Search results for: Extreme Value theory

Authors: Dany Ng Cheong Vee, Preethee Nunkoo Gonpot, Noor-Ul-Hacq Sookia

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In this paper, we consider the application of Extreme Value Theory as a risk measurement tool. The Value at Risk, for a set of indices, from six Stock Exchanges of Frontier markets is calculated using the Peaks over Threshold method and the performance of the model index-wise is evaluated using coverage tests and loss functions. Our results show that “fattailedness” alone of the data is not enough to justify the use of EVT as a VaR approach. The structure of the returns dynamics is also a determining factor. This approach works fine in markets which have had extremes occurring in the past thus making the model capable of coping with extremes coming up (Colombo, Tunisia and Zagreb Stock Exchanges). On the other hand, we find that indices with lower past than present volatility fail to adequately deal with future extremes (Mauritius and Kazakhstan). We also conclude that using EVT alone produces quite static VaR figures not reflecting the actual dynamics of the data.

Keywords: Extreme Value theory, Financial Crisis 2008, Frontier Markets, Value at Risk.

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Authors: Y. Laaroussi, Z. Guennoun, A. Amar

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Modeling and forecasting dynamics of rainfall occurrences constitute one of the major topics, which have been largely treated by statisticians, hydrologists, climatologists and many other groups of scientists. In the same issue, we propose, in the present paper, a new hybrid method, which combines Extreme Values and fractal theories. We illustrate the use of our methodology for transformed Emberger Index series, constructed basing on data recorded in Oujda (Morocco). The index is treated at first by Peaks Over Threshold (POT) approach, to identify excess observations over an optimal threshold u. In the second step, we consider the resulting excess as a fractal object included in one dimensional space of time. We identify fractal dimension by the box counting. We discuss the prospect descriptions of rainfall data sets under Generalized Pareto Distribution, assured by Extreme Values Theory (EVT). We show that, despite of the appropriateness of return periods given by POT approach, the introduction of fractal dimension provides accurate interpretation results, which can ameliorate apprehension of rainfall occurrences.

Keywords: Extreme values theory, Fractals dimensions, Peaks Over Threshold, Rainfall occurrences.

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Authors: Mohamad Mahdavi, Mojtaba Mahdavi

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This paper tries to represent a new method for computing the reliability of a system which is arranged in series or parallel model. In this method we estimate life distribution function of whole structure using the asymptotic Extreme Value (EV) distribution of Type I, or Gumbel theory. We use EV distribution in minimal mode, for estimate the life distribution function of series structure and maximal mode for parallel system. All parameters also are estimated by Moments method. Reliability function and failure (hazard) rate and p-th percentile point of each function are determined. Other important indexes such as Mean Time to Failure (MTTF), Mean Time to repair (MTTR), for non-repairable and renewal systems in both of series and parallel structure will be computed.

Keywords: Reliability, extreme value, parallel, series, lifedistribution

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Authors: Avellino I. Mondlane, Karin Hansson, Oliver Popov

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This paper discusses the application of extreme events distribution taking the Limpopo River Basin at Xai-Xai station, in Mozambique, as a case analysis. We analyze the extreme value concepts, namely Gumbel, Fréchet, Weibull and Generalized Extreme Value Distributions and then extrapolate the original data to 1000, 5000 and 10000 figures for further simulations and we compare their outcomes based on these three main distributions.

Keywords: Catastrophes, extreme event, disasters, mathematical models, simulation.

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Authors: Husna Hasan, Norfatin Salam, Mohd Bakri Adam

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Extreme temperature of several stations in Malaysia is modelled by fitting the monthly maximum to the Generalized Extreme Value (GEV) distribution. The Mann-Kendall (MK) test suggests a non-stationary model. Two models are considered for stations with trend and the Likelihood Ratio test is used to determine the best-fitting model. Results show that half of the stations favour a model which is linear for the location parameters. The return level is the level of events (maximum temperature) which is expected to be exceeded once, on average, in a given number of years, is obtained.

Keywords: Extreme temperature, extreme value, return level.

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Authors: Mahmoud I. Syam, Kamarulzaman Ibrahim, Amer I. Al-Omari

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Stratified double extreme ranked set sampling (SDERSS) method is introduced and considered for estimating the population mean. The SDERSS is compared with the simple random sampling (SRS), stratified ranked set sampling (SRSS) and stratified simple set sampling (SSRS). It is shown that the SDERSS estimator is an unbiased of the population mean and more efficient than the estimators using SRS, SRSS and SSRS when the underlying distribution of the variable of interest is symmetric or asymmetric.

