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2008

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Articles 3721 - 3750 of 4190

Full-Text Articles in Engineering

Effect Of Hydrodynamic Multiplicity On Trickle Bed Reactor Performance, Werner Van Der Merwe, Willie Nicol, Muthanna H. Al-Dahhan Jan 2008

Effect Of Hydrodynamic Multiplicity On Trickle Bed Reactor Performance, Werner Van Der Merwe, Willie Nicol, Muthanna H. Al-Dahhan

Chemical and Biochemical Engineering Faculty Research & Creative Works

Multiple Hydrodynamic States in Trickle Bed Reactors Have Been the Subject of Numerous Hydrodynamic Investigations. the Extent of Variation in the Hydrodynamic Parameters (Like Holdup and Pressure Drop) is Large and This Variation Can Be Expected to Have a Significant Impact on the Conversion in a Reaction System. This Study Presents Reaction Data for Α-Methyl Styrene Hydrogenation in a Trickle Bed Reactor over a Range of Conditions that Include Gas and Liquid Limitations. It is Seen that Liquid Flow Rate Variation Induced Hysteresis Has a Large Impact on the Conversion. for Gas-Limited Reactions, the Upper Branch of the Pressure Drop …


New Classes Of Codes For Cryptologists And Computer Scientists, Florentin Smarandache, W.B. Vasantha Kandasamy Jan 2008

New Classes Of Codes For Cryptologists And Computer Scientists, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

Historically a code refers to a cryptosystem that deals with linguistic units: words, phrases etc. We do not discuss such codes in this book. Here codes are message carriers or information storages or information transmitters which in time of need should not be decoded or read by an enemy or an intruder. When we use very abstract mathematics in using a specific code, it is difficult for non-mathematicians to make use of it. At the same time, one cannot compromise with the capacity of the codes. So the authors in this book have introduced several classes of codes which are …


High Temperature Packaging For Wide Bandgap Semiconductor Devices, Brian Grummel Jan 2008

High Temperature Packaging For Wide Bandgap Semiconductor Devices, Brian Grummel

Electronic Theses and Dissertations

Currently, wide bandgap semiconductor devices feature increased efficiency, higher current handling capabilities, and higher reverse blocking voltages than silicon devices while recent fabrication advances have them drawing near to the marketplace. However these new semiconductors are in need of new packaging that will allow for their application in several important uses including hybrid electrical vehicles, new and existing energy sources, and increased efficiency in multiple new and existing technologies. Also, current power module designs for silicon devices are rife with problems that must be enhanced to improve reliability. This thesis introduces new packaging that is thermally resilient and has reduced …


Automating Material Delivery Records, Joo Hyoung (Jay) Lee, Bob Mccullouch Jan 2008

Automating Material Delivery Records, Joo Hyoung (Jay) Lee, Bob Mccullouch

JTRP Technical Reports

This project investigated methods on automating field data collection of materials. The method chosen and investigated was bar codes. The automated process requires material suppliers to produce delivery forms that can be recorded and tracked using bar codes. The report describes a system configuration that shows a conceptual process to electronically transfer materials information between the material supplier, trucking company, INDOT personnel and contractor. Other activities reported include survey results from other state transportation agencies, material suppliers, and concrete paving companies. Also, investigated was how to interface with SiteManager software. Recommendations described hardware options for using bar codes and industry …


E-Quality Control: A Support Vector Machines Approach, Kalyan Reddy Aleti Jan 2008

E-Quality Control: A Support Vector Machines Approach, Kalyan Reddy Aleti

Open Access Theses & Dissertations

The web-enabled quality control process presents many benefits to industry, such as universal access, remote control capability, and integration of production equipment into information networks for improved efficiency. This capability has a great potential, since engineers can access and control the equipment anytime, anywhere as the design stages evolve. In this context, this work uses innovative methods in remote part tracking and quality control with the aid of the modern equipment and application of Support Vector machine learning approach to predict the outcome of the quality control process. The classifier equations are built on the data obtained from the experiments …


Stereolithography Of Poly(Ethylene Glycol) Hydrogels With Application In Tissue Engineering As Peripheral Nerve Regeneration Scaffolds, Karina Arcaute Jan 2008

Stereolithography Of Poly(Ethylene Glycol) Hydrogels With Application In Tissue Engineering As Peripheral Nerve Regeneration Scaffolds, Karina Arcaute

