Search results for: fuzzy clustering

Authors: Carla Layana Luis Diambra

Abstract:

Microarrays technique allows the simultaneous measurements of the expression levels of thousands of mRNAs. By mining this data one can identify the dynamics of the gene expression time series. By recourse of principal component analysis, we uncover the circadian rhythmic patterns underlying the gene expression profiles from Cyanobacterium Synechocystis. We applied PCA to reduce the dimensionality of the data set. Examination of the components also provides insight into the underlying factors measured in the experiments. Our results suggest that all rhythmic content of data can be reduced to three main components.

Keywords: circadian rhythms, clustering, gene expression, PCA.

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Authors: Mihai Caramihai Ana A Chirvase, Irina Severin

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Bioprocesses are appreciated as difficult to control because their dynamic behavior is highly nonlinear and time varying, in particular, when they are operating in fed batch mode. The research objective of this study was to develop an appropriate control method for a complex bioprocess and to implement it on a laboratory plant. Hence, an intelligent control structure has been designed in order to produce biomass and to maximize the specific growth rate.

Keywords: Fed batch bioprocess, mass-balance model, fuzzy control.

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Authors: E. Y. Igde, S. Aydogan, F. E. Boran, D. Akay

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Patent data have an increasingly important role in economic growth, innovation, technical advantages and business strategies and even in countries competitions. Analyzing of patent data is crucial since patents cover large part of all technological information of the world. In this paper, we have used the linguistic summarization technique to prove the validity of the hypotheses related to patent data stated in the literature.

Keywords: Data mining, fuzzy sets, linguistic summarization, patent data.

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Authors: Claudiu N.Musat

Abstract:

Due to the constant increase in the volume of information available to applications in fields varying from medical diagnosis to web search engines, accurate support of similarity becomes an important task. This is also the case of spam filtering techniques where the similarities between the known and incoming messages are the fundaments of making the spam/not spam decision. We present a novel approach to filtering based solely on layout, whose goal is not only to correctly identify spam, but also warn about major emerging threats. We propose a mathematical formulation of the email message layout and based on it we elaborate an algorithm to separate different types of emails and find the new, numerically relevant spam types.

Keywords: Clustering, layout, k-means, spam.

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Authors: Farhad F. Yusifov

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With the explosive growth of data available on the Internet, personalization of this information space become a necessity. At present time with the rapid increasing popularity of the WWW, Websites are playing a crucial role to convey knowledge and information to the end users. Discovering hidden and meaningful information about Web users usage patterns is critical to determine effective marketing strategies to optimize the Web server usage for accommodating future growth. The task of mining useful information becomes more challenging when the Web traffic volume is enormous and keeps on growing. In this paper, we propose a intelligent model to discover and analyze useful knowledge from the available Web log data.

Keywords: Clustering, Self organizing map, Web log files, Web traffic.

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Authors: Mazin Z. Othman, Maan M. Shaker, Mohammed F. Abdullah

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This study introduces a new method for detecting, sorting, and localizing spikes from multiunit EEG recordings. The method combines the wavelet transform, which localizes distinctive spike features, with Super-Paramagnetic Clustering (SPC) algorithm, which allows automatic classification of the data without assumptions such as low variance or Gaussian distributions. Moreover, the method is capable of setting amplitude thresholds for spike detection. The method makes use of several real EEG data sets, and accordingly the spikes are detected, clustered and their times were detected.

Keywords: EEG time localizations, EEG spike detection, superparamagnetic algorithm, wavelet transform.

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Authors: Benjamin C. Agwah, Paulinus C. Eze

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Antilock braking system (ABS) is one of the important contributions by the automobile industry, designed to ensure road safety in such way that vehicles are kept steerable and stable when during emergency braking. This paper presents a wheel slip-based intelligent controller with variable zero lag compensation for ABS. It is required to achieve a very fast perfect wheel slip tracking during hard braking condition and eliminate chattering with improved transient and steady state performance, while shortening the stopping distance using effective braking torque less than maximum allowable torque to bring a braking vehicle to a stop. The dynamic of a vehicle braking with a braking velocity of 30 ms⁻¹ on a straight line was determined and modelled in MATLAB/Simulink environment to represent a conventional ABS system without a controller. Simulation results indicated that system without a controller was not able to track desired wheel slip and the stopping distance was 135.2 m. Hence, an intelligent control based on fuzzy logic controller (FLC) was designed with a variable zero lag compensator (VZLC) added to enhance the performance of FLC control variable by eliminating steady state error, provide improve bandwidth to eliminate the effect of high frequency noise such as chattering during braking. The simulation results showed that FLC-VZLC provided fast tracking of desired wheel slip, eliminated chattering, and reduced stopping distance by 70.5% (39.92 m), 63.3% (49.59 m), 57.6% (57.35 m) and 50% (69.13 m) on dry, wet, cobblestone and snow road surface conditions respectively. Generally, the proposed system used effective braking torque that is less than the maximum allowable braking torque to achieve efficient wheel slip tracking and overall robust control performance on different road surfaces.

