parameters are tuned to increase the precision of the fuzzy rule base. This network is able to learn and optimize the rule base of a Sugeno like Fuzzy inference system using Hybrid learning algorithm, which combines gradient descent, and least mean square algorithm. This proposed neurofuzzy system has the advantage of determining the number of rules automatically and also reduce the number of rules, decrease computational time, learns faster and consumes less memory. The authors also investigate that how neurofuzzy techniques can be applied in the area of control theory to design a fuzzy controller for linear and nonlinear dynamic systems modelling from a set of input/output data. The simulation analysis on a wide range of processes, to identify nonlinear components on-linely in a control system and a benchmark problem involving the prediction of a chaotic time series is carried out. Furthermore, the well-known examples of linear and nonlinear systems are also simulated under the Matlab/Simulink environment. The above combination is also illustrated in modeling the relationship between automobile trips and demographic factors.

Keywords: Fuzzy control, neuro-fuzzy techniques, fuzzy subtractive clustering, extraction of rules, and optimization of membership functions.

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Authors: Zoran D. Banjac, Branko D. Kovacevic

Abstract:

The problem of FIR system parameter estimation has been considered in the paper. A new robust recursive algorithm for simultaneously estimation of parameters and scale factor of prediction residuals in non-stationary environment corrupted by impulsive noise has been proposed. The performance of derived algorithm has been tested by simulations.

Keywords: Adaptive filtering, Non-Gaussian filtering, Robustestimation, Scale factor estimation.

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Authors: F. Khaber, K. Zehar, A. Hamzaoui

Abstract:

In this paper, we introduce a robust state feedback controller design using Linear Matrix Inequalities (LMIs) and guaranteed cost approach for Takagi-Sugeno fuzzy systems. The purpose on this work is to establish a systematic method to design controllers for a class of uncertain linear and non linear systems. Our approach utilizes a certain type of fuzzy systems that are based on Takagi-Sugeno (T-S) fuzzy models to approximate nonlinear systems. We use a robust control methodology to design controllers. This method not only guarantees stability, but also minimizes an upper bound on a linear quadratic performance measure. A simulation example is presented to show the effectiveness of this method.

Keywords: Takagi-Sugeno fuzzy model, state feedback, linear matrix inequalities, robust stability.

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Authors: Liping Zhang, Kelin Li

Abstract:

In this paper, a class of impulsive BAM fuzzy cellular neural networks with time delays in the leakage terms is formulated and investigated. By establishing a delay differential inequality and M-matrix theory, some sufficient conditions ensuring the existence, uniqueness and global exponential stability of equilibrium point for impulsive BAM fuzzy cellular neural networks with time delays in the leakage terms are obtained. In particular, a precise estimate of the exponential convergence rate is also provided, which depends on system parameters and impulsive perturbation intention. It is believed that these results are significant and useful for the design and applications of BAM fuzzy cellular neural networks. An example is given to show the effectiveness of the results obtained here.

Keywords: Global exponential stability, bidirectional associative memory, fuzzy cellular neural networks, leakage delays, impulses.

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Authors: N. Kumaresan , J. Kavikumar, Kuru Ratnavelu

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In this paper, solution of fuzzy differential equation under general differentiability is obtained by simulink. The simulink solution is equivalent or very close to the exact solution of the problem. Accuracy of the simulink solution to this problem is qualitatively better. An illustrative numerical example is presented for the proposed method.

Keywords: Fuzzy differential equation, Generalized differentiability, H-difference and Simulink.

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Authors: Sandeep Chandana, Rene V. Mayorga

Abstract:

The paper presents a new hybridization methodology involving Neural, Fuzzy and Rough Computing. A Rough Sets based approximation technique has been proposed based on a certain Neuro – Fuzzy architecture. A New Rough Neuron composition consisting of a combination of a Lower Bound neuron and a Boundary neuron has also been described. The conventional convergence of error in back propagation has been given away for a new framework based on 'Output Excitation Factor' and an inverse input transfer function. The paper also presents a brief comparison of performances, of the existing Rough Neural Networks and ANFIS architecture against the proposed methodology. It can be observed that the rough approximation based neuro-fuzzy architecture is superior to its counterparts.