Keywords: Double extreme ranked set sampling, Extreme ranked set sampling, Ranked set sampling, Stratified double extreme ranked set sampling.

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Authors: Ayman M. Mottaleb

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In conducting a case study to analyze the status-quo of the extremists’ dominance in Egypt, the author of this paper uses qualitative research method to analyze the evolution of extreme Islamist groups in Egypt. In conducting this qualitative research, the author of this paper intends to use several lenses to understand the rise and the evolution of the hegemony of extremist groups, such as the Muslim Brotherhood and other groups in Egypt. Therefore, unless he intends to show an important nexus between the Egyptian groups and their sister-groups in other countries, he will intentionally exclude analyzing extreme Islamism of non-Egyptian origins. This case study relies on the moral disengagement theory to shed light on the ideological evolution of extremism in Egypt. The goal of this case study is to help in understanding extreme-Islamism adverse to the mainstream Islam; therefore, understanding the concept here should help in preventing similar groups from threatening the international community.

Keywords: Extremism, International Terrorism, Islamists, Middle East, Muslim Brotherhood.

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Authors: Siti Aisyah Zakaria, Nor Azrita Mohd Amin, Noor Fadhilah Ahmad Radi, Nasrul Hamidin

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Higher ground-level ozone (GLO) concentration adversely affects human health, vegetations as well as activities in the ecosystem. In Malaysia, most of the analysis on GLO concentration are carried out using the average value of GLO concentration, which refers to the centre of distribution to make a prediction or estimation. However, analysis which focuses on the higher value or extreme value in GLO concentration is rarely explored. Hence, the objective of this study is to classify the tail behaviour of GLO using generalized extreme value (GEV) distribution estimation the return level using the corresponding modelling (Gumbel, Weibull, and Frechet) of GEV distribution. The results show that Weibull distribution which is also known as short tail distribution and considered as having less extreme behaviour is the best-fitted distribution for four selected air monitoring stations in Peninsular Malaysia, namely Larkin, Pelabuhan Kelang, Shah Alam, and Tanjung Malim; while Gumbel distribution which is considered as a medium tail distribution is the best-fitted distribution for Nilai station. The return level of GLO concentration in Shah Alam station is comparatively higher than other stations. Overall, return levels increase with increasing return periods but the increment depends on the type of the tail of GEV distribution’s tail. We conduct this study by using maximum likelihood estimation (MLE) method to estimate the parameters at four selected stations in Peninsular Malaysia. Next, the validation for the fitted block maxima series to GEV distribution is performed using probability plot, quantile plot and likelihood ratio test. Profile likelihood confidence interval is tested to verify the type of GEV distribution. These results are important as a guide for early notification on future extreme ozone events.

Keywords: Extreme value theory, generalized extreme value distribution, ground-level ozone, return level.

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Authors: Zhenyu Zhang, Qingbin Gao

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Low-resolution digital encoder (LRDE) is commonly adopted as a position sensor in low-cost and resource-constraint applications. Traditionally, a digital encoder is modeled as a quantizer without considering the initial position of the LRDE. However, it cannot be applied to extreme LRDE for which stroke of angular motion is only a few times of resolution of the encoder. Besides, the actual angular motion is substantially distorted by this extreme LRDE so that the encoder reading does not faithfully represent the actual angular motion. This paper presents a modeling method for extreme LRDE by taking into account the initial position of the LRDE. For a control system with sinusoidal reference signal and extreme LRDE, this paper analyzes the characteristics of angular motion. Specifically, two descriptors of sinusoidal angular motion are studied, which essentially sheds light on the actual angular motion from extreme LRDE.

Keywords: Low resolution digital encoder, resource-constraint control system, sinusoidal reference signal, servo motion control.

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Authors: Karim Hamidi Machekposhti, Hossein Sedghi

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This study was designed to find the best stochastic model (using of time series analysis) for annual extreme streamflow (peak and maximum streamflow) of Karkheh River at Iran. The Auto-regressive Integrated Moving Average (ARIMA) model used to simulate these series and forecast those in future. For the analysis, annual extreme streamflow data of Jelogir Majin station (above of Karkheh dam reservoir) for the years 1958–2005 were used. A visual inspection of the time plot gives a little increasing trend; therefore, series is not stationary. The stationarity observed in Auto-Correlation Function (ACF) and Partial Auto-Correlation Function (PACF) plots of annual extreme streamflow was removed using first order differencing (d=1) in order to the development of the ARIMA model. Interestingly, the ARIMA(4,1,1) model developed was found to be most suitable for simulating annual extreme streamflow for Karkheh River. The model was found to be appropriate to forecast ten years of annual extreme streamflow and assist decision makers to establish priorities for water demand. The Statistical Analysis System (SAS) and Statistical Package for the Social Sciences (SPSS) codes were used to determinate of the best model for this series.