Open Access Theses & Dissertations

In recent years, rapid prototyping (RP) technologies initially developed to create prototypes prior to production for the automotive, aerospace, and other industries, have found applications in tissue engineering (TE). Several different RP technologies are being used to fabricate biocompatible 3D structures with controlled micro- and macro-scale characteristics. The focus of this research was to explore the capabilities of the RP technology, stereolithography (SL), for creating complex, 3D scaffolds with applications in TE using a photocrosslinkable biopolymer, poly(ethylene glycol) (PEG). The primary objective was to create an implantable multi-lumen nerve guidance conduit (NGC) for the regeneration of peripheral nerves.

Studies of …


A Distributed Reconstruction Of Ekg Signals, Gabriel Cordova Jan 2008

A Distributed Reconstruction Of Ekg Signals, Gabriel Cordova

Open Access Theses & Dissertations

In this Thesis the parallel computing methodology is applied to an algorithm used in the reconstruction of electrocardiographic (EKG) measurements. The reconstructions are being performed to obtain a better understanding of the source and behavior of the electrical activity that generates the EKG measurements. The contribution of this Thesis is to identify and eliminate inefficiencies present in the current reconstruction algorithm. Additionally, this Thesis reduces the computation times of the EKG reconstruction by applying distributed computing through the use of Remote Procedure Calls (RPC). Lastly, it provides an analysis of the speed-up and efficiency of the distribution implemented using parallel …


Phonon-Energy-Coupling-Enhancement Effect And Its Applications, Pang-Leen Ong Jan 2008

Phonon-Energy-Coupling-Enhancement Effect And Its Applications, Pang-Leen Ong

University of Kentucky Doctoral Dissertations

Silicon Oxide/Oxynitride (SiO2/SiON) has been the mainstream material used for gate dielectric for MOS transistors for the past 30 years. The aggressive scaling of the feature size of MOS transistor has limited the ability of SiO2/SiON to work effectively as the gate dielectric to modulate the conduction of current of MOS transistors due to excess leakage current dominated by direct quantum tunneling. Due to this constraint, alternative gate dielectric/high-k is being employed to reduce the leakage current in order to maintain the rate of scaling of MOS transistors. However, the cost involved in the implementation of …


Learning Styles Of First Year Level 7 Electrical And Mechanical Engineering Students At Dit, Aidan O'Dwyer Jan 2008

Learning Styles Of First Year Level 7 Electrical And Mechanical Engineering Students At Dit, Aidan O'Dwyer

Conference papers

This paper investigates the learning styles of first year, Level 7, mechanical and electrical engineering students at DIT, using the index of learning styles survey as developed by Felder and Soloman [1]. Student learning styles on these programmes are compared with the results from other such surveys. The correlation between student performance and their individual learning styles is examined in outline. Knowledge of the strongly visual learning style of these cohorts of students may be used to improve the learning environment.


Teaching And Assessment Of Students Taking A First Year, Level 7 Subject: Analysis And Actions, Aidan O'Dwyer Jan 2008

Teaching And Assessment Of Students Taking A First Year, Level 7 Subject: Analysis And Actions, Aidan O'Dwyer

Conference papers

This contribution critically analyses the teaching and assessment strategies used on the core Electrical Systems subject in the first year of a three-year, Level 7, degree programme in Electrical Engineering at Dublin Institute of Technology. The author has the responsibility for development and instruction in the subject since 2004. In the 2004-5 and 2005-6 academic years, the didactic teaching approach and the assessment strategy ensured good educational outcomes. This was not the case in the 2006-7 academic year. The contribution will analyse the reasons for this, taking an evidence-based approach (i.e. analysing the assessment data in detail). Two conclusions that …


Sequence Analysis Based Dsp Controller For Dynamic Voltage Restorer (Dvr), N. G. Jayanti, Malabika Basu, Iurie Axente, Kevin Gaughan, Michael F. Conlon Jan 2008

Sequence Analysis Based Dsp Controller For Dynamic Voltage Restorer (Dvr), N. G. Jayanti, Malabika Basu, Iurie Axente, Kevin Gaughan, Michael F. Conlon

