Search results for: Fuzzy random variables

Authors: Jianwei Ma, Diriba Gemechu

Abstract:

In seismic data processing, attenuation of random noise is the basic step to improve quality of data for further application of seismic data in exploration and development in different gas and oil industries. The signal-to-noise ratio of the data also highly determines quality of seismic data. This factor affects the reliability as well as the accuracy of seismic signal during interpretation for different purposes in different companies. To use seismic data for further application and interpretation, we need to improve the signal-to-noise ration while attenuating random noise effectively. To improve the signal-to-noise ration and attenuating seismic random noise by preserving important features and information about seismic signals, we introduce the concept of anisotropic total fractional order denoising algorithm. The anisotropic total fractional order variation model defined in fractional order bounded variation is proposed as a regularization in seismic denoising. The split Bregman algorithm is employed to solve the minimization problem of the anisotropic total fractional order variation model and the corresponding denoising algorithm for the proposed method is derived. We test the effectiveness of theproposed method for synthetic and real seismic data sets and the denoised result is compared with F-X deconvolution and non-local means denoising algorithm.

Keywords: Anisotropic total fractional order variation, fractional order bounded variation, seismic random noise attenuation, Split Bregman Algorithm.

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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: A. Azadeh, Z. Raoofi

Abstract:

Natural gas, as one of the most important sources of energy for many of the industrial and domestic users all over the world, has a complex, huge supply chain which is in need of heavy investments in all the phases of exploration, extraction, production, transportation, storage and distribution. The main purpose of supply chain is to meet customers’ need efficiently and with minimum cost. In this study, with the aim of minimizing economic costs, different levels of natural gas supply chain in the form of a multi-echelon, multi-period fuzzy linear programming have been modeled. In this model, different constraints including constraints on demand satisfaction, capacity, input/output balance and presence/absence of a path have been defined. The obtained results suggest efficiency of the recommended model in optimal allocation and reduction of supply chain costs.

Keywords: Cost Approach, Fuzzy Theory, Linear Programming, Natural Gas Supply Chain.

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Authors: Yuan-Jye Tseng, Yen-Jung Wang

Abstract:

A product development for green logistics model using the fuzzy analytic network process method is presented for evaluating the relationships among the product design, the manufacturing activities, and the green supply chain. In the product development stage, there can be alternative ways to design the detailed components to satisfy the design concept and product requirement. In different design alternative cases, the manufacturing activities can be different. In addition, the manufacturing activities can affect the green supply chain of the components and product. In this research, a fuzzy analytic network process evaluation model is presented for evaluating the criteria in product design, manufacturing activities, and green supply chain. The comparison matrices for evaluating the criteria among the three groups are established. The total relational values between the three groups represent the relationships and effects. In application, the total relational values can be used to evaluate the design alternative cases for decision-making to select a suitable design case and the green supply chain. In this presentation, an example product is illustrated. It shows that the model is useful for integrated evaluation of design and manufacturing and green supply chain for the purpose of product development for green logistics.

Keywords: Supply chain management, green supply chain, product development for logistics, fuzzy analytic network process.

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Authors: Mao Wei

Abstract:

The main aim of this paper is to investigate the exponential stability of the Euler method for a stochastic age-dependent population equations with Poisson random measures. It is proved that the Euler scheme is exponentially stable in mean square sense. An example is given for illustration.

Keywords: Stochastic age-dependent population equations, poisson random measures, numerical solutions, exponential stability.

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Authors: A. K. Al-Othman, F. S. Al-Fares, K. M. EL-Nagger

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This paper presents a new optimization technique based on quantum computing principles to solve a security constrained power system economic dispatch problem (SCED). The proposed technique is a population-based algorithm, which uses some quantum computing elements in coding and evolving groups of potential solutions to reach the optimum following a partially directed random approach. The SCED problem is formulated as a constrained optimization problem in a way that insures a secure-economic system operation. Real Coded Quantum-Inspired Evolution Algorithm (RQIEA) is then applied to solve the constrained optimization formulation. Simulation results of the proposed approach are compared with those reported in literature. The outcome is very encouraging and proves that RQIEA is very applicable for solving security constrained power system economic dispatch problem (SCED).

