ࡱ > n '` bjbjLULU @ .? .? 6 T l l l Zm , n 5 Nq V s s s s x x x = < 5 0 5 $5 $ 7 h : ~ H5 i Kz xx " x Kz Kz H5 s s 5
Kz
s s
Kz
@ q s Bq 0x l y 6 ) 5 0 5 : & : l q q : x > x ,
y $ (y # x x x H5 H5 N x x x 5 Kz Kz Kz Kz Y l l N i n o s l a v S l a v e k , A l a n J o v i
A p p l i c a t i o n o f G r e y S y s t e m T h e o r y t o S o f t w a r e P r o j e c t s R a n k i n g U D K x x x . x x x . x x I F A C x . x ; x . x . x ( f i l l e d b y e d i t o r s ) P a p e r c l a s s i f i c a t i o n ( f i l l e d b y e d i t o r s )
T h e a i m o f t h i s w o r k i s t h e i d e n t i f i c a t i o n o f s o f t w a r e p r o j e c t q u a l i t y performance measures that would enable valid comparison and ranking of the completed projects. Software projects can be characterized by a set of influence factors. A subset of the influence factors is relevant for software project quality. In order to predict and determine the ranking of software projects by their success, and thus present a valid software project quality performance measure, we employ Grey system theory. Grey relational analysis is a kind of method which enables determination of the relational degree of every factor in the system. The method can be used for systems that are incompletely described with relatively few data available, and for which standard statistical assumptions are not satisfied.
Relational degree between seven relevant software project quality influence factors is calculated for a set of ten software projects. The results demonstrate the usefulness and applicability of the Grey system theory in software project quality assessment.
Key words: grey system theory, software qu a l i t y , i n f l u e n c e f a c t o r s , r e l a t i o n a l a n a l y s i s
P r i m j e n a t e o r i j e s i v i h s u s t a v a n a k v a l i t e t u s o f t v e r s k i h p r o j e k a t a . C i l j r a d a j e i d e n t i f i k a c i j a m j e r a p e r f o r m a n s e k v a l i t e t e s o f t v e r s k o g p r o j e k t a k o j e b i o m o g u i l e u s p o r e d b u i r a n g i r a n j e z a v r ae n i h p r o j e k a t a . S o f t v e r s k i p r o j e k t i m o g u s e o k a r a k t e r i z i r a t i s k u p o m f a k t o r a u t j e c a j a . P o d s k u p t i h f a k t o r a v a ~a n j e z a k v a l i t e t u s o f t v e r s k i h p r o j e k a t a . D a b i s e p r e d v i d i o i o d r e d i o p o r e d a k s o f v e r s k i h p r o j e k a t a p r e m a u s p j e an o s t i i n a t a j n a
i n p r e d s t a v i l o v a l j a n u m j e r u p e r f o r m a n s e k v a l i t e t e s o f v e r s k i h p r o j e k a t a , k o r i s t i s e t e o r i j a s i v i h s u s t a v a . S i v a a n a l i z a o d n o s a j e t a k v a m e t o d a k o j a o m o g u a v a o d r e i v a n j e s t u p n j a o d n o s a s v a k o g f a k t o r a u s u s t a v u . T a k v a m e t o d a k o r i s t i s e z a s u s t a v e k o j i s u n e p o t p u n o o p i s a n i s r e l a t i v n o m a l o p o d a t a k a i z a k o j e s t a n d a r d n e s t a t i s t i
k e p r e t p o s t a v k e n i s u z a d o v o l j e n e .
S t u p a n j o d n o s a i z m e u s e d a m b i t n i h f a k t o r a k v a l i t e t e s o f t v e r s k i h p r o j e k a t a i z r a
u n a t j e n a s k u p u o d d e s e t s o f t v e r s k i h p r o j e k a t a . R e z u l t a t i p o k a z u j u u
i n k o v i t o s t i p r i m i j e n j i v o s t t e o r i j e s i v i h s u s t a v a u o c j e n i k v a l i t e t e s o f t v e r s k i h p r o j e k a t a .
K l j u
n e r i j e
i : t e o r i j a s i v i h s u s t a v a , k v a l i t e t a s o f t v e r a , f a k t o r i u t j e c a j a , a n a l i z a o d n o s a
I N T R O D U C T I O N
T h e i n h e r e n t u n c e r t a i n t y a n d i n c o m p l e t e i n f o r m a t i o n o f t h e s o f t w a r e d e v e l o p m e n t p r o c e s s p r e s e n ts challenges for identifying fault-prone modules and providing a preferred model early enough in a development cycle in order to guide software enhancement estimates under small sample and uncertain conditions.
This work examines the potential benefits for providing a software-quality classification based on Grey relational analysis. It attempts to identify software project quality performance measures that would enable valid comparison between the completed projects.
The advantage of the Grey system theory is that it is designed to study uncertainty. It is shown that Grey theory is superior to other methods in theoretical analysis of systems with uncertain information and incomplete data samples [2]. Especially, it can be used if the large samples are not available or if the user is uncertain whether the data is representative. It can also be used in early effective factor assessment [4]. Therefore, this study adopts Grey system theory approach to propose a feasible and effective software quality analysis method.
Traditional methods require a large number of samples and a data distribution that has to be typical for the process at hand. In contrast, the Grey system theory is designed to work with a system where the available information is insufficient to fully characterize the system [14]. The term "Grey" stands for poor, incomplete and uncertain, and is especially used in relation to the concept of information [8]. The major advantage of Grey theory is that it can handle both incomplete information and unclear problems very precisely [1]. Grey relational analysis (GRA), which is a part of Grey theory, is a kind of method by which the relational degree of every factor in the system can be analyzed [10]. The main function of GRA is to indicate the relational degree between two measurement sequences by using the discrete measurement method to measure the distances [8]. This means that GRA uses information from the Grey system to dynamically compare each influence factor quantitatively. This approach is based on the level of similarity and variability among all factors to establish their relation.
Main contributions to the Grey system theory today come from two parts: GRA and Grey modeling (GM) [10]. GRA can be used for system analysis as an alternative to statistical methods. GM is developed based on requirements for system modeling with limited data, which constitutes a problem for most of the traditional modeling methods.
In this paper we investigate the effectiveness of the Grey system theory to determine the ranking of software projects using relevant influence factors.
The contributions of this paper are:
a) Identification of a set of software project performance measures and influence factors that are used by software development projects so that a valid comparison of performance can be made between the projects when they are completed.
b) Demonstration of applicability of GRA to software projects influence factors analysis, which allows for faster, more robust and more effective software projects comparison.
The structure of this paper is as follows: Section 2 discusses some related work on Grey theory. Section 3 elaborates methodology, data collection, and influence factors for software project quality. In Section 4, the Grey theory is presented and explicated. Section 5 elaborates the calculation of the Grey relational degree for relevant software projects influence factors. Section 6 discusses the results from the perspective of the future projects applicability, and finally the conclusion is given in Section 7.
RELATED WORK
Previously, methods such as Fuzzy Bayes classifier [12], which consists of a Bayesian classifier with weighting factors, have been used in analysis of systems with uncertain information and incomplete samples. The proposition of Grey theory that occurred in the period 1982 to 1999 resulted in the use of Grey theory to a number of fields, and the development and application of the theory is still in progress [1]. Deng [5] proposed Grey system theory in 1982 as a simple and accurate method for multiple attributes decision problems. Grey system as proposed by [5] included GRA for effective selection of relevant attributes.
Since then, the application of Grey system theory has extended to industry, agriculture, economy, energy, transportation, military, legal, financial and other fields, and has successfully resolved a large number of practical problems in production, life, and scientific research [13,17].
