Search results for: Neutrosophic set theory
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 1593

Search results for: Neutrosophic set theory

723 Persistence of Termination for Term Rewriting Systems with Ordered Sorts

Authors: Munehiro Iwami

Abstract:

A property is persistent if for any many-sorted term rewriting system , has the property if and only if term rewriting system , which results from by omitting its sort information, has the property. Zantema showed that termination is persistent for term rewriting systems without collapsing or duplicating rules. In this paper, we show that the Zantema's result can be extended to term rewriting systems on ordered sorts, i.e., termination is persistent for term rewriting systems on ordered sorts without collapsing, decreasing or duplicating rules. Furthermore we give the example as application of this result. Also we obtain that completeness is persistent for this class of term rewriting systems.

Keywords: Theory of computing, Model-based reasoning, term rewriting system, termination

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722 A Comparison of Grey Model and Fuzzy Predictive Model for Time Series

Authors: A. I. Dounis, P. Tiropanis, D. Tseles, G. Nikolaou, G. P. Syrcos

Abstract:

The prediction of meteorological parameters at a meteorological station is an interesting and open problem. A firstorder linear dynamic model GM(1,1) is the main component of the grey system theory. The grey model requires only a few previous data points in order to make a real-time forecast. In this paper, we consider the daily average ambient temperature as a time series and the grey model GM(1,1) applied to local prediction (short-term prediction) of the temperature. In the same case study we use a fuzzy predictive model for global prediction. We conclude the paper with a comparison between local and global prediction schemes.

Keywords: Fuzzy predictive model, grey model, local andglobal prediction, meteorological forecasting, time series.

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721 Sfard’s Commognitive Framework as a Method of Discourse Analysis in Mathematics

Authors: Dong-Joong Kim, Sangho Choi, Woong Lim

Abstract:

This paper discusses Sfard’s commognitive approach and provides an empirical study as an example to illustrate the theory as method. Traditionally, research in mathematics education focused on the acquisition of mathematical knowledge and the didactic process of knowledge transfer. Through attending to a distinctive form of language in mathematics, as well as mathematics as a discursive subject, alternative views of making meaning in mathematics have emerged; these views are therefore “critical,” as in critical discourse analysis. The commognitive discourse analysis method has the potential to bring more clarity to our understanding of students’ mathematical thinking and the process through which students are socialized into school mathematics.

Keywords: Commognitive framework, discourse analysis, mathematical discourse, mathematics education.

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720 Factors Affecting General Practitioners’ Transfer of Specialized Self-Care Knowledge to Patients

Authors: Weidong Xia, Malgorzata Kolotylo, Xuan Tan

Abstract:

This study examines the key factors that influence general practitioners’ learning and transfer of specialized arthritis knowledge and self-care techniques to patients during normal patient visits. Drawing on the theory of planed behavior and using matched survey data collected from general practitioners before and after training sessions provided by specialized orthopedic physicians, the study suggests that the general practitioner’s intention to use and transfer learned knowledge was influenced mainly by intrinsic motivation, organizational learning culture and absorptive capacity, but was not influenced by extrinsic motivation. The results provide both theoretical and practical implications.

Keywords: Empirical study, healthcare knowledge management, patient self-care, physician knowledge transfer.

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719 Novel Approach to Design of a Class-EJ Power Amplifier Using High Power Technology

Authors: F. Rahmani, F. Razaghian, A. R. Kashaninia

Abstract:

This article proposes a new method for application in communication circuit systems that increase efficiency, PAE, output power and gain in the circuit. The proposed method is based on a combination of switching class-E and class-J and has been termed class-EJ. This method was investigated using both theory and simulation to confirm ∼72% PAE and output power of >39dBm. The combination and design of the proposed power amplifier accrues gain of over 15dB in the 2.9 to 3.5GHz frequency bandwidth. This circuit was designed using MOSFET and high power transistors. The loadand source-pull method achieved the best input and output networks using lumped elements. The proposed technique was investigated for fundamental and second harmonics having desirable amplitudes for the output signal.

Keywords: Power Amplifier (PA), GaN HEMT, Class-J and Class-E, High Efficiency.

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718 Do Cultural Differences in Successful ERP Implementations Exist?