Keywords: State Estimation, Fuzzy Linear Regression, FuzzyLinear State Estimator (FLSE) and Measurements Uncertainty.

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Authors: Tarik Rashid, B. Q. Huang, M-T. Kechadi, B. Gleeson

Abstract:

this paper presents an auto-regressive network called the Auto-Regressive Multi-Context Recurrent Neural Network (ARMCRN), which forecasts the daily peak load for two large power plant systems. The auto-regressive network is a combination of both recurrent and non-recurrent networks. Weather component variables are the key elements in forecasting because any change in these variables affects the demand of energy load. So the AR-MCRN is used to learn the relationship between past, previous, and future exogenous and endogenous variables. Experimental results show that using the change in weather components and the change that occurred in past load as inputs to the AR-MCRN, rather than the basic weather parameters and past load itself as inputs to the same network, produce higher accuracy of predicted load. Experimental results also show that using exogenous and endogenous variables as inputs is better than using only the exogenous variables as inputs to the network.

Keywords: Daily peak load forecasting, neural networks, recurrent neural networks, auto regressive multi-context neural network.

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Authors: Seyed Sadegh Naseralavi, Najmeh Bemani

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In this paper, different concrete codes including America, New Zealand, Mexico, Italy, India, Canada, Hong Kong, Euro Code and Britain are compared with the Iranian concrete design code. First, by using Adaptive Neuro Fuzzy Inference System (ANFIS), the codes having the most correlation with the Iranian ninth issue of the national regulation are determined. Consequently, two anticipated methods are used for comparing the codes: Artificial Neural Network (ANN) and Multi-variable regression. The results show that ANN performs better. Predicting is done by using only tensile steel ratio and with ignoring the compression steel ratio.

Keywords: Concrete design code, anticipate method, artificial neural network, multi-variable regression, adaptive neuro fuzzy inference system.

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Authors: Samson Henry Dogo, Allan Clark, Elena Kulinskaya

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The objective of meta-analysis is to combine results from several independent studies in order to create generalization and provide evidence base for decision making. But recent studies show that the magnitude of effect size estimates reported in many areas of research significantly changed over time and this can impair the results and conclusions of meta-analysis. A number of sequential methods have been proposed for monitoring the effect size estimates in meta-analysis. However they are based on statistical theory applicable only to fixed effect model (FEM) of meta-analysis. For random-effects model (REM), the analysis incorporates the heterogeneity variance, τ 2 and its estimation create complications. In this paper we study the use of a truncated CUSUM-type test with asymptotically valid critical values for sequential monitoring in REM. Simulation results show that the test does not control the Type I error well, and is not recommended. Further work required to derive an appropriate test in this important area of applications.

Keywords: Meta-analysis, random-effects model, sequential testing, temporal changes in effect sizes.

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Authors: Amid Ranjkesh, Milan Ambrožič, Samo Kralj

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We study the typical domain size and configuration character of a randomly perturbed system exhibiting continuous symmetry breaking. As a model system we use rod-like objects within a cubic lattice interacting via a Lebwohl–Lasher-type interaction. We describe their local direction with a headless unit director field. An example of such systems represents nematic LC or nanotubes. We further introduce impurities of concentration p, which impose the random anisotropy field-type disorder to directors. We study the domain-type pattern of molecules as a function of p, anchoring strength w between a neighboring director and impurity, temperature, history of samples. In simulations we quenched the directors either from the random or homogeneous initial configuration. Our results show that a history of system strongly influences: i) the average domain coherence length; and ii) the range of ordering in the system. In the random case the obtained order is always short ranged (SR). On the contrary, in the homogeneous case, SR is obtained only for strong enough anchoring and large enough concentration p. In other cases, the ordering is either of quasi long range (QLR) or of long range (LR). We further studied memory effects for the random initial configuration. With increasing external ordering field B either QLR or LR is realized.

Keywords: Lebwohl-Lasher model, liquid crystals, disorder, memory effect, orientational order.