Chih-Hung et al. [3] applied GRA to the vendor evaluation model. Recently this technique was also applied to the field of sports. For example, Hsu [7] used GRA and determined the effects of striking and kicking action on overall scores. Chang-Liang [1] applied GRA to the decathlon evaluation model with satisfying results. Technique was also applied to project selection, prediction analysis, performance evaluation, and factor effect evaluation due to the Grey relational analysis based software development [8].
METHODOLOGY
Data collection
The Competence Center for Software Engineering (CCSE) was established in Osijek, Croatia. It is intended for the development of logistics and information technology in the wider region, while promoting software quality, reliability and diagnostics.
An initiative from CCSE is the implementation of a program for software project performance measurement. It is a process of assessing the results of a company, organization, or individual included in the project. The main goals of the assessment are:
a) to determine the effectiveness of the project operations,
b) to make changes by addressing observed performance gaps, shortfalls, and other unwanted issues.
Companies and organizations measure their performance in a variety of areas using different methods and criteria for different purposes. In order to be able to compare the performance measures, they need to be commonly defined. We used a list of performance measures according to the Software Engineering Institute's Technical report [9] in order to:
(1) define a set of key performance measures that should be used by all software projects,
(2) define the influence factors for these measures.
The list of software projects influence factors with the corresponding performance measures is shown in Table 1 [9].
Table 1. Influence factors of software projects
NumberFactorMeasure1Project sizeFp*2Artifact reuse%3Project typeType**4Application domain***5Average team sizenumber6Maximum team sizenumber7Team expertiseyears8Process maturityCMM****9Functional requirement stabilitynumber10Project efforthours11ProductivityFP* per hour12Project durationdays13Schedule predictability%14Requirements completion ratio%* Functional point
** New software, reengineering, or modification
*** Enterprise, market/industry
**** Capability Maturity Model [11].
Table 2. List of software project quality influence factors
NumberInfluence
factorDefinition1Artifact reuseIt is the use of existing software or software knowledge to built new software or new documents for the project under consideration.2Team expertiseIt is a 5-tuple of measures of the proficiency of the project team during each phase of the development cycle.3Process maturityExtent to which project's processes are explicitly defined, managed, measured, and controlled.4Functional requirement stabilityMeasure that quantifies the cumulative degree to which the requirements changed throughout the life cycle of the project from the original requirements baseline.5Team productivityProject size vs. project effort. Expressed as project size per project hour, project size depends on how the size is measured by an organization (e.g. lines of code, functional points)6Schedule unpredictabilityMeasure of how much the original project duration estimate differs from the actual project duration that was achieved.7Requirements completion ratioMeasures the extent to which planned functional requirement were satisfied in the final product implementation.Out of the influence factors listed in Table 1, those that are considered by experts to be the most relevant from the software projects quality perspective are listed in Table 2, together with a short definition.
3.2 Explanation of influence factors
In this subsection we provide a thorough explanation of the relevant software projects influence factors listed in Table 2, according to [9].
1. Artifact reuse is the use of existing software or software knowledge to build new software or new documents for the project under consideration.
Reusable software knowledge items are referred as reusable artifacts or reusable assets and may include requirements documents, designs, test cases, code, documentation or any other work product that is a part of the projects development process.
An artifact reuse value is determined based on the reuse assessment method that is employed. A proxy measure of artifact reuse is defined by:
EMBED Equation.3 (1),
where EMBED Equation.3 is the project effort that was conserved or saved through the reuse of preexisting work products, and EMBED Equation.3 is the total project effort .
Developing an estimate of artifact reuse relies on judgments made about: (a) the percent of overall project effort required to develop the artifacts, (b) the percent of effort savings realized by artifact reuse.
2. Team expertise is a 5-tuple of measures of the proficiency of the project team during each phase of the development life cycle.
The measure is a subjective one based on the informed expert judgment of those who perform the assessment. The time expertise measure for each phase is an integer in range (1-5) where 1 represents novice proficiency ability and 5 represents expert proficiency:
EMBED Equation.3
(2),
where:
TEreq is expertise rating for team members, who contribute to the Concept and Requirements Analysis Phase,
TEarch is expertise rating for team members, who contribute to Architectural and/or High-Level Design Phase,
TEdd is expertise rating for team members, who contribute to Detailed Design Phase,
TEcode is expertise for Code Construction und Unit Testing Phase, and
TEst is expertise rating for team members, who contribute to System Test Phase.
3. Process maturity is the extent to which a projects processes are explicitly defined, managed, measured, and controlled. Some of the approaches include ISO 9001 and ISO 15504 (SPICE) standards, and SEI CMM [6]. These approaches use different rating schemes to indicate the degree of process maturity.
A maturity level is a defined evolutionary plateau for organizational process improvement. The maturity levels are measured by the achievement of the goals associated with each predefined set of process areas. There are five maturity levels, each one a layer in the foundation for ongoing process improvement, designated by numbers 1 through 5.
4. Functional requirements stability (FRS) is a measure that quantifies the cumulative degree to which the requirements changed throughout the life cycle of the project from the original requirements baseline. FRS is defined as
EMBED Equation.3 (3),
where RT is the total number of requirements that were originally base-lined at the beginning of the project; and RC is the total number of changes to the original base-lined requirements.
The maximum value of FRS is 1.0, indicating complete stability of the functional requirements.
5. Team Productivity of a software project is calculated as follows:
EMBED Equation.3 [units/hour] (4),
where Project size depends on how the project size is measured by an organization (e.g., lines of code, functional points), and Project effort is usually defined in project hours (see also Table 1).
For example, if a developed project acquired 130 FPs and this was accomplished in 5 300 hours, then its Team productivity can be calculated as:
EMBED Equation.3
6. Schedule unpredictability is a measure of how much the original project duration estimate differs from the actual project duration that was achieved. Schedule unpredictability is defined as a percentage:
EMBED Equation.3
[%] (5),
where Project duration is measured in hours, Estimated project duration is the original estimate of project duration as documented in the base-lined version of the project plan.
For example: The estimated duration was documented as 316 days in the project plan. The actual duration realized was 325 days. Therefore, Schedule unpredictability is calculated as
EMBED Equation.3
7. Requirements Completion Ratio. Functional requirements describe what the system, process, product, or service must do in order to fulfill the user requirements.
The Requirements Completion Ratio (RCR) measures the extent to which planned functional requirements were satisfied in the final product implementation.
RCR is expressed as a percentage:
EMBED Equation.3 [%] (6),
where Planned requirements is given as the number of requirements that were originally base-lined at the beginning of the project and that have been added or modified through negotiation with the user, and Satisfied requirements is given as the number of functional requirements that were satisfied in the delivered software product.
For example: The original base-lined functional requirements specification contained 34 requirements, and 28 of those were satisfied, thus
EMBED Equation.3
4 GREY SYSTEMS THEORY
4.1 Grey theory steps
The information that is either incomplete or undetermined is called Grey. The Grey system provides multidisciplinary approaches for analysis and abstract modeling of systems for which the information is limited, incomplete and characterized by random uncertainty [14].
The 1st order one variable Grey model denoted as GM (1, 1) is especially applicable for forecasting. GM (1, 1) model uses the variation within the system to find out the relations between sequential data and then establish the prediction model [14].
The three terms that are typical symbols and features for Grey System are [3]:
a) The Grey number in Grey system is a number with incomplete information.
b) The Grey element represents an element with
incomplete information.
c) The Grey relation is the relation with incomplete
information.