Keywords: Stochastic models, ARIMA, extreme streamflow, Karkheh River.

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Authors: Shruti Taksali

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This paper focuses on the analysis of Nanoptenna for extreme fast communication. The Nanoptenna is basically a nano antenna designed for communication at optical range of frequencies. Since, this range of frequencies includes the visible spectrum of the light, so there is a high possibility of the data transfer at high rates and extreme fast communication (XFC). The shape chosen for the analysis is a bow tie structure due to its various characteristics of electric field enhancement.

Keywords: Nanoptenna, communication, optical range, XFC.

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Authors: Leon Pan

Abstract:

The first programming course within post-secondary education has long been recognized as a challenging endeavor for both educators and students alike. Historically, these courses have exhibited high failure rates and a notable number of dropouts. Instructors often lament students' lack of effort on their coursework, and students often express frustration that the teaching methods employed are not effective. Drawing inspiration from the successful principles of Extreme Programming, this study introduces an approach—the Extremes-based teaching model—aimed at enhancing the teaching of introductory programming courses. To empirically determine the effectiveness of the model, a comparison was made between a section taught using the extreme-based model and another utilizing traditional teaching methods. Notably, the extreme-based teaching class required students to work collaboratively on projects, while also demanding continuous assessment and performance enhancement within groups. This paper details the application of the extreme-based model within the post-secondary online classroom context and presents the compelling results that emphasize its effectiveness in advancing the teaching and learning experiences. The extreme-based model led to a significant increase of 13.46 points in the weighted total average and a commendable 10% reduction in the failure rate.

Keywords: Extreme-based teaching model, innovative pedagogical methods, project-based learning, team-based learning.

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Authors: Jing-Gang Xie

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The research, in this case, considers the integration of the Quantum Field Theory and the General Relativity Theory. As two successful models in explaining behaviors of particles, they are incompatible since they work at different masses and scales of energy, with the evidence that regards the description of black holes and universe formation. It is so considering previous efforts in merging the two theories, including the likes of the String Theory, Quantum Gravity models, and others. In a bid to prove an actionable experiment, the paper’s approach starts with the derivations of the existing theories at present. It goes on to test the derivations by applying the same initial assumptions, coupled with several deviations. The resulting equations get similar results to those of classical Newton model, quantum mechanics, and general relativity as long as conditions are normal. However, outcomes are different when conditions are extreme, specifically with no breakdowns even for less than Schwarzschild radius, or at Planck length cases. Even so, it proves the possibilities of integrating the two theories.

Keywords: General relativity theory, particles, photons, quantum gravity model, gravitational frequency shift.

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Authors: Sung-Hae Jun, Kyung-Whan Oh

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Statistical learning theory was developed by Vapnik. It is a learning theory based on Vapnik-Chervonenkis dimension. It also has been used in learning models as good analytical tools. In general, a learning theory has had several problems. Some of them are local optima and over-fitting problems. As well, statistical learning theory has same problems because the kernel type, kernel parameters, and regularization constant C are determined subjectively by the art of researchers. So, we propose an evolutionary statistical learning theory to settle the problems of original statistical learning theory. Combining evolutionary computing into statistical learning theory, our theory is constructed. We verify improved performances of an evolutionary statistical learning theory using data sets from KDD cup.

Keywords: Evolutionary computing, Local optima, Over-fitting, Statistical learning theory

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Authors: Mohammed Sharif, Donald Burn

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Large scale climate signals and their teleconnections can influence hydro-meteorological variables on a local scale. Several extreme flow and timing measures, including high flow and low flow measures, from 62 hydrometric stations in Canada are investigated to detect possible linkages with several large scale climate indices. The streamflow data used in this study are derived from the Canadian Reference Hydrometric Basin Network and are characterized by relatively pristine and stable land-use conditions with a minimum of 40 years of record. A composite analysis approach was used to identify linkages between extreme flow and timing measures and climate indices. The approach involves determining the 10 highest and 10 lowest values of various climate indices from the data record. Extreme flow and timing measures for each station were examined for the years associated with the 10 largest values and the years associated with the 10 smallest values. In each case, a re-sampling approach was applied to determine if the 10 values of extreme flow measures differed significantly from the series mean. Results indicate that several stations are impacted by the large scale climate indices considered in this study. The results allow the determination of any relationship between stations that exhibit a statistically significant trend and stations for which the extreme measures exhibit a linkage with the climate indices.