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Authors: Insaf Ajili, Malik Mallem, Jean-Yves Didier

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Motion recognition from videos is actually a very complex task due to the high variability of motions. This paper describes the challenges of human motion recognition, especially motion representation step with relevant features. Our descriptor vector is inspired from Laban Movement Analysis method. We propose discriminative features using the Random Forest algorithm in order to remove redundant features and make learning algorithms operate faster and more effectively. We validate our method on MSRC-12 and UTKinect datasets.

Keywords: Human motion recognition, Discriminative LMA features, random forest, features reduction.

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Authors: Amer Ibrahim Falah Al-Omari

Abstract:

In this paper, we suggest new product-type estimators for the population mean of the variable of interest exploiting the first or the third quartile of the auxiliary variable. We obtain mean square error equations and the bias for the estimators. We study the properties of these estimators using simple random sampling (SRS) and ranked set sampling (RSS) methods. It is found that, SRS and RSS produce approximately unbiased estimators of the population mean. However, the RSS estimators are more efficient than those obtained using SRS based on the same number of measured units for all values of the correlation coefficient.

Keywords: Product estimator, auxiliary variable, simple random sampling, extreme ranked set sampling

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Authors: Alexander B. Bichkov, Alla A. Mityureva, Valery V. Smirnov

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In present work are considered the scheme of evaluation the transition probability in quantum system. It is based on path integral representation of transition probability amplitude and its evaluation by means of a saddle point method, applied to the part of integration variables. The whole integration process is reduced to initial value problem solutions of Hamilton equations with a random initial phase point. The scheme is related to the semiclassical initial value representation approaches using great number of trajectories. In contrast to them from total set of generated phase paths only one path for each initial coordinate value is selected in Monte Karlo process.

Keywords: Path integral, saddle point method, semiclassical approximation, transition probability

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Authors: Naiqin Feng, Fang Wang, Yuhui Qiu

Abstract:

A new approach to promote the generalization ability of neural networks is presented. It is based on the point of view of fuzzy theory. This approach is implemented through shrinking or magnifying the input vector, thereby reducing the difference between training set and testing set. It is called “shrinking-magnifying approach" (SMA). At the same time, a new algorithm; α-algorithm is presented to find out the appropriate shrinking-magnifying-factor (SMF) α and obtain better generalization ability of neural networks. Quite a few simulation experiments serve to study the effect of SMA and α-algorithm. The experiment results are discussed in detail, and the function principle of SMA is analyzed in theory. The results of experiments and analyses show that the new approach is not only simpler and easier, but also is very effective to many neural networks and many classification problems. In our experiments, the proportions promoting the generalization ability of neural networks have even reached 90%.

Keywords: Fuzzy theory, generalization, misclassification rate, neural network.

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Authors: Divya Agarwal, Pushpendra S. Bharti

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Autonomous mobile robots (AMR) are expected as smart tools for operations in every automation industry. Path planning and obstacle avoidance is the backbone of AMR as robots have to reach their goal location avoiding obstacles while traversing through optimized path defined according to some criteria such as distance, time or energy. Path planning can be classified into global and local path planning where environmental information is known and unknown/partially known, respectively. A number of sensors are used for data collection. A number of algorithms such as artificial potential field (APF), rapidly exploring random trees (RRT), bidirectional RRT, Fuzzy approach, Purepursuit, A* algorithm, vector field histogram (VFH) and modified local path planning algorithm, etc. have been used in the last three decades for path planning and obstacle avoidance for AMR. This paper makes an attempt to review some of the path planning and obstacle avoidance algorithms used in the field of AMR. The review includes comparative analysis of simulation and mathematical computations of path planning and obstacle avoidance algorithms using MATLAB 2018a. From the review, it could be concluded that different algorithms may complete the same task (i.e. with a different set of instructions) in less or more time, space, effort, etc.

Keywords: Autonomous mobile robots, obstacle avoidance, path planning, and processing time.