There are several steps of the theory of Grey system [16]:
Grey generation: This is data processing to supplement information. It is aimed to process those complicate and tedious data to gain a clear rule, which is called the whitening of a sequence of numbers. The expected goal for each influence factor is determined based on the principle of data processing, as explained in section 4.2
Grey modeling: The modeling is performed in order to establish a set of Grey variation equations and Grey differential equations, which is called the whitening of the model. The Grey model is denoted as GM (n, h), which is a n-th order differential equation of h variables. This Grey differential equitation is used for infinite information. Most of the previous researchers have focused on GM (1, 1) models because of its computational efficiency. GM (1, 1) model have time varying coefficients. It means that the model is renewed as the new data become available to the prediction model. A Grey differential equation having N variables is called GM (1, N).
Grey prediction: Uses the Grey model to conduct a qualitative prediction, which is called the whitening of development. Grey models predict the future values of a time series based on a set of the most recent data.
Grey decision: A decision is made under imperfect countermeasure and unclear situation, which is called the whitening of status. It is primarily concerned with the Grey strategy of situation, Grey group decision making and Grey programming [5]. Grey strategy of situation deals with the strategy making based on multi objects which are contradictory in the ordinary way. It is important to make a satisfactory strategy by means of effect measure maps, which transfer the disconformities samples resulting from different objects into identical scales.
Grey relational analysis: Quantifies all influences of various factors and their relation, which is called the whitening of factor relation. It uses information from the Grey system to dynamically compare each factor quantitatively, based on the level of similarity and variability among factors to establish their relation. GRA analyzes the relational grade for discrete sequences.
Grey control: Work on the data of system behavior and look for any rules of behavior development to predict future behavior. The predicted value can be fed back into the system in order to enable system control.
This study will adopt the above mentioned research steps to develop an influence factors evaluation model based on GRA, and apply to influence factors evaluation and selection. The Grey relational analysis uses information from the Grey system to dynamically compare each factor quantitatively.
4.2 Grey relational analysis
The generation of Grey relation for software projects is shown in Fig. 1. The process is elaborated here.
Let the number of the listed software projects be m, and the number of the influence factors be n. Then a m x n value matrix (called eigenvalue matrix) is set up [15].
X = EMBED Equation.3 (7),
where EMBED Equation.3 is the value of the number i listed project and the number k influence factors.
Usually, three kinds of influence factors are included, they are:
1. Benefit type factor (the bigger the better),
2. Defect type (the smaller the better)
3. Medium type, or nominal-the-best (the nearer to a
certain standard value the better).
SHAPE \* MERGEFORMAT
Figure 1. The generation of Grey relation degree for software projects
It is difficult to compare between the different kinds of factors because they exert a different influence. Therefore, the standardized transformation of these factors must be done. Three formulas can be used for this purpose [3].
EMBED Equation.3 (8).
The first standardized formula is suitable for the benefit type factor.
EMBED Equation.3 (9).
The second standardized formula is suitable for defect type factor.
EMBED Equation.3 (10).
The third standardized formula is suitable for the medium type factor.
The grey relation degree can be calculated by steps as follows:
The absolute difference of the compared series and the referential series should be obtained by using the following formula [15]:
EMBED Equation.3 (11),
and the maximum and the minimum difference should be found.
The distinguishing coefficient p is between 0 and 1. Generally, the distinguishing coefficient p is set to 0.5.
Calculation of the relational coefficient and relational degree by (12) as follows.
In Grey relational analysis, Grey relational coefficient EMBED Equation.3 can be expressed as follows [15]:
EMBED Equation.3 (12),
and then the relational degree follows as:
EMBED Equation.3 (13).
In equation (13), EMBED Equation.3 is the Grey relational coefficient, w (k) is the proportion of the number k influence factor to the total influence indicators. The sum of w (k) is 100%. The result obtained when using (12) can be applied to measure the quality of the listed software projects.
CALCULATION OF THE GREY RELATIONAL DEGREE FOR INFLUENCE FACTORS
Table 3 shows seven influence factors (A1A7) of a small amount of 10 medium and small software projects (X1X10) performed in the CCSE program.
The influence factors are the benefit type factors. Therefore, the reference series is X0 = (0.021, 3.20, 3.20, 0.86, 0.034, 0.025, and 0.965), which are the best results from Table 3.
Equation (8) can be used to do the standardized transformation of this sample, and the result is shown in Table 4.
The next step is to calculate the absolute difference between the compared series and the referential series using (11), and to find the maximum and the minimum. The distinguishing coefficient p is set to 0.5. The Grey relational coefficient can be calculated using (12).
In formula (13), w(k) for every influence factor and for every factor report may be different. If we suppose: w(1) = 0.30, w(2) = 0.20, w(3) = 0.20, w(4) = 0.10, w(5) = 0.008, w(6) = 0.08, w(7) = 0.04, the relational degree can be obtained using (13). The result is listed in Table 5. According to the data of the relational degree in Table 5,
Table 3. The original data of the Influence factors of software projects
Project numberArtifact
reuse
A1Team
expertise
A2Process
maturity
A3Functional
requirement stability A4Productivity (FP per hour)
A5Schedule unpredictability
A6Requirements completion ratio A7X10.0143.02.00.850.0260.0250.955X20.0123.02.00.800.0270.0220.960X30.0152.42.50.800.0270.0240.965X40.0202.43.00.820.0260.0250.907X50.0142.42.80.780.0280.0100.924X60.0112.82.50.860.0340.0100.950X70.0212.82.00.840.0280.0180.944X80.0152.82.80.800.0300.0180.960X90.0123.22.60.750.0280.0200.908X100.0123.23.20.800.0280.0220.954
Table 4. The compared series and the referential series
Project numberArtifact
reuse
A1Team
expertise
A2Process
maturity
A3Functional
requirement stability A4Productivity (FP per hour)
A5Schedule unpredictability
A6Requirements completion ratio A7X01.001.001.001.001.001.001.00X10.300.7500.0901.600.83X20.100.7500.550.130.800.91X30.4000.420.550.131.531X40.9000.830.3601.600X50.3000.670.730.2500.29X60.000.500.430100.74X71.000.5000.180.250.530.64X80.400.500.670.550.50.530.91X90.101.000.501.000.250.660.02X100.101.001.0000.250.800.81
Table 5. The relational degree and the ranking
Artifact
reuse
A1Team
expertise
A2Process
Maturity
A3Functional
requirement stability A4Productivity (FP per hour)
A5Schedule predictability
A6Requirements completion ratio A7Relational degreeRankw(k)0.300.200.200.100.080.080.04- EMBED Equation.3 0.632.501.000.851.000.240.381.0882 EMBED Equation.3 0.832.501.000.480.790.380.351.1041 EMBED Equation.3 0.561.000.540.480.790.250.330.7393 EMBED Equation.3 0.361.000.380.580.500.241.000.5348 EMBED Equation.3 0.631.000.430.410.671.001.580.7334 EMBED Equation.3 00.500.541.000.331.000.400.42010 EMBED Equation.3 0.330.501.000.740.670.490.440.6595 EMBED Equation.3 0.560.500.430.480.500.490.350.4959 EMBED Equation.3 0.830.330.500.330.670.430.960.5687 EMBED Equation.3 0.830.330.331.000.670.380.380.5726 the ranking of the software project based on Grey analysis of the influence factors is:
EMBED Equation.3 .
The ranking is also listed in Table 6. It should be noted that the ranking will change as the weighting value for each evaluating factor are modified. In other words, suitable factors are selected by increasing weights, based on the software project requirements.
Table 6. The ranking of the projects
Rank12345678910Project numberX2X1X3X5X7X10X9X4X8X6
DISCUSSION
The enterprises and organizations try to understand their overall performance of software projects and compare it, with intention to find a way to improve. The software performance measures are core measures that should be identified as a part of a set of critical measures of success because they address important attributes of any software development project.