Authors: Jaideep Motwani, Asli Yagmur Akbulut

Abstract:

Using a methodology grounded in business process change theory, we investigate the critical success factors that affect ERP implementation success in United States and India. Specifically, we examine the ERP implementation at two case study companies, one in each country. Our findings suggest that certain factors that affect the success of ERP implementations are not culturally bound, whereas some critical success factors depend on the national culture of the country in which the system is being implemented. We believe that the understanding of these critical success factors will deepen the understanding of ERP implementations and will help avoid implementation mistakes, thereby increasing the rate of success in culturally different contexts. Implications of the findings and future research directions for both academicians and practitioners are also discussed.

Keywords: Critical Success Factors, Culture, Enterprise Resource Planning Systems, India, United States

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717 Research and Design on a Portable Intravehicular Ultrasonic Leak Detector for Manned Spacecraft

Authors: Yan Rongxin, Sun Wei, Li Weidan

Abstract:

Based on the acoustics cascade sound theory, the mechanism of air leak sound producing, transmitting and signal detecting has been analyzed. A formula of the sound power, leak size and air pressure in the spacecraft has been built, and the relationship between leak sound pressure and receiving direction and distance has been studied. The center frequency in millimeter diameter leak is more than 20 kHz. The situation of air leaking from spacecraft to space has been simulated and an experiment of different leak size and testing distance and direction has been done. The sound pressure is in direct proportion to the cosine of the angle of leak to sensor. The portable ultrasonic leak detector has been developed, whose minimal leak rate is 10-1 Pa·m3/s, the testing radius is longer than 20 mm, the mass is less than 1.0 kg, and the electric power is less than 2.2 W.

Keywords: Leak detection, manned spacecraft, ultrasonic, sound transmitting.

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716 Novel Delay-Dependent Stability Criteria for Uncertain Discrete-Time Stochastic Neural Networks with Time-Varying Delays

Authors: Mengzhuo Luo, Shouming Zhong

Abstract:

This paper investigates the problem of exponential stability for a class of uncertain discrete-time stochastic neural network with time-varying delays. By constructing a suitable Lyapunov-Krasovskii functional, combining the stochastic stability theory, the free-weighting matrix method, a delay-dependent exponential stability criteria is obtained in term of LMIs. Compared with some previous results, the new conditions obtain in this paper are less conservative. Finally, two numerical examples are exploited to show the usefulness of the results derived.

Keywords: Delay-dependent stability, Neural networks, Time varying delay, Linear matrix inequality (LMI).

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715 Exponential Stability of Uncertain Takagi-Sugeno Fuzzy Hopfield Neural Networks with Time Delays

Authors: Meng Hu, Lili Wang

Abstract:

In this paper, based on linear matrix inequality (LMI), by using Lyapunov functional theory, the exponential stability criterion is obtained for a class of uncertain Takagi-Sugeno fuzzy Hopfield neural networks (TSFHNNs) with time delays. Here we choose a generalized Lyapunov functional and introduce a parameterized model transformation with free weighting matrices to it, these techniques lead to generalized and less conservative stability condition that guarantee the wide stability region. Finally, an example is given to illustrate our results by using MATLAB LMI toolbox.

Keywords: Hopfield neural network, linear matrix inequality, exponential stability, time delay, T-S fuzzy model.

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714 Investigation about Structural and Optical Properties of Bulk and Thin Film of 1H-CaAlSi by Density Functional Method

Authors: M. Babaeipour, M. Vejdanihemmat

Abstract:

Optical properties of bulk and thin film of 1H-CaAlSi for two directions (1,0,0) and (0,0,1) were studied. The calculations are carried out by Density Functional Theory (DFT) method using full potential. GGA approximation was used to calculate exchange-correlation energy. The calculations are performed by WIEN2k package. The results showed that the absorption edge is shifted backward 0.82eV in the thin film than the bulk for both directions. The static values of the real part of dielectric function for four cases were obtained. The static values of the refractive index for four cases are calculated too. The reflectivity graphs have shown an intensive difference between the reflectivity of the thin film and the bulk in the ultraviolet region.

Keywords: 1H-CaAlSi, absorption, bulk, optical, thin film.