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Authors: Poo Bee Tin, Rahmah Ismail, Norasmah Othman

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Globalisation is a phenomenon that cannot be avoided. As globalisation allowed free flow of inputs including labour, it may affect job opportunities for the locals. Therefore, investigate the determinants of labour supply is essential in understanding the structure of labour market in the new era of globalization. The objective of this article is to examine labour supply by taking into account the globalisation effect. The study covers 3885 households in Peninsular Malaysia who are chosen using stratified random sampling. The labour supply model will be the basis for the analysis. The basic labour supply determinants are own wage and non-labour income. However, the extended labour supply model incorporates other variables like spouse wage，number of children and individuals characteristics like education level and age. Besides, the globalization indicator will also be incorporated as another independent variable.

Keywords: globalization, head of households, labour supply, wage

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Authors: Pham Luu Trung Duong, Moonyong Lee

Abstract:

To increase precision and reliability of automatic control systems, we have to take into account of random factors affecting the control system. Thus, operational matrix technique is used for statistical analysis of first order plus time delay system with uniform random parameter. Examples with deterministic and stochastic disturbance are considered to demonstrate the validity of the method. Comparison with Monte Carlo method is made to show the computational effectiveness of the method.

Keywords: First order plus dead-time, Operational matrix, Statistical analysis, Walsh function.

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Authors: A. P. Anvar, T. Dowling, T. Putland, A. M. Anvar, S.Grainger

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This paper presents the application of Intelligent Techniques to the various duties of Intelligent Condition Monitoring Systems (ICMS) for Unmanned Aerial Vehicle (UAV) Robots. These Systems are intended to support these Intelligent Robots in the event of a Fault occurrence. Neural Networks are used for Diagnosis, whilst Fuzzy Logic is intended for Prognosis and Remedy. The ultimate goals of ICMS are to save large losses in financial cost, time and data.

Keywords: Intelligent Techniques, Condition Monitoring Systems, ICMS, Robots, Fault, Unmanned Aerial Vehicle, UAV, Neural Networks, Diagnosis, Fuzzy Logic, Prognosis, Remedy.

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Authors: Z. Ghobadi, Z. Hamidi- Esfahani, M. H. Azizi

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In the present study, the oleaginous fungus Mortierella alpina CBS 754.68 was screened for arachidonic acidproduction using inexpensive agricultural by-products as substrate. Four oilcakes were analysed to choose the best substrate among them. Sunflower oilcake was the most effective substrate for ARA production followed by soybean, colza and olive oilcakes. In the next step, seven variables including substrate particle size, moisture content, time, temperature, yeast extract supply, glucose supply and glutamate supply were surveyed and effective variables for ARA production were determined using a Plackett-Burman screening design. Analysis results showed that time (12 days), substrate particle size (1-1.4 mm) and temperature (20ºC) were the most effective variables for the highest level of ARA production respectively.

Keywords: Arachidonic acid, Mortierella alpine, Solid-statefermentation, Plackett-Burman design

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Authors: P. Saravanan, T. Arunkumar

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Vehicular Adhoc Network (VANET) is a new technology which aims to ensure intelligent inter-vehicle communications, seamless internet connectivity leading to improved road safety, essential alerts, and access to comfort and entertainment. VANET operations are hindered by mobile node’s (vehicles) uncertain mobility. Routing algorithms use metrics to evaluate which path is best for packets to travel. Metrics like path length (hop count), delay, reliability, bandwidth, and load determine optimal route. The proposed scheme exploits link quality, traffic density, and intersections as routing metrics to determine next hop. This study enhances Geographical Routing Protocol (GRP) using fuzzy controllers while rules are optimized with Bee Swarm Optimization (BSO). Simulations results are compared to conventional GRP.

Keywords: Bee Swarm Optimization (BSO), Geographical Routing Protocol (GRP), Vehicular Adhoc Network (VANET).