Organizations that are more experienced in measurement of software projects usually want to compare performance with their competitors. Before valid measurement comparison can be conducted, common operational definitions for performance measures have to be in place. In this way, organizations are able to efficiently compare software project performance among projects within their organizations as well as with projects outside of their organization.
Detailed monitoring of influence factors is a prerequisite for successful application of the Grey analysis. Monitoring should be performed by an expert quality assurance (QA) team. Having a QA team is quite common in any major company and it should be encouraged in mid-level companies as well.
In order to simplify the calculation of relation between the completed projects using GRA, a sample of only ten software projects have been chosen for this study. Gray system can be used to compare any number of software projects (two or more). Hence, the Grey theory imposes no restriction regarding the number of potentially analyzed projects.
The Grey system theory has been successfully applied to various fields and had made a success in analyzing uncertain systems. Traditional methods usually require a large amount of historical data in order to obtain a known statistical data distribution function to be able to make an accurate assessment and prediction of the required indicators [18].
In contrast to the traditional prediction methods, the main properties of the Grey theory are: 1) it does not need to make strict assumptions about the data set, and 2) it is used successfully to analyze uncertain systems that have multi-data inputs, discrete data, and insufficient data. These properties greatly simplify data collection and management, and also allow for timely predictions to be made, sometimes even faster and more accurate than artificial neural networks [19].
Grey system theory is somewhat different from Fuzzy logic approach. The emphasis of the Grey theory is on objects that have clearly defined external boundaries but vague or unknown position between the boundaries. The focus of Fuzzy logic is on objects whose properties have fuzzy or unclear external boundaries, but have a clear internal membership. Gathering knowledge about Grey systems makes grey objects more white or precise, while gathering knowledge about Fuzzy logic object makes us surer about its membership value, but the value is still fuzzy [20].
The obtained ranking of the projects is a function of both the seven influence factors and the weights that are used to specify which factor is more significant to take into consideration. Since the weights are specified by the involved subject, whoever he is, the final ranking is only a result of the analysis process by the Grey system theory; it is not the only possible solution. From the perspective of the evaluated projects, those that obtained higher ranking using Grey analysis now have an objective reason to be promoted and/or continued. Other projects will lack such a reason and would be considered as failures from the perspective of QA management, company director, competence centre, or other involved subjects.
CONCLUSION
Grey system based methods provide various tools to cope with situations of limited data, such as correlation analysis and modeling. Grey system theory aims to deal with the uncertainty of a system by using elements of relational analysis, operational research, system control, system modeling and system forecasting. Through quantitative analysis of Grey relation, it provides more accurate and subjective data. Most distinguished Grey theory methods that are in use are Grey relational analysis and Grey modeling.
The purpose of GRA is not to provide a general method for project evaluation, but a practical and applicable one, especially for solving some specific project evaluation question such as project quality control. GM provides a tool for modeling of discrete series with few data. Focus of GRA and GM is more on the method than on theoretical foundations. Further development of the methods and their foundations is required, particularly regarding comparison with known data and expert systems formalisms.
Based on the study in this paper, GRA can be applied to software projects ranking based on software project influence factors. This study adopted Grey system theory to propose a feasible and effective analysis method that could not be achieved using traditional statistical approaches. The final project ranking is dependent on the subjects preference of the influence factors and reflects the goal that needed to be achieved. The results indicate that the Grey system theory is a feasible and effective software project analysis method. This finding may serve as a reference to future studies in this and other research fields.
References
C. L. Chang, C. H. Tsai, L. Chen, Applying Grey Relational Analysis to the Decathlon Evaluation Model, International Journal of the Computer, The Internet and Management, vol. 11, no. 3, pp. 54-62, 2003.
Y. M. Chiang, H. H. Hsieh, The use of the Tagouchi method with grey relational analysis to optimize the thin-film sputtering process with multiple quality characteristics in color filter manufacturing, Computers & Industrial Engineering, vol.56, pp. 648-661, 2009.
T. Chih-Hung, C. Ching-Liang, C. Lieh, Applying Grey Relational Analysis to the Vendor Evaluation Model, International Journal of the Computer, The Internet and Management, vol. 11, no. 3, pp. 45-53, 2003.
N. H. Chiu, An early software quality classification based on improved grey relational classifier, Expert Systems with Applications, vol. 36, issue 7, pp. 10727-10734, 2009.
J. L. Deng, The introduction of grey system, The Journal of Grey System, vol. 1, no. 1, pp. 1-24, 1982.
C. Ebert, R. Dumke, Software Measurement, Berlin, Germany: Springer, 2007.
L. C. Hsu, C. H. Wang, Forecasting integrated circuit output using multivariate grey model and grey relational analysis, Expert Systems with Applications, vol. 36, issue 2, part 1, pp. 1403-1409, 2009.
J. C. Huang, The key factor of the internet information technology on the quality of life for the eldery: application of grey system theory, IEEE SMC eNewsletter, issue 33, 2010.
M. Kasunic, A Data Specification for Software Project Performance Measures: Results of a Collaboration on Performance Measurement, tech. rep., CMUS/SEI-2008-TR-012, 2008.
L. Meng, W. Kees, Grey System Theory and Applications: A way Forward, The Journal of Grey System, vol. 10, pp. 47-54, 2007.
R. S. Pressman, Software engineering a practitioners approach, New York, USA: McGraw Hill, 2005.
T. Stevenson, D. Carrington, P. Strooper, N. Sharon, An industry/university collaboration to upgrade software engineering knowledge and skills in industry, The Journal of Systems and Software, vol. 75, issues 1-2, pp. 29-39, 2005.
S. Suhk-Hook, Fuzzy-Bayes Fault Isolator Design for BLDC Motor Fault Diagnosis, International Journal of Control, Automation, and Systems, vol. 2, no. 3., pp. 354-361, 2004.
L. Sifen, J. Forrest, The Current Developing Status on Grey System Theory, The Journal of Grey System, vol. 2, pp. 111-123, 2007.
Y. Xiong, Grey Relational Evaluation of Financial Situation of Listed Company, Journal of Modern Accounting and Auditing, vol. 3, no. 2, pp. 41-44, 2007.
S. Liu, Y. Liu, Grey information: Theory and Practical Application with 60 Figures, London, England: Springer-Verlag, 2006.
F. Jovic, D. Krmpotic, A. Jovic, M. Jukic, Evaluation of Grey Prediction Method of Energy Consumption, in: Proceedings of the 28th International Convention on Information and Communication Technology, Electronics and Microelectronics MIPRO 2007, (Opatija, Croatia), CTS&CIS, pp. 64-67, 2005.
J. H. Stock, Time Series: Economic Forecasting, in: N. J. Smelser, P. B. Baltes, eds., International Encyclopedia of the Social& Behavioral Sciences, Elsevier Science Ltd., pp. 15721-15724, 2001.