Keywords: flood analysis, low-flow events, climate change, trend analysis, Canada

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Authors: Mahmoud Roushdi, Hany Mostafa, Khaled Kheireldin

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Sinai Peninsula and Suez Canal Corridor are promising and important economic regions in Egypt due to the unique location and development opportunities. Thus, the climate change impacts should be assessed over the mentioned area. Accordingly, this paper aims to assess the climate extreme indices in through the last 35 year over Sinai Peninsula and Suez Canal Corridor in addition to predict the climate extreme indices up to 2100. Present and future climate indices were analyzed with using different RCP scenarios 4.5 and 8.5 from 2010 until 2100 for Sinai Peninsula and Suez Canal Corridor. Furthermore, both CanESM and HadGEM2 global circulation models were used. The results indicate that the number of summer days is predicted to increase, on the other hand the frost days is predicted to decrease. Moreover, it is noted a slight positive trend for the percentile of wet and extremely days R95p and R99p for RCP4.5 and negative trend for RCP8.5.

Keywords: Climate change, extreme indices, RCP, Sinai Peninsula.

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Authors: Chul Kwak, Oh-Wook Kwon

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In this paper, an extreme learning machine with an automatic segmentation algorithm is applied to heart disorder classification by heart sound signals. From continuous heart sound signals, the starting points of the first (S1) and the second heart pulses (S2) are extracted and corrected by utilizing an inter-pulse histogram. From the corrected pulse positions, a single period of heart sound signals is extracted and converted to a feature vector including the mel-scaled filter bank energy coefficients and the envelope coefficients of uniform-sized sub-segments. An extreme learning machine is used to classify the feature vector. In our cardiac disorder classification and detection experiments with 9 cardiac disorder categories, the proposed method shows significantly better performance than multi-layer perceptron, support vector machine, and hidden Markov model; it achieves the classification accuracy of 81.6% and the detection accuracy of 96.9%.

Keywords: Heart sound classification, extreme learning machine

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Authors: Nkongho Ayuketang Arreyndip, Ebobenow Joseph

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In this paper, temperature extremes are forecast by employing the block maxima method of the Generalized extreme value(GEV) distribution to analyse temperature data from the Cameroon Development Corporation (C.D.C). By considering two sets of data (Raw data and simulated data) and two (stationary and non-stationary) models of the GEV distribution, return levels analysis is carried out and it was found that in the stationary model, the return values are constant over time with the raw data while in the simulated data, the return values show an increasing trend but with an upper bound. In the non-stationary model, the return levels of both the raw data and simulated data show an increasing trend but with an upper bound. This clearly shows that temperatures in the tropics even-though show a sign of increasing in the future, there is a maximum temperature at which there is no exceedence. The results of this paper are very vital in Agricultural and Environmental research.

Keywords: Return level, Generalized extreme value (GEV), Meteorology, Forecasting.

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Authors: Pauline E. Ngo-Henha

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Existing turnover intention theories are reviewed in this paper. This review was conducted with the help of the search keyword “turnover intention theories” in Google Scholar during the month of July 2017. These theories include: The Theory of Organizational Equilibrium (TOE), Social Exchange Theory, Job Embeddedness Theory, Herzberg’s Two-Factor Theory, the Resource-Based View, Equity Theory, Human Capital Theory, and the Expectancy Theory. One of the limitations of this review paper is that data were only collected from Google Scholar where many papers were sometimes not freely accessible. However, this paper attempts to contribute to the research in clarifying the distinction between theories and models in the context of turnover intention.

Keywords: Job embeddedness theory, theory of organizational equilibrium (TOE), Herzberg’s two-factor theory, turnover intention theories, theories and models.

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Authors: Nkongho Ayuketang Arreyndip, Ebobenow Joseph

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In this paper, to model a real life wind turbine, a probabilistic approach is proposed to model the dynamics of the blade elements of a small axial wind turbine under extreme stochastic wind speeds conditions. It was found that the power and the torque probability density functions even-dough decreases at these extreme wind speeds but are not infinite. Moreover, we also fund that it is possible to stabilize the power coefficient (stabilizing the output power)above rated wind speeds by turning some control parameters. This method helps to explain the effect of turbulence on the quality and quantity of the harness power and aerodynamic torque.