Keywords: ABS, Fuzzy Logic Controller, Variable Zero Lag Compensator, Wheel Slip Tracking.

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Authors: Hemanth KumarA.R, Sudhakara G., Satyanarayana B.S.

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The Cluster Dimension of a network is defined as, which is the minimum cardinality of a subset S of the set of nodes having the property that for any two distinct nodes x and y, there exist the node Si, s2 (need not be distinct) in S such that ld(x,s1) — d(y, s1)1 > 1 and d(x,s2) < d(x,$) for all s E S — {s2}. In this paper, strictly non overlap¬ping clusters are constructed. The concept of LandMarks for Unique Addressing and Clustering (LMUAC) routing scheme is developed. With the help of LMUAC routing scheme, It is shown that path length (upper bound)PLN,d < PLD, Maximum memory space requirement for the networkMSLmuAc(Az) < MSEmuAc < MSH3L < MSric and Maximum Link utilization factor MLLMUAC(i=3) < MLLMUAC(z03) < M Lc

Keywords: Metric dimension, Cluster dimension, Cluster.

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Authors: Wann-Ming Wey, Yi-Chih Huang

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Proper maintenance and preservation of significant cultural heritages or historic buildings is necessary. It can not only enhance environmental benefits and a sense of community, but also preserve a city's history and people’s memory. It allows the next generation to be able to get a glimpse of our past, and achieve the goal of sustainable preserved cultural assets. However, the management of maintenance work has not been appropriate for many designated heritages or historic buildings so far. The planning and implementation of the reuse has yet to have a breakthrough specification. It leads the heritages to a mere formality of being “reserved”, instead of the real meaning of “conservation”. For the restoration and preservation of cultural heritages study issues, it is very important due to the consideration of historical significance, symbolism, and economic benefits effects. However, the decision makers such as the officials from public sector they often encounter which heritage should be prioritized to be restored first under the available limited budgets. Only very few techniques are available today to determine the appropriately restoration priorities for the diverse historical heritages, perhaps because of a lack of systematized decision-making aids been proposed before. In the past, the discussions of management and maintenance towards cultural assets were limited to the selection of reuse alternatives instead of the allocation of resources. In view of this, this research will adopt some integrated research methods to solve the existing problems that decision-makers might encounter when allocating resources in the management and maintenance of heritages and historic buildings.

The purpose of this study is to develop a sustainable decision making model for local governments to resolve these problems. We propose an alternative decision support model to prioritize restoration needs within the limited budgets. The model is constructed based on fuzzy Delphi, fuzzy analysis network process (FANP) and goal programming (GP) methods. In order to avoid misallocate resources; this research proposes a precise procedure that can take multi-stakeholders views, limited costs and resources into consideration. Also, the combination of many factors and goals has been taken into account to find the highest priority and feasible solution results. To illustrate the approach we propose in this research, seven cultural heritages in Taipei city as one example has been used as an empirical study, and the results are in depth analyzed to explain the application of our proposed approach.

Keywords: Cultural Heritage, Historic Buildings, Priority Evaluation, Multi-Criteria Decision Making, Goal Programming, Fuzzy Analytic Network Process, Resource Allocation.

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Authors: S. Barbosa, M. Pinto, J. A. Almeida, E. Carvalho, C. Diamantino

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The aim of this work was to test a methodology able to generate spatial-temporal maps that can synthesize simultaneously the trends of distinct hydrochemical indicators in an old radium-uranium tailings dam deposit. Multidimensionality reduction derived from principal component analysis and subsequent data aggregation derived from clustering analysis allow to identify distinct hydrochemical behavioral profiles and generate synthetic evolutionary hydrochemical maps.