Conference papers

The paper examines the behaviour of a dynamic voltage restorer (DVR) under balanced/unbalanced supply voltage sag condition, and restricted DVR injection capability (e.g. limited to 50% of the supply voltage injection). Sequence components of the supply voltage are extracted to generate the reference injected voltage for the DVR. The control determines the maximum possible positive sequence injection within the capacity of the compensator to achieve balanced voltage conditions at the load terminals. The control is verified through simulation and experimentation. The control algorithm has been implemented in a TI320F2812 fixed point DSP and the effectiveness of the controller is verified …


Structural Division Procedure For Efficient Ic Analysis, Michael Brutscheck, St. Berger, M. Franke, Andreas Schwarzbacher, St. Becker Jan 2008

Structural Division Procedure For Efficient Ic Analysis, Michael Brutscheck, St. Berger, M. Franke, Andreas Schwarzbacher, St. Becker

Conference papers

The efficient and structured analysis of unknown CMOS integrated circuits (ICs) has become a topic of great relevance in recent years. Up until now, different invasive [1], [2] and non-invasive [3], [4] strategies have been developed for procedure of analysis. However, invasive procedures always lead to the destruction of system under investigation. The non-invasive approaches published so far have the disadvantage that ICs are analysed by using complex algorithms. Here, no subdivision exists to avoid extensive analysis times in the case that only simple structures are investigated. Moreover, traditional procedures cannot automatically distinguish between input and output pin types, which …


Interaction Of Rf-Hyperthermia Applicator With High Fidelity Human Body Model, Sergio Curto, T.S. P. See, Z. N. Chen, Patrick Mcevoy, Max Ammann Jan 2008

Interaction Of Rf-Hyperthermia Applicator With High Fidelity Human Body Model, Sergio Curto, T.S. P. See, Z. N. Chen, Patrick Mcevoy, Max Ammann

Conference papers

A compact patch antenna working at the 434 MHz ISM frequency band is proposed as an RF-Hyperthermia applicator. The electromagnetic interaction in terms of S11, SAR and E-Field distribution of the antenna with a High Fidelity human body model is investigated. This analysis provides useful information for engineers and clinical staff to develop more efficient and smaller antennas for medical applications, in particular for RF-Hyperthermia cancer therapy, where the size of the antenna determines tumor accessibility.


1 Gbit/S Radio Over Fiber Downlink At A 32 Ghz Carrier, Marcus Junker, Thomas Schneider, Kai-Uwe Lauterbach, Ronny Henker, Max Ammann, Andreas Schwarzbacher Jan 2008

1 Gbit/S Radio Over Fiber Downlink At A 32 Ghz Carrier, Marcus Junker, Thomas Schneider, Kai-Uwe Lauterbach, Ronny Henker, Max Ammann, Andreas Schwarzbacher

Conference papers

The carrier frequency of the presented radio over fiber downlink at 32 GHz is generated by stimulated Brillouin scattering and an error free 1 Gbit/s data transmission is realized.


Spatial Group Delay Patterns For Three Ultra Wideband Spline Antennas, Patrick Mcevoy, Matthias John, Sergio Curto, Max Ammann Jan 2008

Spatial Group Delay Patterns For Three Ultra Wideband Spline Antennas, Patrick Mcevoy, Matthias John, Sergio Curto, Max Ammann

Conference papers

The IEEE ultra wideband (UWB) standard includes both a multiple frequency carrier (MB-OFDM) and an impulse spectrum (DS-UWB) method, for which application antennas should be appropriately optimized. Small printed monopoles with outline features that can be defined by a Bezier-spline [1] have good matched impedance performance across the 3.1 - 10.6 GHz band. For communications applications, an omni-directional pattern, where the gain pattern varies by less than plusmn5 dBi, and a stable frequency-gain profile in the azimuth plane, allow for an even spatial coverage in all directions. In the case of an impulse system, any non-linear phase transfer performance in …


Optimization Of The Brillouin Spectrum For Fiber Based Slow Light Systems, Ronny Henker, Andrzej Wiatrek, Kai-Uwe Lauterbach, Thomas Schneider, Max Ammann, Andreas Schwarzbacher Jan 2008

Optimization Of The Brillouin Spectrum For Fiber Based Slow Light Systems, Ronny Henker, Andrzej Wiatrek, Kai-Uwe Lauterbach, Thomas Schneider, Max Ammann, Andreas Schwarzbacher

Conference papers

This article shows simulation results and first practical investigations of the optimization of a Brillouin spectrum with the natural bandwidth superimposed with two losses for fiber based slow light systems.