Keywords: Probability, Stochastic, Probability density function, Turbulence.

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Authors: Milan Rippel, Petr Teply

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This paper focuses on operational risk measurement techniques and on economic capital estimation methods. A data sample of operational losses provided by an anonymous Central European bank is analyzed using several approaches. Loss Distribution Approach and scenario analysis method are considered. Custom plausible loss events defined in a particular scenario are merged with the original data sample and their impact on capital estimates and on the financial institution is evaluated. Two main questions are assessed – What is the most appropriate statistical method to measure and model operational loss data distribution? and What is the impact of hypothetical plausible events on the financial institution? The g&h distribution was evaluated to be the most suitable one for operational risk modeling. The method based on the combination of historical loss events modeling and scenario analysis provides reasonable capital estimates and allows for the measurement of the impact of extreme events on banking operations.

Keywords: operational risk, scenario analysis, economic capital, loss distribution approach, extreme value theory, stress testing

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Authors: Gabi Nehme

Abstract:

The relationship between different types of Molybdenum disulfide greases under extreme pressure loading and different speed situations have been studied using Design of Experiment (DOE) under 1200rpm steady state rotational speed and cyclic frequencies between 2400 and 1200rpm using a Plint machine software to set up the different rotational speed situations.  Research described here is aimed at providing good friction and wear performance while optimizing cyclic frequencies and MoS2 concentration due to the recent concern about grease behavior in extreme pressure applications. Extreme load of 785 Newton was used in conjunction with different cyclic frequencies (2400rpm -3.75min, 1200rpm -7.5min, 2400rpm -3.75min, 1200rpm -7.5min), to examine lithium based grease with and without MoS2 for equal number of revolutions, and a total run of 36000 revolutions; then compared to 1200rpm steady speed for the same total number of revolutions. 4 Ball wear tester was utilized to run large number of experiments randomly selected by the DOE software. The grease was combined with fine grade MoS2 or technical grade then heated to 750C and the wear scar width was collected at the end of each test. DOE model validation results verify that the data were very significant and can be applied to a wide range of extreme pressure applications. Based on simulation results and Scanning Electron images (SEM), it has been found that wear was largely dependent on the cyclic frequency condition. It is believed that technical grade MoS2 greases under faster cyclic speeds perform better and provides antiwear film that can resist extreme pressure loadings. Figures showed reduced wear scars width and improved frictional values.

 

Keywords: MoS2 grease, wear, friction, extreme load, cyclic frequencies, aircraft grade bearing.

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Authors: Ajay Gupta, Arvind Bhardwaj, Arun Kanda

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Dr Eliyahu Goldratt has done the pioneering work in the development of Theory of Constraints. Since then, many more researchers around the globe are working to enhance this body of knowledge. In this paper, an attempt has been made to compile the salient features of this theory from the work done by Goldratt and other researchers. This paper will provide a good starting point to the potential researchers interested to work in Theory of Constraints. The paper will also help the practicing managers by clarifying their concepts on the theory and will facilitate its successful implementation in their working areas.

Keywords: Drum-Buffer-Rope, Goldratt, ProductionScheduling, Theory of Constraints.

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Authors: Karim Hamidi Machekposhti, Hossein Sedghi

Abstract:

The probability distributions are the best method for forecasting of extreme hydrologic phenomena such as rainfall and flood flows. In this research, in order to determine suitable probability distribution for estimating of annual extreme rainfall and flood flows (discharge) series with different return periods, precipitation with 40 and discharge with 58 years time period had been collected from Karkheh River at Iran. After homogeneity and adequacy tests, data have been analyzed by Stormwater Management and Design Aid (SMADA) software and residual sum of squares (R.S.S). The best probability distribution was Log Pearson Type III with R.S.S value (145.91) and value (13.67) for peak discharge and Log Pearson Type III with R.S.S values (141.08) and (8.95) for maximum discharge in Jelogir Majin and Pole Zal stations, respectively. The best distribution for maximum precipitation in Jelogir Majin and Pole Zal stations was Log Pearson Type III distribution with R.S.S values (1.74&1.90) and then Pearson Type III distribution with R.S.S values (1.53&1.69). Overall, the Log Pearson Type III distributions are acceptable distribution types for representing statistics of extreme hydrologic phenomena in Karkheh River at Iran with the Pearson Type III distribution as a potential alternative.