Keywords: Contamination plume migration, K-means of PCA scores, groundwater and mine water monitoring, spatial-temporal hydrochemical trends.

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Authors: P. S. Bhowmik, D. V. Rajan, S. P. Bose

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The load flow study in a power system constitutes a study of paramount importance. The study reveals the electrical performance and power flows (real and reactive) for specified condition when the system is operating under steady state. This paper gives an overview of different techniques used for load flow study under different specified conditions.

Keywords: Load Flow Studies, Y-matrix and Z-matrix iteration, Newton-Raphson method, Fast Decoupled method, Fuzzy logic, Artificial Neural Network.

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Authors: Dmitry K. Shaytan, Georgy D. Laptev

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In our research we aimed to test a managerial approach for the fuzzy front end (FFE) of innovation by creating controlled experiment/ business case in a breakthrough innovation development. The experiment was in the sport industry and covered all aspects of the customer discovery stage from ideation to prototyping followed by patent application. In the paper we describe and analyze mile stones, tasks, management challenges, decisions made to create the break through innovation, evaluate overall managerial efficiency that was at the considered FFE stage. We set managerial outcome of the FFE stage as a valid product concept in hand. In our paper we introduce hypothetical construct “Q-factor” that helps us in the experiment to distinguish quality of FFE outcomes. The experiment simulated for entrepreneur the FFE of innovation and put on his shoulders responsibility for the outcome of valid product concept. While developing managerial approach to reach the outcome there was a decision to look on product concept from the cognitive psychology and cognitive science point of view. This view helped us to develop the profile of a person whose projection (mental representation) of a new product could optimize for a manager or entrepreneur FFE activities. In the experiment this profile was tested to develop breakthrough innovation for swimmers. Following the managerial approach the product concept was created to help swimmers to feel/sense water. The working prototype was developed to estimate the product concept validity and value added effect for customers. Based on feedback from coachers and swimmers there were strong positive effect that gave high value for customers, and for the experiment – the valid product concept being developed by proposed managerial approach for the FFE. In conclusions there is a suggestion of managerial approach that was derived from experiment.

Keywords: Concept development, concept testing, customer discovery, entrepreneurship, entrepreneurial management, idea generation, idea screening, startup management.

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Authors: W. Chattinnawat

Abstract:

Consider a mass production of HDD arms where hundreds of CNC machines are used to manufacturer the HDD arms. According to an overwhelming number of machines and models of arm, construction of separate control chart for monitoring each HDD arm model by each machine is not feasible. This research proposed a strategy to optimize the SPC management on shop floor. The procedure started from identifying the clusters of the machine with similar manufacturing performance using clustering technique. The three way control chart ( I - MR - R ) is then applied to each clustered group of machine. This proposed research has advantageous to the manufacturer in terms of not only better performance of the SPC but also the quality management paradigm.

Keywords: Three way control chart. I - MR - R , between/within variation, HDD arm.

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Authors: Mou-Yuan Liao, Chien-Wei Wu, Chien-Hua Lin

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Process capability index Cpk is the most widely used index in making managerial decisions since it provides bounds on the process yield for normally distributed processes. However, existent methods for assessing process performance which constructed by statistical inference may unfortunately lead to fine results, because uncertainties exist in most real-world applications. Thus, this study adopts fuzzy inference to deal with testing of Cpk . A brief score is obtained for assessing a supplier’s process instead of a severe evaluation.

Keywords: Process capability analysis, quality control.

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Authors: Si-Gwan Kim

Abstract:

Small-size and low-power sensors with sensing, signal processing and wireless communication capabilities is suitable for the wireless sensor networks. Due to the limited resources and battery constraints, complex routing algorithms used for the ad-hoc networks cannot be employed in sensor networks. In this paper, we propose node-disjoint multi-path hexagon-based routing algorithms in wireless sensor networks. We suggest the details of the algorithm and compare it with other works. Simulation results show that the proposed scheme achieves better performance in terms of efficiency and message delivery ratio.

Keywords: Clustering, multi-path, routing protocol, sensor network.

