Search results for: (ANFIS) Adaptive Neuro Fuzzy Inference System

Authors: Jian Shi, Baoguo Yu, Haonan Jia, Meng Liu, Ping Huang

Abstract:

Adapting to the flexibility of war, a large number of guided weapons launch from aircraft. Therefore, the inertial navigation system loaded in the weapon needs to undergo an alignment process in the air. This article proposes the following methods to the problem of inaccurate modeling of the system under large misalignment angles, the accuracy reduction of filtering caused by outliers, and the noise changes in GPS signals: first, considering the large misalignment errors of Strapdown Inertial Navigation System (SINS)/GPS, a more accurate model is made rather than to make a small-angle approximation, and the Unscented Kalman Filter (UKF) algorithms are used to estimate the state; then, taking into account the impact of GPS noise changes on the fine alignment algorithm, the innovation adaptive filtering algorithm is introduced to estimate the GPS’s noise in real-time; at the same time, in order to improve the anti-interference ability of the air fine alignment algorithm, a robust filtering algorithm based on outlier detection is combined with the air fine alignment algorithm to improve the robustness of the algorithm. The algorithm can improve the alignment accuracy and robustness under interference conditions, which is verified by simulation.

Keywords: Air alignment, fine alignment, inertial navigation system, integrated navigation system, UKF.

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Authors: Marzieh. Savoj, S. Amirhassan. Monadjemi

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Iris localization is a very important approach in biometric identification systems. Identification process usually is implemented in three levels: iris localization, feature extraction, and pattern matching finally. Accuracy of iris localization as the first step affects all other levels and this shows the importance of iris localization in an iris based biometric system. In this paper, we consider Daugman iris localization method as a standard method, propose a new method in this field and then analyze and compare the results of them on a standard set of iris images. The proposed method is based on the detection of circular edge of iris, and improved by fuzzy circles and surface energy difference contexts. Implementation of this method is so easy and compared to the other methods, have a rather high accuracy and speed. Test results show that the accuracy of our proposed method is about Daugman method and computation speed of it is 10 times faster.

Keywords: Convolution, Edge detector filter, Fuzzy circle, Identification

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Authors: T. Sopapirm, K-N. Areerak, K-L. Areerak, A. Srikaew

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The paper presents the applications of artificial intelligence technique called adaptive tabu search to design the controller of a buck converter. The averaging model derived from the DQ and generalized state-space averaging methods is applied to simulate the system during a searching process. The simulations using such averaging model require the faster computational time compared with that of the full topology model from the software packages. The reported model is suitable for the work in the paper in which the repeating calculation is needed for searching the best solution. The results will show that the proposed design technique can provide the better output waveforms compared with those designed from the classical method.

Keywords: Buck converter, adaptive tabu search, DQ method, generalized state-space averaging method, modeling and simulation

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

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

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

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Authors: Frank Emmert Streib, Matthias Dehmer, Gökhan H. Bakır, Max Mühlhauser

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In this paper we investigate the influence of external noise on the inference of network structures. The purpose of our simulations is to gain insights in the experimental design of microarray experiments to infer, e.g., transcription regulatory networks from microarray experiments. Here external noise means, that the dynamics of the system under investigation, e.g., temporal changes of mRNA concentration, is affected by measurement errors. Additionally to external noise another problem occurs in the context of microarray experiments. Practically, it is not possible to monitor the mRNA concentration over an arbitrary long time period as demanded by the statistical methods used to learn the underlying network structure. For this reason, we use only short time series to make our simulations more biologically plausible.

Keywords: Dynamic Bayesian networks, structure learning, gene networks, Markov chain Monte Carlo, microarray data.