D. Lim, P. Anthony, H. C. Mun, N. K. Wai, 6 8 : r p r x z
Ժ䱦zjbWOWOWOWGWO h=n CJ aJ hfP CJ aJ hG hU. CJ aJ hV8 CJ aJ hG h(7 5CJ( aJ( mHsHh 5CJ aJ h CJ aJ h&` CJ aJ h CJ aJ h0J h CJ aJ h0J h' CJ aJ h' 5CJ aJ h a CJ aJ h{ CJ aJ h3 CJ aJ h r 2 B ` 2 r ȸxp؈h h=n CJ aJ h`* CJ aJ hf>a CJ aJ h{ CJ aJ hXPr CJ aJ h a h
z* h 7 hXPr h 7 h 7 OY ! @" f" S# $ & & ( ) + + + , - - . g. h. / #0 Y0 T^T`gdGr ` gd
/ T:^T`:gdGr ` gd_9c gd_9c gdx gdQ gd{" ` gdXPr O& P& Q& f& l& & & & & & & & ' ' ' ' '' 3' G' Z' e' k' ' ' ' ' ' ( 1( 2( ]( ^( ( ( ) =) >) K) ) ) ) ) ) ) ) ) ) ) * * * * M* O* * * * * * * * * * + + + + + + + + + , ž hx hx h_9c hx hx hx mHsH h, h 7 h8t h 7 hk`k h 7 hk\ h8t h 7 h&A h 7 hx hi H , /, <, @, , , , , , , , , , 1- 2- n- - - - - - - - - - - - - - - . . -. U. ^. f. g. h. . . . . . 6/ / / / / / / 0 #0 X0 Z0 f0 0 0 0 0 0 0 0 0 1 1 ûҳ h_9c h_9c 5CJ aJ h& h_9c 5h
/ hi h h_9c hx mHsH hGr h_9c mHsH hk`k mHsH hx hx mHsH h8t hx hx hk`k @Y0 Z0 0 0 1 1 1 1 1 1 S kd $$If l F
1 "
t 0 4 4
l a yt_9c $$If a$gd_9c $a$gd_9c ` gd
/ 1 1 1 "1 *1 +1 >1 ?1 U1 V1 o1 p1 1 1 1 1 1 1 1 1 2 2 2 2 =2 >2 W2 X2 u2 v2 2 2 3 3 3 3 23 33 63 73 s3 t3 3 3 .4 /4 4 4 "5 #5 5 5 6 6 J7 K7 7 7
8 8 8 8 H8 ǿdzǨǨǨǨǨǨǨǤ h
/ h h ha h_9c CJ aJ ha h_9c 5CJ aJ ha h_9c 5 ha h_9c hi CJ aJ ha CJ aJ h_9c ha CJ aJ h? CJ aJ h_9c h_9c CJ aJ h_9c >1 &1 *1 +1 -1 <1 >1 ^ R $$If a$gd_9c kd $$If l F
1 "
t 0 4 4
l a yt_9c $If gd 8 $If gd? >1 ?1 A1 N1 U1 p d [ [ $If gd 8 $$If a$gd_9c kdV $$If l F
1 "
t 0 4 4
l a yt_9c U1 V1 X1 k1 o1 p d [ [ $If gd 8 $$If a$gd_9c kd $$If l F
1 "
t 0 4 4
l a yt_9c o1 p1 r1 1 1 p d [ [ $If gd 8 $$If a$gd_9c kd $$If l F
1 "
t 0 4 4
l a yt_9c 1 1 1 1 1 p d [ [ $If gd 8 $$If a$gd_9c kdW $$If l F
1 "
t 0 4 4
l a yt_9c 1 1 1 1 1 p d [ [ $If gd 8 $$If a$gd_9c kd $$If l F
1 "
t 0 4 4
l a yt_9c 1 1 1 1 1 p d [ [ $If gd 8 $$If a$gd_9c kd $$If l F
1 "
t 0 4 4
l a yt_9c 1 1 1 1 2 p d [ [ $If gd 8 $$If a$gd_9c kdX $$If l F
1 "
t 0 4 4
l a yt_9c 2 2
2 2 2 p d [ [ $If gd 8 $$If a$gd_9c kd $$If l F
1 "
t 0 4 4
l a yt_9c 2 2 #2 02 =2 p d [ [ $If gd 8 $$If a$gd_9c kd $$If l F
1 "
t 0 4 4
l a yt_9c =2 >2 A2 R2 W2 p d [ [ $If gd 8 $$If a$gd_9c kdY $$If l F
1 "
t 0 4 4
l a yt_9c W2 X2 [2 s2 u2 p d [ [ $If gd 8 $$If a$gd_9c kd $$If l F
1 "
t 0 4 4
l a yt_9c u2 v2 y2 2 2 p d [ [ $If gd 8 $$If a$gd_9c kd $$If l F
1 "
t 0 4 4
l a yt_9c 2 2 2 2 3 63 73 83 t3 p k k k k b Y M $ ` a$gd_9c ` gd_9c ` gd
/ gd_9c kdZ $$If l F
1 "
t 0 4 4
l a yt_9c t3 {3 3 3 3 3 3 3 ^ N N $ $If ` a$gd_9c kd
$$If l F 0
t 0 6 4 4
l a yt= $ $If ` a$gd= 3 .4 /4 14 @4 4 a Q Q $ $If ` a$gd_9c kd
$$If l F 0
t 0 6 4 4
l a yt_9c
$If ` gd_9c 4 4 4 4 "5 n ^ ^ Q
$If ` gd_9c $ $If ` a$gd_9c kdm $$If l F 0
t 0 6 4 4
l a yt_9c "5 #5 %5 F5 5 n ^ ^ Q
$If ` gd_9c $ $If ` a$gd_9c kd! $$If l F 0
t 0 6 4 4
l a yt_9c 5 5 5 5 6 n ^ ^ Q
$If ` gd_9c $ $If ` a$gd_9c kd $$If l F 0
t 0 6 4 4
l a yt_9c 6 6 6 6 J7 n ^ ^ Q
$If ` gd_9c $ $If ` a$gd_9c kd
$$If l F 0
t 0 6 4 4
l a yt_9c J7 K7 M7 k7 7 n ^ ^ Q
$If ` gd_9c $ $If ` a$gd_9c kd= $$If l F 0
t 0 6 4 4
l a yt_9c 7 7 8 8 d9 e9 9 : n e Q H H e e ` gdl+ Bd x < ^B`gdl+ ` gda kd $$If l F 0
t 0 6 4 4
l a yt_9c H8 8 8 8 9 9 `9 a9 c9 d9 e9 w9 ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; '< (< ;< << Ȼϭȋȓ}pȓb jbQ
ha ha UVjP ha ha EHUjbQ
ha ha UVh
/ ha 6j ha ha U j ha ha 6EHU jbQ
ha ha UVj ha ha 6U ha ha ha ha 6 ha h hl+ hi ha hl+ ha hl+ 5h h
/ h !: ; ; ]< 1= 2= = > > %? ,? ? @ X@ @ @ @ !B zC {C _D D JE E E ` gd< = = 2= D= > !> > > > > > > > > !? "? $? %? *? +? ,? 2? O? W? ? ? ? ? ? ? ? ? ? @ @ @ )@ -@ .@ 3@ Q@ X@ ^@ _@ @ @ @ @ ǿԄ hU 6U 7U HU MU U U U
V V V W 5W W W W 4X MX YX X Y Y !Z >Z qZ Z Z Z Z Z [ [ [ [ [ \ \ \ 7\ 8\ e\ f\ j\ k\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ӹӴӴӬӥӥӚ h mHsH h} h mHsH h@ h h8 h 6 h 6h@ h 6h hA h( 5 hYrt 5h hny h`* hX hX h8 hpf hM hM hM hX hX 97U V 5X Y Z [ [ 8\ \
] y] ] ] ^ Q^ $ d ` a$gdq $ d ` a$gdYrt
d ` gdh $ d ` a$gd'^ $ x < ^ ` a$gdYrt $ d ` a$gdA $
& F
) d ^ `a$gd \ \ \ \ \ \ \ \ ] ] ] ] ]