Measuring Agility Of Organizations - A Comprehensive Agility Measurement Tool (Camt), Ameya S. Erande, Alok K. Verma Jan 2008

Measuring Agility Of Organizations - A Comprehensive Agility Measurement Tool (Camt), Ameya S. Erande, Alok K. Verma

Engineering Technology Faculty Publications

Since "Agility" is ability to respond to unpredictable changes with quick response and profitability, it is not industry specific. This "not industry specific" nature of agility makes it hard to assess and measure it on a fixed scale. Measurement of agility of an enterprise has been a major topic of research since inception of agility in 1991. Though some methods have been developed to measure agility, they mainly remain tied to manufacturing industry. As agility is present in all the industries, comprehensive tool to measure it is a necessity in order to determine responsiveness of an enterprise to external turbulences. …


Real-Time Implementation Of A Statcom On A Wind Farm Equipped With Doubly Fed Induction Generators, Wei Qiao, Ganesh K. Venayagamoorthy, Ronald G. Harley Jan 2008

Real-Time Implementation Of A Statcom On A Wind Farm Equipped With Doubly Fed Induction Generators, Wei Qiao, Ganesh K. Venayagamoorthy, Ronald G. Harley

Electrical and Computer Engineering Faculty Research & Creative Works

Voltage stability is a key issue to achieve the uninterrupted operation of wind farms equipped with doubly fed induction generators (DFIGs) during grid faults. This paper investigates the application of a static synchronous compensator (STATCOM) to assist with the uninterrupted operation of a wind turbine driving a DFIG, which is connected to a power network, during grid faults. The control schemes of the DFIG rotor- and grid-side converters and the STATCOM are suitably designed and coordinated. The system is implemented in real-time on a real time digital simulator. Results show that the STATCOM improves the transient voltage stability and therefore …


Wavelength Selection Using The Measure Of Topological Relevance On The Self-Organizing Map, Francesco Corona, Satu Pia Reinikainen, Kari Aaljoki, Annikki Perkiö, Elia Liitiäinen, Roberto Baratti, Olli Simula, Amaury Lendasse Jan 2008

Wavelength Selection Using The Measure Of Topological Relevance On The Self-Organizing Map, Francesco Corona, Satu Pia Reinikainen, Kari Aaljoki, Annikki Perkiö, Elia Liitiäinen, Roberto Baratti, Olli Simula, Amaury Lendasse

Engineering Management and Systems Engineering Faculty Research & Creative Works

In This Work, We Investigated the Possibility to Perform Wavelength Selection by Exploiting the Metric Structure of the Spectrophotoscopic Measurements. the Topologically Preserving Representation of the Data is Performed using the Self-Organizing Map (Som) Where the Inputs' Significance to the Output is Computed with the Measure of Topological Relevance (MTR) on Som. the MTR on Som is a Metric Measuring the Similarity between Local Distance Matrices and We Found that Spectral Inputs with a Topology, Which Is, Close to the Outputs Are Also Associated to the Wavelengths that Chemically Explain the Influence of the Spectra to the Property of Interest. …


Gaussian Basis Functions For Chemometrics, Tuomas Kärnä, Francesco Corona, Amaury Lendasse Jan 2008

Gaussian Basis Functions For Chemometrics, Tuomas Kärnä, Francesco Corona, Amaury Lendasse

Engineering Management and Systems Engineering Faculty Research & Creative Works

High-Dimensional Data Are Becoming More and More Common, especially in the Field of Chemometrics. Nevertheless, it is Generally Known that Most of the Commonly Used Prediction Models Suffer from Curse of Dimensionality that is the Prediction Performance Degrades as Data Dimension Grows. Therefore, It is Important to Develop Methodology for Reliable Dimensionality Reduction. in This Paper, We Propose a Method that is based on Functional Approximation using Gaussian Basis Functions. the Basis Functions Are Optimized to Accurately Fit the Spectral Data using Nonlinear Gauss-Newton Algorithm. the Fitting Weights Are Then Used as Training Data to Build a Least-Squares Support Vector …


The Effects Of Congressional Elections On Future Equity Market Returns, Vincent Louis Ovlia, David Lee Enke, Michael C. Davis Jan 2008

The Effects Of Congressional Elections On Future Equity Market Returns, Vincent Louis Ovlia, David Lee Enke, Michael C. Davis

Engineering Management and Systems Engineering Faculty Research & Creative Works

As the primary entity responsible for new legislation, Congress is capable of enacting legislation that may affect future market returns. To examine potential effects, the percentage of the House of Representatives and Senate controlled by a political party is examined. Additionally, the effect on returns in a change in the percentage of seats gained or lost in Congressional elections is analyzed. To test both theories, a modified “partisan view” model is adopted. Results point to the fact that equity markets perform better in situations in which power is distributed between political parties.