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713 An Institutional Analysis of IFRS Adoption in Poor Jurisdictions

Authors: C. F. Pricope

Abstract:

The last two decades witnessed a movement towards harmonization of international financial reporting standards (IFRS) throughout the global economy. This investigation seeks to identify the factors that could explain the adoption of IFRS by poor jurisdictions. While there has been a considerable amount of literature published on the effects and key drivers of IFRS adoption in both developed and developing countries, little attention has been paid to jurisdictions with less developed capital markets and low income levels exclusively. Drawing upon the Institutional Isomorphism theory and analyzing a sample of 45 poor jurisdictions between 2008 and 2013, the study empirically shows that poor jurisdictions are driven by legitimacy concerns rather than by economic reasoning to adopt an international accounting perspective. This in turn has implications for the IASB, as it should seek to influence institutional pressures within a particular jurisdiction in order to promote IFRS adoption.

Keywords: IFRS Adoption, isomorphism, poor jurisdictions, accounting harmonization.

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712 Marangoni Convection in a Fluid Saturated Porous Layer with a Deformable Free Surface

Authors: Nor Fadzillah Mohd Mokhtar, Norihan Md Arifin, Roslinda Nazar, Fudziah Ismail, MohamedSuleiman

Abstract:

The stability analysis of Marangoni convection in porous media with a deformable upper free surface is investigated. The linear stability theory and the normal mode analysis are applied and the resulting eigenvalue problem is solved exactly. The Darcy law and the Brinkman model are used to describe the flow in the porous medium heated from below. The effect of the Crispation number, Bond number and the Biot number are analyzed for the stability of the system. It is found that a decrease in the Crispation number and an increase in the Bond number delay the onset of convection in porous media. In addition, the system becomes more stable when the Biot number is increases and the Daeff number is decreases.

Keywords: Deformable, Marangoni, Porous, Stability.

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711 Simulation of Activity Stream inside Energy Social Business Environment using Assemblage Theory and Simplicial Complex Tool

Authors: Eddie Soulier, Philippe Calvez, Florie Bugeaud, Francis Rousseaux, Jacky Legrand

Abstract:

Social, mobility and information aggregation inside business environment need to converge to reach the next step of collaboration to enhance interaction and innovation. The following article is based on the “Assemblage" concept seen as a framework to formalize new user interfaces and applications. The area of research is the Energy Social Business Environment, especially the Energy Smart Grids, which are considered as functional and technical foundations of the revolution of the Energy Sector of tomorrow. The assemblages are modelized by means of mereology and simplicial complexes. Its objective is to offer new central attention and decision-making tools to end-users.

Keywords: Activity Streams, Assemblage, Energy Social Business Environment, Simplicial Complex, Smart Grid

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710 Ads on Social Issues: A Tool for Improving Critical Thinking Skills in a Foreign Language Classroom

Authors: Fonseca Jully, Chia Maribel, Rodríguez Ilba

Abstract:

This paper is a qualitative research report. A group of students form a public university in a small town in Colombia participated in this study which aimed at describing to what extend the use of social ads, published on the internet, helped to develop their critical thinking skills. Students’ productions, field notes, video recordings and direct observation were the instruments and techniques used by the researches in order to gather the data which was analyzed under the principles of grounded theory and triangulation. The implementation of social ads into the classroom evidenced a noticeable improvement in students’ ability to interpret and argue social issues, as well as, their self-improvement in oral and written production in English, as a foreign language.

Keywords: Ads, critical argumentation, critical thinking, social issues.

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709 Wavelet and K-L Seperability Based Feature Extraction Method for Functional Data Classification

Authors: Jun Wan, Zehua Chen, Yingwu Chen, Zhidong Bai

Abstract:

This paper proposes a novel feature extraction method, based on Discrete Wavelet Transform (DWT) and K-L Seperability (KLS), for the classification of Functional Data (FD). This method combines the decorrelation and reduction property of DWT and the additive independence property of KLS, which is helpful to extraction classification features of FD. It is an advanced approach of the popular wavelet based shrinkage method for functional data reduction and classification. A theory analysis is given in the paper to prove the consistent convergence property, and a simulation study is also done to compare the proposed method with the former shrinkage ones. The experiment results show that this method has advantages in improving classification efficiency, precision and robustness.

Keywords: classification, functional data, feature extraction, K-Lseperability, wavelet.