] ] ] $] %] &] '] (] *] C] E] c] e] x] y] u^ v^ ^ ^ ^ ^ ^ ^ ^ qf^ h h 5j1 hS h Uj h UmH nH u h j h Uhq hYrt ha h_9c 6hA j/ ha h_9c EHUj =Q
ha h_9c UV ha hh hl+ ha h'^ j, ha hh EHUjWQ
ha hh UVj ha h_9c U ha h_9c h@ h $Q^ u^ ^ ^ _ _ /` X` ` ` a a Wa a b Eb $
d ^ a$gd'^ $
& F
d 7$8$^ ` a$gd'^ $ d ` a$gd'^ $ d ` a$gd'^ $ d ` a$gdO $ a$gd gd
$d a$gdA ^ ^ ^ ^ ^ ^ _ _ D_ S_ s_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ /` 0` C` D` E` F` K` P` R` S` ´wjfhc^ j5 hc^ hc^ EHUj(R
hc^ UVj ha h_9c U ha h'^ hl+ ha h'^ CJ aJ !jv2 ha h'^ CJ EHUaJ jWQ
ha h'^ UVha h_9c CJ aJ j ha h_9c CJ UaJ ha hO ha h_9c h hA 5h h 5 h 5 (S` U` V` W` X` b` c` p` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` Va Wa a a a a a a a a a a a a a a a a b b b =b Cb db fb b b b b b c
c 'c Cc ha h_9c 6jq; ha ha EHUjbQ
ha ha UVhi h( ha hh j|8 hc^ hc^ EHUjR
hc^ UVj ha h_9c U ha hO ha h'^ ha h_9c hl+ 9Eb b c
c |c c c ed e e ef g g h i ` gd$ ` gd( ` gd
& F ^ ` gd(
` gd $ d ` a$gd'^ $ d ` a$gd'^ $
& F
d 7$8$^ ` a$gd'^ Cc Dc Wc Xc Yc Zc uc xc yc zc |c }c c c c c c c c c c c c c c c c c c c d d d Hd dd ed pd td wd xd d d ÿ홒wpp홠 ha h'^ j&C ha h! EHUj.lQ
ha h! UV ha hh ha hO hl+ j+@ ha h'^ EHUjWQ
ha h'^ UVhYrt hi h( ha h) j8> ha h_9c EHUjQQ
ha h_9c UV ha h_9c j ha h_9c U )d d d d d d d d d e e 3e @e He Je Se Ze e e e e e e e e e e e f =f Af df ef jf f g g g *g +g Ag ag g g g g g g h
h 6h 7h Ah Uh »´ѴѴʹѴѴ¥ h4 h( hl+ mHsH h< h( mHsH h( mHsH ha h( ha h h( h( h( ha h hl+ ha hO ha h_9c 6 ha h_9c j ha h_9c UjE ha h_9c EHU 5Uh Wh ch eh kh h h h h h h h h i i i i !i -i .i :i ;i Gi Hi Ui Vi bi ci i i i i i i i j j Ij j j k l wl h h CJ aJ hc 5CJ aJ h h 5CJ aJ h h 5 h 5 h?g 5h?g h?g mHsH h mHsH h( mHsH hn h( mHsH h h( 6h h 6h h h( hT h
/ hl+ h&] h4 h( h( h( 6 )i i j Ij Xj aj gj jj oj yj |j j j j j j j j j j k k k $ $If ` a$gd FfH $ d $If ` a$gd $a$gd $ a$gd?g k k k #k (k .k 4k :k $ $If ` a$gd :k ;k kdJ $$If T l ִ g
IZk O$ ~ ~ C
t 0 6 4 4
l a yt T ;k >k Dk Hk Lk Qk Wk ]k ck $ $If ` a$gd ck dk kdK $$If T l ִ g
IZk O$ ~ ~ C
t 0 6 4 4
l a yt T dk gk mk qk uk zk k k k $ $If ` a$gd k k kdL $$If T l ִ g
IZk O$ ~ ~ C
t 0 6 4 4
l a yt T k k k k k k k k k $ $If ` a$gd k k kdM $$If T l ִ g
IZk O$ ~ ~ C
t 0 6 4 4
l a yt T k k k k k k k k k $ $If ` a$gd k k kdN $$If T l ִ g
IZk O$ ~ ~ C
t 0 6 4 4
l a yt T k k k k k k k l l $ $If ` a$gd l l kdO $$If T l ִ g
IZk O$ ~ ~ C
t 0 6 4 4
l a yt T l l l l l l $l *l 0l $ $If ` a$gd 0l 1l kdP $$If T l ִ g
IZk O$ ~ ~ C
t 0 6 4 4
l a yt T 1l 4l :l >l Bl Gl Ml Sl Yl $ $If ` a$gd Yl Zl kdQ $$If T l ִ g
IZk O$ ~ ~ C
t 0 6 4 4
l a yt T Zl ]l cl gl kl pl vl |l l $ $If ` a$gd l l kdS $$If T l ִ g
IZk O$ ~ ~ C
t 0 6 4 4
l a yt T l l l l l l l l l $ $If ` a$gd l l kdT $$If T l ִ g
IZk O$ ~ ~ C
t 0 6 4 4
l a yt T l l l l l l m m m m m m #m ,m /m :m Sm nm qm m m m $ $If ` a$gdf>a $ ` a$gd ` gd ` gd l l l l l l #m $m om pm m 1o 2o 3o 4o ;o a 5CJ aJ hc, 5CJ aJ hc, hc, 5CJ aJ hc, hR 5CJ aJ hf>a 5mHsHhR hR mHsH hR hR 5mHsHhc, 5mHsHh$ 5mHsHh
/ 5mHsHh h h CJ aJ hc hc 5CJ aJ hc 5CJ aJ hc h 5CJ aJ h h 5 h$ 5 h 5h m m kd U $$If T l ִ g
IZk O$~ ~ C
t 0 6 4 4
l a ytf>a T m m m m m m m m m $ $If ` a$gd m m kdV $$If T l ִ g
IZk O$ ~ ~ C
t 0 6 4 4
l a ytc T m m m m m m m m m $ $If ` a$gd m m kdW $$If T l ִ g
IZk O$ ~ ~ C
t 0 6 4 4
l a ytc T m m n n n
n n n n $ $If ` a$gd n n kdX $$If T l ִ g
IZk O$ ~ ~ C
t 0 6 4 4
l a ytc T n n %n 'n ,n 1n 6n ;n =n $ $If ` a$gd =n >n kd Y $$If T l ִ g
IZk O$ ~ ~ C
t 0 6 4 4
l a ytc T >n An Fn Hn Mn Rn Tn Yn [n $ $If ` a$gd [n \n kd#Z $$If T l ִ g
IZk O$ ~ ~ C
t 0 6 4 4
l a ytc T \n _n dn fn kn pn un wn |n $ $If ` a$gd |n }n kd'[ $$If T l ִ g
IZk O$ ~ ~ C
t 0 6 4 4
l a ytc T }n n n n n n n n n $ $If ` a$gd n n kd+\ $$If T l ִ g
IZk O$ ~ ~ C
t 0 6 4 4
l a ytc T n n n n n n n n n $ $If ` a$gd n n kd/] $$If T l ִ g
IZk O$ ~ ~ C
t 0 6 4 4
l a ytc T n n n n n n n n n $ $If ` a$gd n n kd3^ $$If T l ִ g
IZk O$ ~ ~ C
t 0 6 4 4
l a ytc T n n n n n n o o o $ $If ` a$gd o o kd7_ $$If T l ִ g
IZk O$ ~ ~ C
t 0 6 4 4
l a ytc T o o o o o !o &o +o 0o $ $If ` a$gd 0o 1o kd;` $$If T l ִ g