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Authors: Adi A. Maaita, Hamza A. A. Al_Sewadi

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One of the crucial parameters of digital cryptographic systems is the selection of the keys used and their distribution. The randomness of the keys has a strong impact on the system’s security strength being difficult to be predicted, guessed, reproduced, or discovered by a cryptanalyst. Therefore, adequate key randomness generation is still sought for the benefit of stronger cryptosystems. This paper suggests an algorithm designed to generate and test pseudo random number sequences intended for cryptographic applications. This algorithm is based on mathematically manipulating a publically agreed upon information between sender and receiver over a public channel. This information is used as a seed for performing some mathematical functions in order to generate a sequence of pseudorandom numbers that will be used for encryption/decryption purposes. This manipulation involves permutations and substitutions that fulfill Shannon’s principle of “confusion and diffusion”. ASCII code characters were utilized in the generation process instead of using bit strings initially, which adds more flexibility in testing different seed values. Finally, the obtained results would indicate sound difficulty of guessing keys by attackers.

Keywords: Cryptosystems, Information Security agreement, Key distribution, Random numbers.

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Authors: Halil Ibrahim Demir, Caner Erden, Mumtaz Ipek, Ozer Uygun

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Traditionally, the three important manufacturing functions, which are process planning, scheduling and due-date assignment, are performed separately and sequentially. For couple of decades, hundreds of studies are done on integrated process planning and scheduling problems and numerous researches are performed on scheduling with due date assignment problem, but unfortunately the integration of these three important functions are not adequately addressed. Here, the integration of these three important functions is studied by using genetic, random-genetic hybrid, simulated annealing, random-simulated annealing hybrid and random search techniques. As well, the importance of the integration of these three functions and the power of meta-heuristics and of hybrid heuristics are studied.

Keywords: Process planning, weighted scheduling, weighted due-date assignment, genetic search, simulated annealing, hybrid meta-heuristics.

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Authors: V. Vidučić, T. Brešan Ančić, M. Tomelić Ćurlin

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Prior to quantifying the variables of the information model for using school terminology in Croatia's region of Dalmatia from 1884 to 2014, the most relevant model variables had to be determined: historical circumstances, standard of living, education system, linguistic situation, and media. The research findings show that there was no significant transfer of the 1884 school terms into 1949 usage; likewise, the 1949 school terms were not widely used in 2014. On the other hand, the research revealed that the meaning of school terms changed over the decades. The quantification of the variables will serve as the groundwork for creating an information model for using school terminology in Dalmatia from 1884 to 2014 and for defining direct growth rates in further research.

Keywords: Education system, historical circumstances, linguistic situation, media, school terminology, standard of living.

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Authors: Mohammad Najafi Nobar, Bahareh Pourmehr, Mehdi Hajimirarab

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One of the main processes of supply chain management is supplier selection process which its accurate implementation can dramatically increase company competitiveness. In presented article model developed based on the features of second tiers suppliers and four scenarios are predicted in order to help the decision maker (DM) in making up his/her mind. In addition two tiers of suppliers have been considered as a chain of suppliers. Then the proposed approach is solved by a method combined of concepts of fuzzy set theory (FST) and linear programming (LP) which has been nourished by real data extracted from an engineering design and supplying parts company. At the end results reveal the high importance of considering second tier suppliers features as criteria for selecting the best supplier.

Keywords: Supply Chain Management (SCM), SupplierSelection, Second Tier Supplier, Scenario Planning, Green Factor, Linear Programming, Fuzzy Set Theory

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Authors: Dinesh Acharya U., N. V. Subba Reddy, Krishnamoorthi Makkithaya

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The recognition of handwritten numeral is an important area of research for its applications in post office, banks and other organizations. This paper presents automatic recognition of handwritten Kannada numerals based on structural features. Five different types of features, namely, profile based 10-segment string, water reservoir; vertical and horizontal strokes, end points and average boundary length from the minimal bounding box are used in the recognition of numeral. The effect of each feature and their combination in the numeral classification is analyzed using nearest neighbor classifiers. It is common to combine multiple categories of features into a single feature vector for the classification. Instead, separate classifiers can be used to classify based on each visual feature individually and the final classification can be obtained based on the combination of separate base classification results. One popular approach is to combine the classifier results into a feature vector and leaving the decision to next level classifier. This method is extended to extract a better information, possibility distribution, from the base classifiers in resolving the conflicts among the classification results. Here, we use fuzzy k Nearest Neighbor (fuzzy k-NN) as base classifier for individual feature sets, the results of which together forms the feature vector for the final k Nearest Neighbor (k-NN) classifier. Testing is done, using different features, individually and in combination, on a database containing 1600 samples of different numerals and the results are compared with the results of different existing methods.