Keywords: Karkheh river, log pearson type III, probability distribution, residual sum of squares.

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Authors: Rado Flajs

Abstract:

In the present paper the extreme shear stresses with the corresponding planes are established using the freely available computer tools like the Gnuplot, Sage, R, Python and Octave. In order to support these freely available computer tools, their strong symbolical and graphical abilities are illustrated. The nature of the stationary points obtained by the Method of Lagrangian Multipliers can be determined using freely available computer symbolical tools like Sage. The characters of the stationary points can be explained in the easiest way using freely available computer graphical tools like Gnuplot, Sage, R, Python and Octave. The presented figures improve the understanding of the problem and the obtained solutions for the majority of students of civil or mechanical engineering.

Keywords: engineering, continuum mechanics, extreme shear stresses, Gnuplot, Sage, R, Python, Octave

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Authors: C. Y. Chen

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As the global climate changes, the threat from landslides and debris flows increases. Learning how a watershed initiates landslides under abnormal rainfall conditions and predicting landslide magnitude and frequency distribution is thus important. Landslides show a power-law distribution in the frequency-area distribution. The distribution curve shows an exponent gradient 1.0 in the Sandpile model test. Will the landslide frequency-area statistics show a distribution similar to the Sandpile model under extreme rainfall conditions? The purpose of the study is to identify the extreme rainfall-induced landslide frequency-area distribution in the Laonong River Basin in southern Taiwan. Results of the analysis show that a lower gradient of landslide frequency-area distribution could be attributed to the transportation and deposition of debris flow areas that are included in the landslide area.

Keywords: Landslide, power-law distribution, GIS.

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Authors: Th. Arti Devi, Parthasarthi Choudhury

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Extreme rainfall frequency analysis for Meteorological Sub-Division 4 of India was analyzed using L-moments approach. Serial Correlation and Mann Kendall tests were conducted for checking serially independent and stationarity of the observations. The discordancy measure for the sites was conducted to detect the discordant sites. The regional homogeneity was tested by comparing with 500 generated homogeneous regions using a 4 parameter Kappa distribution. The best fit distribution was selected based on Z^DIST statistics and L-moments ratio diagram from the five extreme value distributions GPD, GLO, GEV, P3 and LP3. The LN3 distribution was selected and regional rainfall frequency relationship was established using index-rainfall procedure. A regional mean rainfall relationship was developed using multiple linear regression with latitude and longitude of the sites as variables.

Keywords: L-moments, ZDIST statistics, Serial correlation, Mann Kendall test.

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Authors: Chung-Hung Tsai

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Global environmental changes lead to increased frequency and scale of natural disaster, Taiwan is under the influence of global warming and extreme weather. Therefore, the vulnerability was increased and variability and complexity of disasters is relatively enhanced. The purpose of this study is to consider the source and magnitude of hazard characteristics on the tourism industry. Using modern risk management concepts, integration of related domestic and international basic research, this goes beyond the Taiwan typhoon disaster risk assessment model and evaluation of loss. This loss evaluation index system considers the impact of extreme weather, in particular heavy rain on the tourism industry in Taiwan. Consider the extreme climate of the compound impact of disaster for the tourism industry; we try to make multi-hazard risk assessment model, strategies and suggestions. Related risk analysis results are expected to provide government department, the tourism industry asset owners, insurance companies and banking include tourist disaster risk necessary information to help its tourism industry for effective natural disaster risk management.

Keywords: Tourism industry, extreme weather, multi-hazard, vulnerability analysis, loss exceeding probability, risk management.

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Authors: Haiyan Wang

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Constuctivism learning theory lays emphasis on the learners' active learning, such as learning initiative, sociality and context. By analyzing the relationship between constructivism learning theory and learner autonomy, this paper explores how to cultivate learners' learner autonomy under the guidance of constructivism learning theory.

Keywords: Constructivism learning theory, learner autonomy, relationship, cultivation.

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Authors: Serkan Narlı, Ahmet Z. Ozcelik

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The theory of rough sets is generalized by using a filter. The filter is induced by binary relations and it is used to generalize the basic rough set concepts. The knowledge representations and processing of binary relations in the style of rough set theory are investigated.

Keywords: Rough set, fuzzy set, membership function, knowledge representation and processing, information theory

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