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Authors: Raghad Alhusari, Farag Omar, Moustafa Fadel

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A traditional greenhouse is a metal frame agricultural building used for cultivation plants in a controlled environment isolated from external climatic changes. Using greenhouses in agriculture is an efficient way to reduce the water consumption, where agriculture field is considered the biggest water consumer world widely. Controlling greenhouse environment yields better productivity of plants but demands an increase of electric power. Although various control approaches have been used towards greenhouse automation, most of them are applied to traditional greenhouses with ventilation fans and/or evaporation cooling system. Such approaches are still demanding high energy and water consumption. The aim of this research is to develop a fuzzy control system that minimizes water and energy consumption by utilizing outside weather conditions and underground heat exchanger to maintain the optimum climate of the greenhouse. The proposed control system is implemented on an experimental model of thermally isolated greenhouse structure with dimensions of 6x5x2.8 meters. It uses fans for extracting heat from the ground heat exchanger system, motors for automatic open/close of the greenhouse windows and LED as lighting system. The controller is integrated also with environmental condition sensors. It was found that using the air-to-air horizontal ground heat exchanger with 90 mm diameter and 2 mm thickness placed 2.5 m below the ground surface results in decreasing the greenhouse temperature of 3.28 ˚C which saves around 3 kW of consumed energy. It also eliminated the water consumption needed in evaporation cooling systems which are traditionally used for cooling the greenhouse environment.

Keywords: Automation, earth-to-air heat exchangers, fuzzy control, greenhouse, sustainable buildings.

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Authors: Oshmita Dey, Debjani Chakraborty

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In this paper, a single period inventory model with resalable returns has been analyzed in an imprecise and uncertain mixed environment. Demand has been introduced as a fuzzy random variable. In this model, a single order is placed before the start of the selling season. The customer, for a full refund, may return purchased products within a certain time interval. Returned products are resalable, provided they arrive back before the end of the selling season and are found to be undamaged. Products remaining at the end of the season are salvaged. All demands not met directly are lost. The probabilities that a sold product is returned and that a returned product is resalable, both imprecise in a real situation, have been assumed to be fuzzy in nature.

Keywords: Fuzzy random variable, Modified graded meanintegration, Internet mail order, Inventory.

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Authors: Somayeh Alizadeh, Mehdi Ghazanfari, Mohammad Fathian

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Fuzzy Cognitive Maps (FCMs) have successfully been applied in numerous domains to show relations between essential components. In some FCM, there are more nodes, which related to each other and more nodes means more complex in system behaviors and analysis. In this paper, a novel learning method used to construct FCMs based on historical data and by using data mining and DEMATEL method, a new method defined to reduce nodes number. This method cluster nodes in FCM based on their cause and effect behaviors.

Keywords: Clustering, Data Mining, Fuzzy Cognitive Map(FCM), Learning.

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Authors: A. Zaher, A. Traore, F. Thiéry, T. Talbert, B. Shaer

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In this paper, an intelligent approach is proposed to optimize the orientation of continuous solar tracking systems on cloudy days. Considering the weather case, the direct sunlight is more important than the diffuse radiation in case of clear sky. Thus, the panel is always pointed towards the sun. In case of an overcast sky, the solar beam is close to zero, and the panel is placed horizontally to receive the maximum of diffuse radiation. Under partly covered conditions, the panel must be pointed towards the source that emits the maximum of solar energy and it may be anywhere in the sky dome. Thus, the idea of our approach is to analyze the images, captured by ground-based sky camera system, in order to detect the zone in the sky dome which is considered as the optimal source of energy under cloudy conditions. The proposed approach is implemented using experimental setup developed at PROMES-CNRS laboratory in Perpignan city (France). Under overcast conditions, the results were very satisfactory, and the intelligent approach has provided efficiency gains of up to 9% relative to conventional continuous sun tracking systems.

Keywords: Clouds detection, fuzzy inference systems, images processing, sun trackers.

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Authors: Swathi Sampath, V. Kalaichelvi

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The assessment of the risk posed by a borrower to a lender is one of the common problems that financial institutions have to deal with. Consumers vying for a mortgage are generally compared to each other by the use of a number called the Credit Score, which is generated by applying a mathematical algorithm to information in the applicant’s credit report. The higher the credit score, the lower the risk posed by the candidate, and the better he is to be taken on by the lender. The objective of the present work is to use fuzzy logic and linguistic rules to create a model that generates Credit Scores.

Keywords: Credit scoring, fuzzy logic, mortgage, risk assessment.