IZk O$ ~ ~ C
t 0 6 4 4
l a ytc T 1o 2o 3o 4o co do mo so vo {o o o o o o o o o o o o p -p 2p 3p Ffb $ $If ` a$gdc, $ ` a$gdc, ` gd
/ gd
/ 3p 4p ^p _p `p sp tp up vp p p p p p p p p p p p p p p *q +q ,q ?q @q Aq Bq nq 蟐~o]N jx hc, hR CJ UaJ #jqAQ
hc, hR CJ UVaJ jCs hc, hR CJ UaJ #j%AQ
hc, hR CJ UVaJ jm hc, hR CJ UaJ #jAQ
hc, hR CJ UVaJ j#h hc, hR CJ UaJ #jAQ
hc, hR CJ UVaJ j hc, hR CJ UaJ hR hR hc, hR CJ aJ hSE hSE 6CJ aJ 3p 8p =p Bp Gp Lp Qp Vp [p ]p ^p _p wp |p p p p p p p p p p p p p p Ffk Ffe $ $If ` a$gdc, p p p p p p p p p q q q q q q "q (q *q +q Cq Hq Mq Rq Wq \q aq fq Ffv Ff q $ $If ` a$gdc, fq lq nq oq q q q q q q q q q q q q q q q q q q q q q q
r Ff[ Ff́ Ff<| $ $If ` a$gdc, nq oq pq q q q q q q q q q q q q q q r
r r r 8r 9r :r Mr Nr Or Pr |r }r ~r r ;߬ߋ|j[ j hc, hR CJ UaJ #j AQ
hc, hR CJ UVaJ j hc, hR CJ UaJ #jAQ
hc, hR CJ UVaJ j hc, hR CJ UaJ #jAQ
hc, hR CJ UVaJ jc~ hc, hR CJ UaJ #jAQ
hc, hR CJ UVaJ hc, hR CJ aJ j hc, hR CJ UaJ hR hR
r r r r !r &r +r 0r 6r 8r 9r Qr Vr [r `r er jr or tr zr |r }r r r r r r Ff{ Ff $ $If ` a$gdc, r r r r r r r r r r r s s s ]s ^s _s rs ss ts us ws xs |s s s ĽīĽyn]yYQIQ hf>a mHsH hpf mHsH hR !j h7 h$ EHUmHsHj,PTQ
h$ UVj h$ UmHsHh( h$ mHsH h$ mHsH hc, j1 hc, hR CJ UaJ #jVAQ
hc, hR CJ UVaJ hR hR hc, hR CJ aJ j hc, hR CJ UaJ j hc, hR CJ UaJ #j>AQ
hc, hR CJ UVaJ r r r r r r r r r r r r r r r s s s s ^s ws xs t $a$gdc, $ a$gd$ ` gd$ ` gd'^ Ff Ff
$ $If ` a$gdc, s s s s s s s t
t t 0t 4t =t Jt Tt t t t t t t t t t t t t t t t teVetR h hf>a hf>a CJ aJ mHsH hf>a hc, CJ aJ mHsH hc, hc, CJ aJ mHsH hc, hc, 5CJ aJ mHsHhf>a 5CJ aJ mHsHhf>a 5mHsHhc, hc, 5mHsHhc, 5mHsHhc, mHsH h{ mHsH h?g mHsH h'X1 mHsH hpf mHsH h( hpf mHsH h( hpf mHnHsHtH t t t t t t t t t t t t t t t t t t t t t t t t $ $If ` a$gdf>a Ff $ $If ` a$gd^b ` gdc, $a$gdc, t t t t t t hv .x Uy z | } & $ d ` a$gd $ d ` a$gdc, gdc, ` gd0 ` gdkN $ d ` a$gdkN $ ` a$gd"D gd ` gd'^ Ff $ $If ` a$gd^b t t !u Iu Ju Mu Nu ^u bu ou u u u u u u u u v v v v v v v Iw Uw ^w zw ~w w w w w w +x .x /x Ex Wx x x x x Uy yy y y y y y &z iz xz z z z z z z z z z { { | | } } } }
~ ~ -~ ʿʿʻʻ h0 h'X1 h0 h0 h0 hkN h"D h"D h-# h-# h-# h"D hW h"D hW h$ h$ h0 h I-~ .~ 6~ 7~ 8~ 9~ f~ j~ ~ ~ 1 6 = > G S " % &
) = @ q
4 < l { ~ + , ( , 0 8 = N O P ļļļģğ hH h0 h h0 h h h hc, h hk! h0 hc, h0 hSE h+G hHp{ h&] hSE h h'X1 h$ h0 h0 hkN h0 h~Q >P X j r ߇ % Lj ҈ Y { | } ى 4 W X ^ f l q r s t " # $ F X ĸx h? h_qi CJ aJ h? hc, 6CJ aJ h? CJ aJ h? h^b CJ aJ h? hc, CJ aJ h? h? CJ aJ h? CJ aJ mHsH h_qi CJ aJ mHsH h hc, h0 h h0 h 7 h+G h h0 h h0 hc, hH / } W c 4 R k # ԏ S N Ғ n
& F e^e`gd
& F e^e`gdy
& F e^e`gdi
& F e^e`gd_qi
& F gdc, $ d ` a$gd X c d g q u ŋ Ƌ ͋ ϋ 4 5 ; ? @ A B nj Ќ 1 D E R S V ] ` g { : @ A E V Y Z k ¶hi hc, 6CJ aJ hi hi 6CJ aJ hi CJ aJ h? hc, 6CJ aJ h? CJ aJ h? h_qi CJ aJ h? hc, CJ aJ Hk l r w x y z " # ' * 3 4 ԏ ۏ ݏ 6 8 R S Y c Ϲ⭞}n hy hc, CJ aJ mHsH hy hy CJ aJ mHsH "hy hy 6CJ ]aJ mHsH hy 6CJ ]aJ mHsH h'X1 hy 6CJ aJ hy hy CJ aJ hy hc, CJ aJ hy CJ aJ hi hc, CJ aJ h? hc, CJ aJ hi CJ aJ h? h_qi CJ aJ 'c P S v x } ) 4 : H L M N V X c d e ̒ Ғ Ւ ܒ ݒ ! " # L N O R S V W Y Z ] h m n x h? h CJ aJ hy h^b 6CJ aJ hy 6CJ aJ hy hc, 6CJ aJ hy hc, CJ aJ hy CJ aJ h? hc, CJ aJ h? hc, 6CJ aJ Ax ~ Ó ӓ W ? @ F I U _ f g Ε ԕ { | T V W ÷ï֤ˍ֤֤֤֍֤֤tl h+\ CJ aJ h? h0 CJ aJ h? hkN 6CJ aJ Uh| hkN 6CJ aJ h| hkN CJ aJ h? hkN CJ aJ h, CJ aJ h'X1 h'X1 6CJ aJ h'X1 CJ aJ h| h| CJ aJ h| CJ aJ h| hM CJ aJ h? hM 6CJ aJ h? hM CJ aJ * ԕ ؍ ٍ ڍ ۍ ܍ ލ ߍ * + R gdJ gd gdJ e ^e` gd ` gd0
& F e^e`gd
& F e^e`gd Assessing the Accuracy of Grey System Theory Against Artificial Neural Network in Predicting Online Auction Closing Price, in: Proceedings of the International Multi Conference of Engineers and Computer Scientists 2008, Vol. 1 IMECS 2008, (Honk Kong, China), pp. 19-24, 2008.
Y. Yang, R. John, Grey Systems and Interval Valued Fuzzy Sets, in: Proceedings of the 3rd Conference of the European Society for Fuzzy Logic and Technology, (Zittau, Germany), pp. 193-197, 2003.