Composition Dependence Of The In-Plane Cu-O Bond-Stretching Lo Phonon Mode In Y⁢Ba2⁢Cu3⁢O6+X, Ferenc Stercel, Takeshi Egami, Herbert A. Mook, Mohana Yethiraj, J-H Chung, M. Arai, C. Frost, Fatih Dogan Jan 2008

Composition Dependence Of The In-Plane Cu-O Bond-Stretching Lo Phonon Mode In Y⁢Ba2⁢Cu3⁢O6+X, Ferenc Stercel, Takeshi Egami, Herbert A. Mook, Mohana Yethiraj, J-H Chung, M. Arai, C. Frost, Fatih Dogan

Materials Science and Engineering Faculty Research & Creative Works

An inelastic pulsed neutron scattering study was performed on the dependence of the dispersion and spectral intensity of the in-plane Cu-O bond-stretching LO phonon mode on doped charge density. The measurements were made in the time-of-flight mode with the multiangle position sensitive spectrometer of the ISIS facility on single crystals of Y⁢Ba2⁢Cu3⁢O6+x (x=0.15, 0.35, 0.6, 0.7, and 0.95). The focus of the study is the in-plane Cu-O bond-stretching LO phonon mode, which is known for strong electron-phonon coupling and unusual dependence on composition and temperature. It is shown that the dispersions for the samples with …


Thickness Effects On The Ac And Dc Electrical Behavior Of Rf-Sputtered Batio3 Nano-Capacitors With Pt And Ni Electrodes, James N. Reck, Matthew O'Keefe, Fatih Dogan Jan 2008

Thickness Effects On The Ac And Dc Electrical Behavior Of Rf-Sputtered Batio3 Nano-Capacitors With Pt And Ni Electrodes, James N. Reck, Matthew O'Keefe, Fatih Dogan

Materials Science and Engineering Faculty Research & Creative Works

Nanoscale BaTiO3 capacitors were deposited on Si wafers at dielectric thicknesses of approximately 25, 50, 100, and 200 nm using RF-magnetron sputtering with either 25 nm thick Ni or Pt electrodes. Multiple DC and AC tests were conducted on these devices to determine the effects of BaTiO3 thickness on the measured dielectric behaviors. All films were observed to have non-linear responses for resistance, permittivity, and loss with respect to dielectric thickness. The permittivity was found to follow a standard dead layer model behavior with measured values ranging from approximately 350 to 1700 for Ni electrodes and approximately 100 …


Progress In Effect Of Jominy End Quench On The Microstructure And Mechanical Properties Of Cast Aluminum Alloys, Qingcai Liu, C. Lu, Joseph William Newkirk Jan 2008

Progress In Effect Of Jominy End Quench On The Microstructure And Mechanical Properties Of Cast Aluminum Alloys, Qingcai Liu, C. Lu, Joseph William Newkirk

Materials Science and Engineering Faculty Research & Creative Works

In this review, the current knowledge related to the relationship between the heat treatment process and the microstructure and mechanical properties of A356 aluminum alloys are summarized. The review also examines the use of the Jominy end quench (JEQ) specimen and its application to the examination of the effects of quench rate and subsequent processing. Using the design of experimental methods combined with the Jominy end quench technique, desired changes in microstructure and mechanical properties of alloys can be obtained. So, the experimental technique of the Jominy end quench was concerned in this work.