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Authors: Liming Zhang

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There have been different approaches to compute the analytic instantaneous frequency with a variety of background reasoning and applicability in practice, as well as restrictions. This paper presents an adaptive Fourier decomposition and (α-counting) based instantaneous frequency computation approach. The adaptive Fourier decomposition is a recently proposed new signal decomposition approach. The instantaneous frequency can be computed through the so called mono-components decomposed by it. Due to the fast energy convergency, the highest frequency of the signal will be discarded by the adaptive Fourier decomposition, which represents the noise of the signal in most of the situation. A new instantaneous frequency definition for a large class of so-called simple waves is also proposed in this paper. Simple wave contains a wide range of signals for which the concept instantaneous frequency has a perfect physical sense. The α-counting instantaneous frequency can be used to compute the highest frequency for a signal. Combination of these two approaches one can obtain the IFs of the whole signal. An experiment is demonstrated the computation procedure with promising results.

Keywords: Adaptive Fourier decomposition, Fourier series, signal processing, instantaneous frequency

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Authors: Ju-Hong Lee, Ching-Wei Liao, Kun-Che Lee

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This paper deals with the problem of using antenna sensors for adaptive beamforming in the presence of random steering mismatch. We present an efficient adaptive array beamformer with robustness to deal with the considered problem. The robustness of the proposed beamformer comes from the efficient designation of the steering vector. Using the received array data vector, we construct an appropriate correlation matrix associated with the received array data vector and a correlation matrix associated with signal sources. Then, the eigenvector associated with the largest eigenvalue of the constructed signal correlation matrix is designated as an appropriate estimate of the steering vector. Finally, the adaptive weight vector required for adaptive beamforming is obtained by using the estimated steering vector and the constructed correlation matrix of the array data vector. Simulation results confirm the effectiveness of the proposed method.

Keywords: Adaptive beamforming, antenna array, linearly constrained minimum variance, robustness, steering vector.

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Authors: C. Ganesh Babu, P. T. Vanathi

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In this paper we present an enhanced noise reduction method for robust speech recognition using Adaptive Gain Equalizer with Non linear Spectral Subtraction. In Adaptive Gain Equalizer method (AGE), the input signal is divided into a number of subbands that are individually weighed in time domain, in accordance to the short time Signal-to-Noise Ratio (SNR) in each subband estimation at every time instant. Instead of focusing on suppression the noise on speech enhancement is focused. When analysis was done under various noise conditions for speech recognition, it was found that Adaptive Gain Equalizer method algorithm has an obvious failing point for a SNR of -5 dB, with inadequate levels of noise suppression for SNR less than this point. This work proposes the implementation of AGE when coupled with Non linear Spectral Subtraction (AGE-NSS) for robust speech recognition. The experimental result shows that out AGE-NSS performs the AGE when SNR drops below -5db level.

Keywords: Adaptive Gain Equalizer, Non Linear Spectral Subtraction, Speech Enhancement, and Speech Recognition.

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Authors: Nastaran Hajiheydari, Mohammad Soltani Delgosha

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Vendor (supplier) selection is a group decision-making (GDM) process, in which, based on some predetermined criteria, the experts’ preferences are provided in order to rank and choose the most desirable suppliers. In the real business environment, our attitudes or our choices would be made in an uncertain and indecisive situation could not be expressed in a crisp framework. Intuitionistic fuzzy sets (IFSs) could handle such situations in the best way. VIKOR method was developed to solve multi-criteria decision-making (MCDM) problems. This method, which is used to determine the compromised feasible solution with respect to the conflicting criteria, introduces a multi-criteria ranking index based on the particular measure of 'closeness' to the 'ideal solution'. Until now, there has been a little investigation of VIKOR with IFS, therefore we extended the intuitionistic fuzzy (IF) VIKOR to solve vendor selection problem under IF GDM environment. The present study intends to develop an IF VIKOR method in a GDM situation. Therefore, a model is presented to calculate the criterion weights based on entropy measure. Then, the interval-valued intuitionistic fuzzy weighted geometric (IFWG) operator utilized to obtain the total decision matrix. In the next stage, an approach based on the positive idle intuitionistic fuzzy number (PIIFN) and negative idle intuitionistic fuzzy number (NIIFN) was developed. Finally, the application of the proposed method to solve a vendor selection problem illustrated.

Keywords: Group decision making, intuitionistic fuzzy entropy measure, intuitionistic fuzzy set, vendor selection VIKOR.

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Authors: A. Hasankhani, H. Saadat, M. M. Zahedi

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In this paper some properties of the uniformity topology on a BCI-algebras are discussed.