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708 A Simple Approach of Three phase Distribution System Modeling for Power Flow Calculations

Authors: J. B. V. Subrahmanyam, C. Radhakrishna

Abstract:

This paper presents a simple three phase power flow method for solution of three-phase unbalanced radial distribution system (RDN) with voltage dependent loads. It solves a simple algebraic recursive expression of voltage magnitude, and all the data are stored in vector form. The algorithm uses basic principles of circuit theory and can be easily understood. Mutual coupling between the phases has been included in the mathematical model. The proposed algorithm has been tested with several unbalanced radial distribution networks and the results are presented in the article. 8- bus and IEEE 13 bus unbalanced radial distribution system results are in agreements with the literature and show that the proposed model is valid and reliable.

Keywords: radial distribution networks, load flow, circuitmodel, three-phase four-wire, unbalance.

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707 Radar Task Schedulers based on Multiple Queue

Authors: María I. Jiménez, Alberto Izquierdo, Juan J. Villacorta, Lara del Val, Mariano Raboso

Abstract:

There are very complex communication systems, as the multifunction radar, MFAR (Multi-Function Array Radar), where functions are integrated all together, and simultaneously are performed the classic functions of tracking and surveillance, as all the functions related to the communication, countermeasures, and calibration. All these functions are divided into the tasks to execute. The task scheduler is a key element of the radar, since it does the planning and distribution of energy and time resources to be shared and used by all tasks. This paper presents schedulers based on the use of multiple queue. Several schedulers have been designed and studied, and it has been made a comparative analysis of different performed schedulers. The tests and experiments have been done by means of system software simulation. Finally a suitable set of radar characteristics has been selected to evaluate the behavior of the task scheduler working.

Keywords: Queue Theory, Radar, Scheduler, Task.

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706 Analysis of Distribution of Thrust, Torque and Efficiency of a Constant Chord, Constant Pitch C.R.P. Fan by H.E.S. Method

Authors: Morteza Abbaszadeh, Parvin Nikpoorparizi, Mina Shahrooz

Abstract:

For the first time since 1940 and presentation of theodorson-s theory, distribution of thrust, torque and efficiency along the blade of a counter rotating propeller axial fan was studied with a novel method in this research. A constant chord, constant pitch symmetric fan was investigated with Reynolds Stress Turbulence method in this project and H.E.S. method was utilized to obtain distribution profiles from C.F.D. tests outcome. C.F.D. test results were validated by estimation from Playlic-s analytical method. Final results proved ability of H.E.S. method to obtain distribution profiles from C.F.D test results and demonstrated interesting facts about effects of solidity and differences between distributions in front and rear section.

Keywords: C.F.D Test, Counter Rotating Propeller, H.E.S. Method, R.S.M. Method

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705 Autonomous Virtual Agent Navigation in Virtual Environments

Authors: Jafreezal Jaafar, Eric McKenzie

Abstract:

This paper presents a solution for the behavioural animation of autonomous virtual agent navigation in virtual environments. We focus on using Dempster-Shafer-s Theory of Evidence in developing visual sensor for virtual agent. The role of the visual sensor is to capture the information about the virtual environment or identifie which part of an obstacle can be seen from the position of the virtual agent. This information is require for vitual agent to coordinate navigation in virtual environment. The virual agent uses fuzzy controller as a navigation system and Fuzzy α - level for the action selection method. The result clearly demonstrates the path produced is reasonably smooth even though there is some sharp turn and also still not diverted too far from the potential shortest path. This had indicated the benefit of our method, where more reliable and accurate paths produced during navigation task.

Keywords: Agent, Navigation, Demster Shafer, Fuzzy Logic.

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704 Knowledge Sharing Behaviour among Academic Staff at a Public Higher Education Institution in Malaysia

Authors: Noor Asilah Nordin, Normala Daud, Wan Ummi Kalsom Meor Osman

Abstract:

This study applied Theory of Planned Behaviour (TPB) to explain the knowledge sharing behaviour among academic staff at a Public Higher Education Institution (HEI) in Malaysia. The main objectives of this study are; to identify the components that influence knowledge sharing behaviour and to determine the levels of knowledge sharing behaviour among academic staff. A total of 200 respondents were participated in answering questionnaires. The findings of this study revealed that level of perceiving and implementing knowledge sharing behaviour among academic staff at a Public HEI in Malaysia exist but not openly or strongly practiced. The findings were discussed and recommendations for the future research were also addressed.

Keywords: Attitude, Knowledge Sharing Behaviour, Perceived Behavioural Control, Subjective Norm.