Estimation Of Earthquake Loss Due To Bridge Damage In The St. Louis Metropolitan Area. Ii: Indirect Losses, David Lee Enke, Chakkaphan Tirasirichai, Ronaldo Luna Jan 2008

Estimation Of Earthquake Loss Due To Bridge Damage In The St. Louis Metropolitan Area. Ii: Indirect Losses, David Lee Enke, Chakkaphan Tirasirichai, Ronaldo Luna

Engineering Management and Systems Engineering Faculty Research & Creative Works

An approach to estimate the indirect economic loss due to damaged bridges within the highway system from an earthquake event is presented. The indirect cost considered refers to the increased highway transportation cost only. The study zone covers the St. Louis metropolitan area and its surrounding suburban regions. An earthquake scenario centered in St. Louis, with a magnitude 7.0 is used. The direct earthquake loss was primarily damage to bridges, which causes an increase in travel time and distance within the transportation network. This information is then used as input for the indirect loss model. The indirect loss is examined …


Phantom For Evaluating Accuracy Of Image Registration Software, B. Y. Choe, H. S. Jin, R. H. Juh, Hyoung-Koo Lee, J. Y. Song, T. S. Suh Jan 2008

Phantom For Evaluating Accuracy Of Image Registration Software, B. Y. Choe, H. S. Jin, R. H. Juh, Hyoung-Koo Lee, J. Y. Song, T. S. Suh

Nuclear Engineering and Radiation Science Faculty Research & Creative Works

Provided is a phantom for evaluating the accuracy of image registration software based on a result of matching tomograms of a predetermined position of the phantom, taken using two or more imaging apparatuses. Accordingly, it is possible to more efficiently evaluate the accuracy of the image registration software by comparing the tomograms with one another using a three-dimensional analysis. In addition, it is possible to facilitate the comparison of the tomograms with one another by installing a plurality of indicating bars in the phantom so that their cross sections can appear on each of the tomograms.


Fit Numerical Modeling For Emi Discovery And "Design", James L. Drewniak Jan 2008

Fit Numerical Modeling For Emi Discovery And "Design", James L. Drewniak

Electrical and Computer Engineering Faculty Research & Creative Works

No abstract provided.


Exploring Stochastic Characteristics Of Freeway Traffic Breakdown And Recovery Conditions, Chaitanya Mamidala Jan 2008

Exploring Stochastic Characteristics Of Freeway Traffic Breakdown And Recovery Conditions, Chaitanya Mamidala

LSU Master's Theses

In recent times, the term ‘congestion’ has gained a lot of attention due to its negative impact on the mobility and efficiency of transportation network. Congestion control and mitigation of its effects has become a prime concern to many transportation agencies. With breakthroughs in transportation technologies, effective management and utilization of existing infrastructure capacities has been possible. One of the key functions of technological advancements is the ability to understand the different characteristics of traffic that prevail on major freeways and arterials, and to model short-term predictions of traffic conditions with reasonable accuracy. Providing accurate, real-time information makes travelers aware …


Parametric Study Of A Pulsed Vertical Jet In Cross-Flow, Guillaume Francois Bidan Jan 2008

Parametric Study Of A Pulsed Vertical Jet In Cross-Flow, Guillaume Francois Bidan

LSU Master's Theses

The potential of pulsed vertical jet in cross-flow for film cooling purposes was experimentally studied and is discussed in this Thesis. A single vertical jet placed in laminar cross-flow conditions was first characterized in steady state at relatively low blowing ratios ranging from 0.150 to 0.600, using Mie scattering visualization methods and hot-wire measurements. Wavelet spectral analysis and image quantification algorithms were applied to the velocity records and averaged visualizations to obtain quantitative data on the jet characteristic frequencies, penetration and coverage. Two different regimes characterized by different structures are identified and adapted scaling variables are provided. Trends in the …


New Method For Approximating Vague Sets To Fuzzy Sets Based On Voting Model, Jian Liu, Zhizhan Liu, Shunxiang Wu, Yongjian Zhang Jan 2008

New Method For Approximating Vague Sets To Fuzzy Sets Based On Voting Model, Jian Liu, Zhizhan Liu, Shunxiang Wu, Yongjian Zhang

Electrical and Computer Engineering Faculty Research & Creative Works

By analyzing Vague Sets voting model, we bring forth a new method for approximating Vague Sets to Fuzzy Sets, and its general process is presented in the article. In a voting model, firstly, we suppose that the abstainers must vote for once more, and the results are close studied. Then the randomicity, uncertainty, and conformity of voting are found. As we know, an abstainer may favor somebody, oppose somebody, or just abstain. In this article, we suppose the distribution of results is consistent with a normal distribution. So, we advance the new approximation method based on Gauss Distribution. © 2008 …