Keywords: (Fuzzy) ideal, (Fuzzy) subalgebra, Uniformity, clopen sets.

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Authors: Ardeshir Karami Mohammadi

Abstract:

A Variable Structure Model Reference Adaptive Controller using state variables is proposed for a class of multi input-multi output systems. Adaptation law is of variable structure type and switching functions is designed based on stability requirements. Global exponential stability is proved based on Lyapunov criterion. Transient behavior is analyzed using sliding mode control and shows perfect model following at a finite time.

Keywords: Adaptive control, Model reference, Variablestructure, MIMO system.

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Authors: Masao Okabe

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Nowadays, in Japan, variety of students get into a university and one of the main roles of introductory courses for freshmen is to make such students well prepared for subsequent intermediate courses. For that purpose, the flipped-mastery model is not enough because videos usually used in a flipped classroom is not adaptive and does not fit all freshmen with different academic performances. This paper proposes an ontology-navigated tutoring system called EduGraph. Using EduGraph, students can prepare for and review a class, in a more flexibly personalizable way than by videos. Structuralizing learning materials by its ontology, EduGraph also helps students integrate what they learn as knowledge, and makes learning materials sharable. EduGraph was used for an introductory course for freshmen. This application suggests that EduGraph is effective.

Keywords: Adaptive e-learning, flipped classroom, mastery learning, ontology.

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Authors: Ahmed Abbas Helmy, M. R. M. Rizk, Mohamed El-Sayed

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A model predictive controller based on recursive learning is proposed. In this SISO adaptive controller, a model is automatically updated using simple recursive equations. The identified models are then stored in the memory to be re-used in the future. The decision for model update is taken based on a new control performance index. The new controller allows the use of simple linear model predictive controllers in the control of nonlinear time varying processes.

Keywords: Adaptive control, model predictive control, dynamic matrix control, online model identification

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Authors: Kazumoto Tanaka, Takayuki Fujino

Abstract:

Sports games conducted as a group are a form of therapeutic exercise for aged people with decreased strength and for people suffering from permanent damage of stroke and other conditions. However, it is difficult for patients with different athletic abilities to play a game on an equal footing. This study specifically examines a computer video game designed for therapeutic exercise, and a game system with support given depending on athletic ability. Thereby, anyone playing the game can participate equally. This video-game, to be specific, is a popular variant of balloon volleyball, in which players hit a balloon by hand before it falls to the floor. In this game system, each player plays the game watching a monitor on which the system displays tailor-made video-game images adjusted to the person’s athletic ability, providing players with player-adaptive assist support. We have developed a multiplayer game system with an image generation technique for the tailor-made video-game and conducted tests to evaluate it.

Keywords: Therapeutic exercise, computer video game, disability-adaptive assist, tailor-made video-game image.

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Authors: Wisam F. Al-Azzo, Borhanuddin Mohd. Ali

Abstract:

This paper addresses the problem of peak-to-average power ratio (PAPR) in orthogonal frequency division multiplexing (OFDM) systems. It also introduces a new PAPR reduction technique based on adaptive square-rooting (SQRT) companding process. The SQRT process of the proposed technique changes the statistical characteristics of the OFDM output signals from Rayleigh distribution to Gaussian-like distribution. This change in statistical distribution results changes of both the peak and average power values of OFDM signals, and consequently reduces significantly the PAPR. For the 64QAM OFDM system using 512 subcarriers, up to 6 dB reduction in PAPR was achieved by square-rooting technique with fixed degradation in bit error rate (BER) equal to 3 dB. However, the PAPR is reduced at the expense of only -15 dB out-ofband spectral shoulder re-growth below the in-band signal level. The proposed adaptive SQRT technique is superior in terms of BER performance than the original, non-adaptive, square-rooting technique when the required reduction in PAPR is no more than 5 dB. Also, it provides fixed amount of PAPR reduction in which it is not available in the original SQRT technique.

Keywords: complementary cumulative distribution function(CCDF), OFDM, peak-to-average power ratio (PAPR), adaptivesquare-rooting PAPR reduction technique.