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Authors: Dejan Stantic, Jun Jo

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There have been significant improvements in automatic voice recognition technology. However, existing systems still face difficulties, particularly when used by non-native speakers with accents. In this paper we address a problem of identifying the English accented speech of speakers from different backgrounds. Once an accent is identified the speech recognition software can utilise training set from appropriate accent and therefore improve the efficiency and accuracy of the speech recognition system. We introduced the Q factor, which is defined by the sum of relationships between frequencies of the formants. Four different accents were considered and experimented for this research. A scoring method was introduced in order to effectively analyse accents. The proposed concept indicates that the accent could be identified by analysing their formants.

Keywords: Accent Identification, Formants, Q Factor.

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Authors: Darby Tien-Hao Chang, Guan-Yu Shiu, You-Jie Sun

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Various cis-regulatory module (CRM) predictors have been proposed in the last decade. Several well-established CRM predictors adopted different categories of prediction strategies, including window clustering, probabilistic modeling and phylogenetic footprinting. Appropriate integration of them has a potential to achieve high quality CRM prediction. This study analyzed four existing CRM predictors (ClusterBuster, MSCAN, CisModule and MultiModule) to seek a predictor combination that delivers a higher accuracy than individual CRM predictors. 465 CRMs across 140 Drosophila melanogaster genes from the RED fly database were used to evaluate the integrated CRM predictor proposed in this study. The results show that four predictor combinations achieved superior performance than the best individual CRM predictor.

Keywords: Cis-regulatory module, transcription factor binding site.

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Authors: Sung Ho Ha, Seong Hyeon Joo, Hyun U. Pae

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In terms of total online audience, newspapers are the most successful form of online content to date. The online audience for newspapers continues to demand higher-quality services, including personalized news services. News providers should be able to offer suitable users appropriate content. In this paper, a news article recommender system is suggested based on a user-s preference when he or she visits an Internet news site and reads the published articles. This system helps raise the user-s satisfaction, increase customer loyalty toward the content provider.

Keywords: Content classification, content recommendation, customer profiling, documents clustering.

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Authors: Yuji Mizuno, Hiroshi Mabuchi

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Initial values of reference vectors have significant influence on recognition accuracy in LVQ. There are several existing techniques, such as SOM and k-means, for setting initial values of reference vectors, each of which has provided some positive results. However, those results are not sufficient for the improvement of recognition accuracy. This study proposes an ACO-used method for initializing reference vectors with an aim to achieve recognition accuracy higher than those obtained through conventional methods. Moreover, we will demonstrate the effectiveness of the proposed method by applying it to the wine data and English vowel data and comparing its results with those of conventional methods.

Keywords: Clustering, LVQ, ACO, SOM, k-means.

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Authors: Satyendra Nath Mandal, J. Pal Choudhury, Dilip De, S. R. Bhadra Chaudhuri

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The selection for plantation of a particular type of mustard plant depending on its productivity (pod yield) at the stage of maturity. The growth of mustard plant dependent on some parameters of that plant, these are shoot length, number of leaves, number of roots and roots length etc. As the plant is growing, some leaves may be fall down and some new leaves may come, so it can not gives the idea to develop the relationship with the seeds weight at mature stage of that plant. It is not possible to find the number of roots and root length of mustard plant at growing stage that will be harmful of this plant as roots goes deeper to deeper inside the land. Only the value of shoot length which increases in course of time can be measured at different time instances. Weather parameters are maximum and minimum humidity, rain fall, maximum and minimum temperature may effect the growth of the plant. The parameters of pollution, water, soil, distance and crop management may be dominant factors of growth of plant and its productivity. Considering all parameters, the growth of the plant is very uncertain, fuzzy environment can be considered for the prediction of shoot length at maturity of the plant. Fuzzification plays a greater role for fuzzification of data, which is based on certain membership functions. Here an effort has been made to fuzzify the original data based on gaussian function, triangular function, s-function, Trapezoidal and L –function. After that all fuzzified data are defuzzified to get normal form. Finally the error analysis (calculation of forecasting error and average error) indicates the membership function appropriate for fuzzification of data and use to predict the shoot length at maturity. The result is also verified using residual (Absolute Residual, Maximum of Absolute Residual, Mean Absolute Residual, Mean of Mean Absolute Residual, Median of Absolute Residual and Standard Deviation) analysis.

Keywords: Fuzzification, defuzzification, gaussian function, triangular function, trapezoidal function, s-function, , membership function, residual analysis.