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703 An Approach to Control Design for Nonlinear Systems via Two-stage Formal Linearization and Two-type LQ Controls

Authors: Kazuo Komatsu, Hitoshi Takata

Abstract:

In this paper we consider a nonlinear control design for nonlinear systems by using two-stage formal linearization and twotype LQ controls. The ordinary LQ control is designed on almost linear region around the steady state point. On the other region, another control is derived as follows. This derivation is based on coordinate transformation twice with respect to linearization functions which are defined by polynomials. The linearized systems can be made up by using Taylor expansion considered up to the higher order. To the resulting formal linear system, the LQ control theory is applied to obtain another LQ control. Finally these two-type LQ controls are smoothly united to form a single nonlinear control. Numerical experiments indicate that this control show remarkable performances for a nonlinear system.

Keywords: Formal Linearization, LQ Control, Nonlinear Control, Taylor Expansion, Zero Function.

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702 Temperature Field Study of Brake Disc in a Belt Conveyor Brake

Authors: Hou Youfu, Wang Daoming, Meng Qingrui

Abstract:

To reveal the temperature field distribution of disc brake in downward belt conveyor, mathematical models of heat transfer for disc brake were established combined with heat transfer theory. Then, the simulation process was stated in detail and the temperature field of disc brake under conditions of dynamic speed and dynamic braking torque was numerically simulated by using ANSYS software. Finally the distribution and variation laws of temperature field in the braking process were analyzed. Results indicate that the maximum surface temperature occurs at a time before the brake end and there exist large temperature gradients in both radial and axial directions, while it is relatively small in the circumferential direction.

Keywords: Downward belt conveyor, Disc brake, Temperature field, Numerical simulation.

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701 The Relationship between Internal Corporate Social Responsibility and Organizational Commitment within the Banking Sector in Jordan

Authors: Al-bdour, A. Ali., Ellisha Nasruddin., Soh Keng Lin

Abstract:

This study attempts to investigate the relationship between internal CSR practices and organizational commitment based on the social exchange theory (SET). Specifically, we examine the impact of five dimensions of internal CSR practices on organizational commitment: health and safety, human rights, training and education, work life balance and workplace diversity. The proposed model was tested on a sample of 336 frontline employees within the banking sector in Jordan. Results showed that all internal CSR dimensions are significantly and positively related to affective and normative commitment. In addition, the findings of this study indicate that all internal CSR dimensions did not have a significant relationship with continuance commitment. Limitations of the study, directions for future research, and implications of the findings are discussed.

Keywords: Internal CSR, organizational commitment, Jordan, banking sector.

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700 A Multi-Attribute Utility Model for Performance Evaluation of Sustainable Banking

Authors: Sonia Rebai, Mohamed Naceur Azaiez, Dhafer Saidane

Abstract:

In this study, we develop a performance evaluation model based on a multi-attribute utility approach aiming at reaching the sustainable banking (SB) status. This model is built accounting for various banks’ stakeholders in a win-win paradigm. In addition, it offers the opportunity for adopting a global measure of performance as an indication of a bank’s sustainability degree. This measure is referred to as banking sustainability performance index (BSPI). This index may constitute a basis for ranking banks. Moreover, it may constitute a bridge between the assessment types of financial and extra-financial rating agencies. A real application is performed on three French banks.

Keywords: Multi-attribute utility theory, Performance, Sustainable banking.

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699 Solving Partially Monotone Problems with Neural Networks

Authors: Marina Velikova, Hennie Daniels, Ad Feelders

Abstract:

In many applications, it is a priori known that the target function should satisfy certain constraints imposed by, for example, economic theory or a human-decision maker. Here we consider partially monotone problems, where the target variable depends monotonically on some of the predictor variables but not all. We propose an approach to build partially monotone models based on the convolution of monotone neural networks and kernel functions. The results from simulations and a real case study on house pricing show that our approach has significantly better performance than partially monotone linear models. Furthermore, the incorporation of partial monotonicity constraints not only leads to models that are in accordance with the decision maker's expertise, but also reduces considerably the model variance in comparison to standard neural networks with weight decay.

Keywords: Mixture models, monotone neural networks, partially monotone models, partially monotone problems.