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Authors: Ahmad Habibizad Navin, Mehdi Naghian Fesharaki, Mirkamal Mirnia, Mohamad Teshnelab, Ehsan Shahamatnia

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In this paper we introduce new data oriented modeling of uniform random variable well-matched with computing systems. Due to this conformity with current computers structure, this modeling will be efficiently used in statistical inference.

Keywords: Uniform random variable, Data oriented modeling, Statistical inference, Prodigraph, Statistically complete tree, Uniformdigital probability digraph, Uniform n-complete probability tree.

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Authors: Abolfazl Jalilvand, Mohammad Reza Feyzi, Sohrab Khanmohammad, Mohammad Bagher Bana Sharifian, Ali Sajjadi

Abstract:

Nowadays the control of stator voltage at a constant frequency is one of the traditional and low expense methods in order to control the speed of induction motors near its nominal speed. The torque of induction motor is a nonlinear function of the firing angle, phase angle and speed. In this paper the speed control of induction motor regarding various load torque and under different conditions will be investigated based on a fuzzy controller with inverse training.

Keywords: Three phase induction motor, AC converter, speedcontrol, fuzzy control.

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Authors: Yu-Lin Liao, Ya-Fu Peng

Abstract:

An adaptive dynamic cerebellar model articulation controller (DCMAC) neural network used for solving the prediction and identification problem is proposed in this paper. The proposed DCMAC has superior capability to the conventional cerebellar model articulation controller (CMAC) neural network in efficient learning mechanism, guaranteed system stability and dynamic response. The recurrent network is embedded in the DCMAC by adding feedback connections in the association memory space so that the DCMAC captures the dynamic response, where the feedback units act as memory elements. The dynamic gradient descent method is adopted to adjust DCMAC parameters on-line. Moreover, the analytical method based on a Lyapunov function is proposed to determine the learning-rates of DCMAC so that the variable optimal learning-rates are derived to achieve most rapid convergence of identifying error. Finally, the adaptive DCMAC is applied in two computer simulations. Simulation results show that accurate identifying response and superior dynamic performance can be obtained because of the powerful on-line learning capability of the proposed DCMAC.

Keywords: adaptive, cerebellar model articulation controller, CMAC, prediction, identification

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Authors: Yoshitaka Fujiwara, Jun-ichirou Fukushima, Yasunari Maeda

Abstract:

Keys to high-quality face-to-face education are ensuring flexibility in the way lectures are given, and providing care and responsiveness to learners. This paper describes a face-to-face education support system that is designed to raise the satisfaction of learners and reduce the workload on instructors. This system consists of a lecture adaptation assistance part, which assists instructors in adapting teaching content and strategy, and a Q&A assistance part, which provides learners with answers to their questions. The core component of the former part is a “learning achievement map", which is composed of a Bayesian network (BN). From learners- performance in exercises on relevant past lectures, the lecture adaptation assistance part obtains information required to adapt appropriately the presentation of the next lecture. The core component of the Q&A assistance part is a case base, which accumulates cases consisting of questions expected from learners and answers to them. The Q&A assistance part is a case-based search system equipped with a search index which performs probabilistic inference. A prototype face-to-face education support system has been built, which is intended for the teaching of Java programming, and this approach was evaluated using this system. The expected degree of understanding of each learner for a future lecture was derived from his or her performance in exercises on past lectures, and this expected degree of understanding was used to select one of three adaptation levels. A model for determining the adaptation level most suitable for the individual learner has been identified. An experimental case base was built to examine the search performance of the Q&A assistance part, and it was found that the rate of successfully finding an appropriate case was 56%.

Keywords: Bayesian network, face-to-face education, lecture adaptation, Q&A assistance.

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Authors: Gülcin Büyüközkan, Mehmet Sakir Ersoy

Abstract:

The decision of information technology (IT) outsourcing requires close attention to the evaluation of supplier selection process because the selection decision involves conflicting multiple criteria and is replete with complex decision making problems. Selecting the most appropriate suppliers is considered an important strategic decision that may impact the performance of outsourcing engagements. The objective of this paper is to aid decision makers to evaluate and assess possible IT outsourcing suppliers. An axiomatic design based fuzzy group decision making is adopted to evaluate supplier alternatives. Finally, a case study is given to demonstrate the potential of the methodology. KeywordsIT outsourcing, Supplier selection, Multi-criteria decision making, Axiomatic design, Fuzzy logic.