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Authors: R. Matousek, S. Lang, P. Minar, P. Pivonka

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In the control theory one attempts to find a controller that provides the best possible performance with respect to some given measures of performance. There are many sorts of controllers e.g. a typical PID controller, LQR controller, Fuzzy controller etc. In the paper will be introduced polynomial controller with novel tuning method which is based on the special pole placement encoding scheme and optimization by Genetic Algorithms (GA). The examples will show the performance of the novel designed polynomial controller with comparison to common PID controller.

Keywords: Evolutionary design, Genetic algorithms, PID controller, Pole placement, Polynomial controller

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Authors: Sofia Matoug, Amr Abdel-Dayem

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This paper presents a comprehensive survey of recent research studies to segment and classify brain MR (magnetic resonance) images in order to detect significant changes to brain ventricles. The paper also presents a general framework for detecting regions that atrophy, which can help neurologists in detecting and staging Alzheimer. Furthermore, a prototype was implemented to segment brain MR images in order to extract the region of interest (ROI) and then, a classifier was employed to differentiate between normal and abnormal brain tissues. Experimental results show that the proposed scheme can provide a reliable second opinion that neurologists can benefit from.

Keywords: Alzheimer, brain images, classification techniques, Magnetic Resonance Images, MRI.

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Authors: O. S. Ebrahim, K. O. Shawky, M. A. Badr, P. K. Jain

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This paper proposes an intelligent, supervisory, hysteresis liquid-level control with three-state energy saving mode (ESM) for induction motor (IM) in fluid transportation system (FTS) including storage tank. The IM pump drive comprises a modified star/delta switch and hydromantic coupler. Three-state ESM is defined, along with the normal running, and named analog to the computer’s ESMs as follows: Sleeping mode in which the motor runs at no load with delta stator connection, hibernate mode in which the motor runs at no load with a star connection, and motor shutdown is the third energy saver mode. Considering the motor’s thermal capacity used (TCU) and grid-compatible tariff structure, a logic flow-chart is synthesized to select the motor state at no-load for best energetic cost reduction. Fuzzy-logic (FL) based availability assessment is designed and deployed on cloud, in order to provide mobilized service for the star/delta switch and highly reliable contactors. Moreover, an artificial neural network (ANN) state estimator, based on the recurrent architecture, is constructed and learned in order to provide fault-tolerant capability for the supervisory controller. Sequential test of Wald is used for sensor fault detection. Theoretical analysis, preliminary experimental testing and computer simulations are performed to demonstrate the validity and effectiveness of the proposed control system in terms of reliability, power quality and operational cost reduction with a motivation of power factor correction.

Keywords: Artificial Neural Network, ANN, Contactor Health Assessment, Energy Saving Mode, Induction Machine, IM, Supervisory Control, Fluid Transportation, Fuzzy Logic, FL, cloud computing, pumped storage.

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Authors: Charline David, Alexandre Blondin Massé, Arnaud Zinflou

Abstract:

We present a multiple equation time series approach for the short-term load forecasting applied to the electrical power load consumption for the whole Quebec province, in Canada. More precisely, we take into account three meteorological variables — temperature, cloudiness and wind speed —, and we use meteorological measurements taken at different locations on the territory. Our final model shows an average MAPE score of 1.79% over an 8-years dataset.

Keywords: Short-term load forecasting, special days, time series, multiple equations, parallelization, clustering.

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Authors: M. Jarocka

Abstract:

The paper contains a review of the literature in terms of the critical analysis of methodologies of university ranking systems. Furthermore, the initiatives supported by the European Commission (U-Map, U-Multirank) and CHE Ranking are described. Special attention is paid to the tendencies in the development of ranking systems. According to the author, the ranking organizations should abandon the classic form of ranking, namely a hierarchical ordering of universities from “the best" to “the worse". In the empirical part of this paper, using one of the method of cluster analysis called k-means clustering, the author presents university classifications of the top universities from the Shanghai Jiao Tong University-s (SJTU) Academic Ranking of World Universities (ARWU).

Keywords: Classification, cluster analysis, ranking, university.