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698 Organization as System, Psychic Dynamism as Equilibration: A Conceptualization

Authors: Abbas Moshref Razavi, Rodina Ahmad

Abstract:

Organizations are supposed to be systems and consequently require defining the notion of equilibrium within. However, organizations comprise people and unavoidably entail their irrational aspects. Then, the question is what is the organizational equilibrium and equilibrating mechanisms considering these aspects. Hence, some arguments are provided here to conceptualize human unconsciousness, irrationalities and consequent uncertainties within organizations in the form of a system of psychic dynamism. The assumption is this dynamism maintains the psychic balance of the organization through a psychodynamic point of view. The resultant conceptualization expected to promote the understanding of such aspects in different organizational settings by hypothesizing organizational equilibration from this perspective. As a result, the main expectation is, if it is known that how the organization equilibrates in this sense, we can explain and deal with such irrationalities and unconsciousness by rational and, of course conscious, planning and accomplishing.

Keywords: Equilibration, General System Theory, Organization, Psychodynamic.

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697 A System of Automatic Speech Recognition based on the Technique of Temporal Retiming

Authors: Samir Abdelhamid, Noureddine Bouguechal

Abstract:

We report in this paper the procedure of a system of automatic speech recognition based on techniques of the dynamic programming. The technique of temporal retiming is a technique used to synchronize between two forms to compare. We will see how this technique is adapted to the field of the automatic speech recognition. We will expose, in a first place, the theory of the function of retiming which is used to compare and to adjust an unknown form with a whole of forms of reference constituting the vocabulary of the application. Then we will give, in the second place, the various algorithms necessary to their implementation on machine. The algorithms which we will present were tested on part of the corpus of words in Arab language Arabdic-10 [4] and gave whole satisfaction. These algorithms are effective insofar as we apply them to the small ones or average vocabularies.

Keywords: Continuous speech recognition, temporal retiming, phonetic decoding, algorithms, vocal signal, dynamic programming.

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696 Constructing a Fuzzy Net Present Value Method to Evaluating the BOT Sport Facilities

Authors: Huei-Fu Lu

Abstract:

This paper is to develop a fuzzy net present value (FNPV) method by taking vague cash flow and imprecise required rate of return into account for evaluating the value of the Build-Operate-Transfer (BOT) sport facilities. In order to clearly manifest a more realistic capital budgeting model based on the classical net present value (NPV) method, some uncertain financial elements in NPV formula will be fuzzified as triangular fuzzy numbers. Through the conscientious manipulation of fuzzy set theory, we will find that the proposed FNPV model is a more explicit extension of classical (crisp) model and could be more practicable for the financial managers to capture the essence of capital budgeting of sport facilities than non-fuzzy model.

Keywords: Fuzzy sets; Capital budgeting, Sport facility, Net present value (NPV), Build-Operate-Transfer (BOT) scheme

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695 Knowledge Creation and Innovation in Classroom

Authors: Salina Daud, Rabiah Eladwiah Abdul Rahim, Rusnita Alimun

Abstract:

The concepts of knowledge creation and innovation have a strong relationship but this relationship has not been examined systematically. This study examines the utilization of knowledge creation processes of the Theory of Knowledge Creation in Higher Education Institutions. These processes consist of socialization, externalization, combination and internalization. This study suggests that the utilization of these processes will give impacts on innovation in academic performance. A cross-sectional study was conducted using survey questionnaires to collect data of the utilization of knowledge creation processes and classroom-s innovation. The samples are Business Management students of a Malaysian Higher Education Institution. The results of this study could help Higher Education Institutions to enrich the learning process of students through knowledge creation and innovation.

Keywords: Knowledge creation, innovation, business schools.

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694 Properties and Approximation Distribution Reductions in Multigranulation Rough Set Model

Authors: Properties, Approximation Distribution Reductions in Multigranulation Rough Set Model

Abstract:

Some properties of approximation sets are studied in multi-granulation optimist model in rough set theory using maximal compatible classes. The relationships between or among lower and upper approximations in single and multiple granulation are compared and discussed. Through designing Boolean functions and discernibility matrices in incomplete information systems, the lower and upper approximation sets and reduction in multi-granulation environments can be found. By using examples, the correctness of computation approach is consolidated. The related conclusions obtained are suitable for further investigating in multiple granulation RSM.

Keywords: Incomplete information system, maximal compatible class, multi-granulation rough set model, reduction.

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