Keywords: IT outsourcing, Supplier selection, Multi-criteria decision making, Axiomatic design, Fuzzy logic

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Authors: M. S. Annie Christi

Abstract:

Transportation Problem (TP) is based on supply and demand of commodities transported from one source to the different destinations. Usual methods for finding solution of TPs are North-West Corner Rule, Least Cost Method Vogel’s Approximation Method etc. The transportation costs tend to vary at each time. We can use fuzzy numbers which would give solution according to this situation. In this study the Best Candidate Method (BCM) is applied. For ranking Centroid Ranking Technique (CRT) and Robust Ranking Technique have been adopted to transform the fuzzy TP and the above methods are applied to EDWARDS Vacuum Company, Crawley, in West Sussex in the United Kingdom. A Comparative study is also given. We see that the transportation cost can be minimized by the application of CRT under BCM.

Keywords: Best candidates method, centroid ranking technique, robust ranking technique, transportation problem, fuzzy transportation problem.

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Authors: M. G. C. A. Cimino, G. Frosini, B. Lazzerini, F. Marcelloni

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In the last decades, a number of robust fuzzy clustering algorithms have been proposed to partition data sets affected by noise and outliers. Robust fuzzy C-means (robust-FCM) is certainly one of the most known among these algorithms. In robust-FCM, noise is modeled as a separate cluster and is characterized by a prototype that has a constant distance δ from all data points. Distance δ determines the boundary of the noise cluster and therefore is a critical parameter of the algorithm. Though some approaches have been proposed to automatically determine the most suitable δ for the specific application, up to today an efficient and fully satisfactory solution does not exist. The aim of this paper is to propose a novel method to compute the optimal δ based on the analysis of the distribution of the percentage of objects assigned to the noise cluster in repeated executions of the robust-FCM with decreasing values of δ . The extremely encouraging results obtained on some data sets found in the literature are shown and discussed.

Keywords: noise prototype, robust fuzzy clustering, robustfuzzy C-means

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Authors: S.M. Bahri, F.T. Bendimerad

Abstract:

We propose a downlink multiple-input multipleoutput (MIMO) multi-carrier code division multiple access (MCCDMA) system with adaptive beamforming algorithm for smart antennas. The algorithm used in this paper is based on the Least Mean Square (LMS), with pilot channel estimation (PCE) and the zero forcing equalizer (ZFE) in the receiver, requiring reference signal and no knowledge channel. MC-CDMA is studied in a multiple antenna context in order to efficiently exploit robustness against multipath effects and multi-user flexibility of MC-CDMA and channel diversity offered by MIMO systems for radio mobile channels. Computer simulations, considering multi-path Rayleigh Fading Channel, interference inter symbol and interference are presented to verify the performance. Simulation results show that the scheme achieves good performance in a multi-user system.

Keywords: Adaptive Beamforming, LMS Algorithm, MCCDMA, MIMO System, Smart Antenna.

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Authors: Mubarak Alhajri

Abstract:

This paper addresses certain inherent limitations of local priority hysteresis switching logic. Our main result establishes that under persistent excitation assumption, it is possible to relax constraints requiring strict positivity of local priority and hysteresis switching constants. Relaxing these constraints allows the adaptive system to reach optimality which implies the performance improvement. The unconstrained local priority hysteresis switching logic is examined and conditions for global convergence are derived.

Keywords: Adaptive control, convergence, hysteresis constant, hysteresis switching.

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Authors: K. Geetha, P. Thangaraj

Abstract:

Mobile Ad Hoc Networks (MANETs) is a collection of mobile devices forming a communication network without infrastructure. MANET is vulnerable to security threats due to network’s limited security, dynamic topology, scalability and the lack of central management. The Quality of Service (QoS) routing in such networks is limited by network breakage caused by node mobility or nodes energy depletions. The impact of node mobility on trust establishment is considered and its use to propagate trust through a network is investigated in this paper. This work proposes an enhanced Associativity Based Routing (ABR) with Fuzzy based Trust (Fuzzy- ABR) routing protocol for MANET to improve QoS and to mitigate network attacks.

Keywords: Mobile Ad hoc Networks (MANET), Associativity Based Routing (ABR), Fuzzy based Computed Trust.

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