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Authors: Bing-Fei Wu, Yen-Lin Chen, Chung-Cheng Chiu

Abstract:

In this study, a new criterion for determining the number of classes an image should be segmented is proposed. This criterion is based on discriminant analysis for measuring the separability among the segmented classes of pixels. Based on the new discriminant criterion, two algorithms for recursively segmenting the image into determined number of classes are proposed. The proposed methods can automatically and correctly segment objects with various illuminations into separated images for further processing. Experiments on the extraction of text strings from complex document images demonstrate the effectiveness of the proposed methods.1

Keywords: image segmentation, multilevel thresholding, clustering, discriminant analysis

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Authors: Younis Jabarzadeh, Rahim Sarvari, Negar Ahmadi Alghalandis

Abstract:

Entrepreneurship at both individual and organizational level is one of the most driving forces in economic development and leads to growth and competition, job generation and social development. Especially in developing countries, the role of entrepreneurship in economic and social prosperity is more emphasized. But the effect of global economic development on the environment is undeniable, especially in negative ways, and there is a need to rethink current business models and the way entrepreneurs act to introduce new businesses to address and embed environmental issues in order to achieve sustainable development. In this paper, green or sustainable entrepreneurship is addressed in Iran to identify challenges and barriers entrepreneurs in the economic and social sectors face in developing green business solutions. Sustainable or green entrepreneurship has been gaining interest among scholars in recent years and addressing its challenges and barriers need much more attention to fill the gap in the literature and facilitate the way those entrepreneurs are pursuing. This research comprised of two main phases: qualitative and quantitative. At qualitative phase, after a thorough literature review, fuzzy Delphi method is utilized to verify those challenges and barriers by gathering a panel of experts and surveying them. In this phase, several other contextually related factors were added to the list of identified barriers and challenges mentioned in the literature. Then, at the quantitative phase, Interpretive Structural Modeling is applied to construct a network of interactions among those barriers identified at the previous phase. Again, a panel of subject matter experts comprised of academic and industry experts was surveyed. The results of this study can be used by policymakers in both the public and industry sector, to introduce more systematic solutions to eliminate those barriers and help entrepreneurs overcome challenges of sustainable entrepreneurship. It also contributes to the literature as the first research in this type which deals with the barriers of sustainable entrepreneurship and explores their interaction.

Keywords: Green entrepreneurship, barriers, Fuzzy Delphi Method, interpretive structural modeling.

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Authors: Sylvia Encheva

Abstract:

Students in high education are presented with new terms and concepts in nearly every lecture they attend. Many of them prefer Web-based self-tests for evaluation of their concepts understanding since they can use those tests independently of tutors- working hours and thus avoid the necessity of being in a particular place at a particular time. There is a large number of multiple-choice tests in almost every subject designed to contribute to higher level learning or discover misconceptions. Every single test provides immediate feedback to a student about the outcome of that test. In some cases a supporting system displays an overall score in case a test is taken several times by a student. What we still find missing is how to secure delivering of personalized feedback to a user while taking into consideration the user-s progress. The present work is motivated to throw some light on that question.

Keywords: Clustering, rough sets, many valued logic, predictions

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Authors: K. D. Mroczek

Abstract:

In the study presented institutional context is discussed in terms of companies’ entry mode choice. In contrary to many previous analyses, instead of using one or two aggregated variables, a set of eleven determinants is used to establish equity and non-equity internationalization friendly conditions. Based on secondary data, 140 countries are analyzed and grouped into clusters revealing similar framework. The range of the economies explored is wide as it covers all regions distinguished by The World Bank. The results can prove a useful alternative for operationalization of institutional variables in further research concerning entry modes or strategic management in international markets.

Keywords: Clustering, entry mode choice, institutional environment, transaction costs.

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Authors: S. Sarumathi, N. Shanthi, S. Vidhya

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In the present world, predicting rainfall is considered to be an essential and also a challenging task. Normally, the climate and rainfall are presumed to have non-linear as well as intricate phenomena. For predicting accurate rainfall, we necessitate advanced computer modeling and simulation. When there is an enhanced understanding of the spatial and temporal distribution of precipitation then it becomes enrichment to applications such as hydrologic, climatic and ecological. Conversely, there may be some kind of challenges occur in the community due to some application which results in the absence of consistent precipitation observation in remote and also emerging region. This survey paper provides a multifarious collection of methodologies which are epitomized by various researchers for predicting the rainfall. It also gives information about some technique to forecast rainfall, which is appropriate to all methods like numerical, traditional and statistical.

Keywords: Satellite Image, Segmentation, Feature Extraction, Classification, Clustering, Precipitation Estimation.

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