Keywords: Fuzzy k Nearest Neighbor, Multiple Classifiers, Numeral Recognition, Structural features.

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Authors: Pradeep Kumar, Abdul Wahid

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Accurate software reliability prediction not only enables developers to improve the quality of software but also provides useful information to help them for planning valuable resources. This paper examines the performance of three well-known data mining techniques (CART, TreeNet and Random Forest) for predicting software reliability. We evaluate and compare the performance of proposed models with Cascade Correlation Neural Network (CCNN) using sixteen empirical databases from the Data and Analysis Center for Software. The goal of our study is to help project managers to concentrate their testing efforts to minimize the software failures in order to improve the reliability of the software systems. Two performance measures, Normalized Root Mean Squared Error (NRMSE) and Mean Absolute Errors (MAE), illustrate that CART model is accurate than the models predicted using Random Forest, TreeNet and CCNN in all datasets used in our study. Finally, we conclude that such methods can help in reliability prediction using real-life failure datasets.

Keywords: Classification, Cascade Correlation Neural Network, Random Forest, Software reliability, TreeNet.

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Authors: N. Zainol, J. Salihon, R. Abdul-Rahman

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Factor analysis was applied to two stages biogas production from banana stem waste allowing a screening of the experimental variables second stage temperature (T), organic loading rates (OLR) and hydraulic retention times (HRT). Biogas production was found to be strongly influenced by all the above experimental variables. Results from factorial analysis have shown that all variables which were HRT, OLR and T have significant effect to biogas production. Increased in HRT and OLR could increased the biogas yield. The performance was tested under the conditions of various T (35oC-60oC), OLR (0.3 g TS/l.d–1.9 gTS/l.d), and HRT (3 d–15 d). Conditions for temperature, OLR and HRT in this study were based on the best range obtained from literature review.

Keywords: Biogas, factor analysis, banana stem waste

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Authors: Mohd Iz'aan Paiz Bin Zamri, Anis Salwa Mohd Khairuddin, Norrima Mokhtar, Rubiyah Yusof

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Effective statistical feature extraction and classification are important in image-based automatic inspection and analysis. An automatic wood species recognition system is designed to perform wood inspection at custom checkpoints to avoid mislabeling of timber which will results to loss of income to the timber industry. The system focuses on analyzing the statistical pores properties of the wood images. This paper proposed a fuzzy-based feature extractor which mimics the experts’ knowledge on wood texture to extract the properties of pores distribution from the wood surface texture. The proposed feature extractor consists of two steps namely pores extraction and fuzzy pores management. The total number of statistical features extracted from each wood image is 38 features. Then, a backpropagation neural network is used to classify the wood species based on the statistical features. A comprehensive set of experiments on a database composed of 5200 macroscopic images from 52 tropical wood species was used to evaluate the performance of the proposed feature extractor. The advantage of the proposed feature extraction technique is that it mimics the experts’ interpretation on wood texture which allows human involvement when analyzing the wood texture. Experimental results show the efficiency of the proposed method.

Keywords: Classification, fuzzy, inspection system, image analysis.

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Authors: E. Bárcena-Martín, S. Pérez-Moreno

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This paper explores the extent of the gap in poverty rates between immigrant and native households in Spanish regions and assess to what extent regional differences in individual and contextual characteristics can explain the divergences in such a gap. By using multilevel techniques and European Union Survey on Income and Living Conditions, we estimate immigrant households experiments an increase of 76 per cent in the odds of being poor compared with a native one when we control by individual variables. In relation to regional differences in the risk of poverty, regionallevel variables have higher effect in the reduction of these differences than individual variables.

Keywords: Immigration, Multilevel Analysis, Poverty, Spanish Regions

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