Keywords: Boundary neuron, neuro-fuzzy, output excitation factor, RANFIS, rough approximation, rough neural computing.

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Authors: Roozbeh Keshmiri, Alireza Mohamad Shahri

Abstract:

Fuzzy controllers are potential candidates for the control of nonlinear, time variant and also complicated systems. Anti lock brake system (ABS) which is a nonlinear system, may not be easily controlled by classical control methods. An intelligent Fuzzy control method is very useful for this kind of nonlinear system. A typical antilock brake system (ABS) by sensing the wheel lockup, releases the brakes for a short period of time, and then reapplies again the brakes when the wheel spins up. In this paper, an intelligent fuzzy ABS controller is designed to adjust slipping performance for variety of roads. There are tow major sections in the proposing control system. First section consists of tow Fuzzy-Logic Controllers (FLC) providing optimal brake torque for both front and rear wheels. Second section which is also a FLC provides required amount of slip and torque references properties for different kind of roads. Simulation results of our proposed intelligent ABS for three different kinds of road show more reliable and better performance in compare with two other break systems.

Keywords: Fuzzy Logic Control, ABS, Anti lock BrakingSystem.

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Authors: Jurifa Mat Lazi, Zulkifilie Ibrahim, Marizan Sulaiman, Fizatul Aini Patakor, Siti Noormiza Mat Isa

Abstract:

Dual motor drives fed by single inverter is purposely designed to reduced size and cost with respect to single motor drives fed by single inverter. Previous researches on dual motor drives only focus on the modulation and the averaging techniques. Only a few of them, study the performance of the drives based on different speed controller other than Proportional and Integrator (PI) controller. This paper presents a detailed comparative study on fuzzy rule-base in Fuzzy Logic speed Controller (FLC) for Dual Permanent Magnet Synchronous Motor (PMSM) drives. Two fuzzy speed controllers which are standard and simplified fuzzy speed controllers are designed and the results are compared and evaluated. The standard fuzzy controller consists of 49 rules while the proposed controller consists of 9 rules determined by selecting the most dominant rules only. Both designs are compared for wide range of speed and the robustness of both controllers over load disturbance changes is tested to demonstrate the effectiveness of the simplified/reduced rulebase.

Keywords: Dual Motor Drives, Fuzzy Logic Speed Controller, Reduced Rule-Base, PMSM

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Authors: E. Ansari-Piri, N. Eghbali

Abstract:

Let A and B be two linear algebras. A linear map ϕ : A → B is called an n-homomorphism if ϕ(a1...an) = ϕ(a1)...ϕ(an) for all a1, ..., an ∈ A. In this note we have a verification on the behavior of almost n-multiplicative linear maps with n > 2 in the fuzzy normed spaces

Keywords: Almost multiplicative maps, n-homomorphism maps, almost n-multiplicative maps, fuzzy normed space, stability.

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Authors: Binyamin Yusoff, Imran Taib, Lazim Abdullah, Abd Fatah Wahab

Abstract:

Intuitionistic fuzzy sets as proposed by Atanassov, have gained much attention from past and latter researchers for applications in various fields. Similarity measures between intuitionistic fuzzy sets were developed afterwards. However, it does not cater the conflicting behavior of each element evaluated. We therefore made some modification to the similarity measure of IFS by considering conflicting concept to the model. In this paper, we concentrate on Zhang and Fu-s similarity measures for IFSs and some examples are given to validate these similarity measures. A simple modification to Zhang and Fu-s similarity measures of IFSs was proposed to find the best result according to the use of degree of indeterminacy. Finally, we mark up with the application to real decision making problems.

Keywords: Intuitionistic fuzzy sets, similarity measures, multicriteriadecision making.

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