Set up the ranking of software projects based on influence factors
Calculation of Grey relational degree:
getting absolute difference of compared series and
referential series using formula (11)
find out minimum and maximum
choose the constant p (set to 0.5)
calculation of relational coeficient and relational degree
using formulas (12) and (13)
Standardized data transformation, formulas:
I) the bigger the better (8),
II) the smaller the better (9), or
III) nominal-the best (10)
Setting up eigenvalue
matrix, input original data
W X l n Í ō Ǎ ȍ Ѝ ؍ ٍ ڍ ܍ ݍ ߍ * + I P ˎ ώ ߎ Ƚ{o{{ hx CJ aJ mHsH h CJ aJ mHsH h! CJ aJ mHsH hx h CJ aJ mHsH h(7 j hEh UhEh h hWIW CJ aJ hWIW h CJ aJ h? h0 CJ aJ h? h CJ aJ h+\ h 6CJ H*aJ h+\ h 6CJ aJ h| CJ aJ %R ˎ * H I v ď e ^e` gd h7$8$^hgdx 7$8$gdx gd gdJ q 7$8$^q gdx
& F"
q 7$8$^q `gdx ߎ + F H I V [ v ď Ə ȏ Џ я ༱༱Ģ h hWIW CJ aJ h hx h CJ aJ hx CJ aJ h(7 h CJ aJ mHsH hx CJ aJ mHsH hx h CJ aJ mHsH hx h 6CJ aJ mHsH > &P 1 P :p($/ . A!"# $% P T= 0 &P 1 P :p . A!"# $% T= 0 &P 1 P :p . A!"# $% T= 0 &P 1 P :pc, . A!"# $% TA 0 &P 1 P :p . A!"# $% P T $$If !v h5 15" 5#v 1#v" #v:V l
t 0 5 15" 5yt_9c $$If !v h5 15" 5#v 1#v" #v:V l
t 0 5 15" 5yt_9c $$If !v h5 15" 5#v 1#v" #v:V l
t 0 5 15" 5yt_9c $$If !v h5 15" 5#v 1#v" #v:V l
t 0 5 15" 5yt_9c $$If !v h5 15" 5#v 1#v" #v:V l
t 0 5 15" 5yt_9c $$If !v h5 15" 5#v 1#v" #v:V l
t 0 5 15" 5yt_9c $$If !v h5 15" 5#v 1#v" #v:V l
t 0 5 15" 5yt_9c $$If !v h5 15" 5#v 1#v" #v:V l
t 0 5 15" 5yt_9c $$If !v h5 15" 5#v 1#v" #v:V l
t 0 5 15" 5yt_9c $$If !v h5 15" 5#v 1#v" #v:V l
t 0 5 15" 5yt_9c $$If !v h5 15" 5#v 1#v" #v:V l
t 0 5 15" 5yt_9c $$If !v h5 15" 5#v 1#v" #v:V l
t 0 5 15" 5yt_9c $$If !v h5 15" 5#v 1#v" #v:V l
t 0 5 15" 5yt_9c $$If !v h5 15" 5#v 1#v" #v:V l
t 0 5 15" 5yt_9c $$If !v h5 15" 5#v 1#v" #v:V l
t 0 5 15" 5yt_9c $$If !v h5 055
#v 0#v#v
:V l
t 0 6 , 5 055
yt= $$If !v h5 055
#v 0#v#v
:V l
t 0 6 , 5 055
yt_9c $$If !v h5 055
#v 0#v#v
:V l
t 0 6 , 5 055
yt_9c $$If !v h5 055
#v 0#v#v
:V l
t 0 6 , 5 055
yt_9c $$If !v h5 055
#v 0#v#v
:V l
t 0 6 , 5 055
yt_9c $$If !v h5 055
#v 0#v#v
:V l
t 0 6 , 5 055
yt_9c $$If !v h5 055
#v 0#v#v
:V l
t 0 6 , 5 055
yt_9c $$If !v h5 055
#v 0#v#v
:V l
t 0 6 , 5 055
yt_9c D d
, b
! " # $ % & ' ( ) * + , - . / 0 1 2 3 4 5 6 7 8 9 : ; < = > ? @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z [ \ ] ^ _ ` a b c d e f g h i j k l m n o p q r s t u v w x y z { | } ~ R o o t E n t r y F 0% 7 D a t a
U W o r d D o c u m e n t @ O b j e c t P o o l j0% _ 1 3 6 5 4 3 5 8 2 7 F j O l e
C o m p O b j f O b j I n f o
# & ' ( + . / 0 3 6 7 8 9 : = @ A D G H I L O P S V W X Y Z [ ^ a d g h i l o p q t w x y |
F Microsoft Equation 3.0 DS Equation Equation.3 9q zª wY LV
A r t i f a c t r e u s e = P E S a v e d
P E T o t a l
"1 0 0 E q u a t i o n N a t i v e _ 1 3 6 5 4 3 5 8 6 5 F O l e
C o m p O b j
f
F Microsoft Equation 3.0 DS Equation Equation.3 9q z. {Y V
P E S a v e d
F Microsoft Equation 3.0 DS Eq O b j I n f o
E q u a t i o n N a t i v e J _ 1 3 6 5 4 3 5 8 8 3 F O l e
C o m p O b j f O b j I n f o E q u a t i o n N a t i v e J _ 1 3 6 5 4 3 6 0 8 3 F uation Equation.3 9q z. Z V
P E T o t a l
F Microsoft Equation 3.0 DS Equation Equation.3 9q O l e
C o m p O b j f O b j I n f o E q u a t i o n N a t i v e z 5 L2
T E = ( T E r e q , T E a r c h , T E d d , T E c o d e , T E s t )
F Microsoft Equation 3.0 DS Equation Equation.3 9q z[ @X LV
F R S = R _ 1 3 6 5 4 4 4 3 1 6 6 F O l e
C o m p O b j f O b j I n f o E q u a t i o n N a t i v e w _ 1 3 6 6 0 4 1 2 4 1 1 ' F O l e
! C o m p O b j " f T
"R C
R T
F Microsoft Equation 3.0 DS Equation Equation.3 9q $ 8X LV
T e a m P r o d u c t i v i t y = P r o j e c t s i z e P r o j e c t O b j I n f o ! $ E q u a t i o n N a t i v e % _ 1 3 6 6 0 4 1 2 9 6 $ F O l e
) e f f o r t
F Microsoft Equation 3.0 DS Equation Equation.3 9q $ X V
T e a m P r o d u c t i v i t y = 1 3 0 5 3 0 0 = 0 . 0 2 5 ) F P C o m p O b j # % * f O b j I n f o & , E q u a t i o n N a t i v e - _ 1 3 6 6 0 4 1 3 0 7 " O ) F h o u r [ ]
F Microsoft Equation 3.0 DS Equation Equation.3 9q $* pjZ |V
S P = P r o j e c t d u r a t . "E s t i m . p r o j e c t d u r a O l e
1 C o m p O b j ( * 2 f O b j I n f o + 4 E q u a t i o n N a t i v e 5 F t . E s t i m a t e d p r o j e c t d u r a t i o n "1 0 0
F Microsoft Equation 3.0 DS Equation Equation.3 9q zn ) &
S P = 3 2 5 _ 1 3 6 5 4 3 8 2 8 8 . F O l e
; C o m p O b j - / < f O b j I n f o 0 > E q u a t i o n N a t i v e ? _ 1 3 6 5 4 4 3 0 3 5 , 3 F O l e
B C o m p O b j 2 4 C f "3 1 6 3 1 6 "1 0 0 = 2 . 8 5 %
F Microsoft Equation 3.0 DS Equation Equation.3 9q z (Z LW
R C R = S a t i s f i e d r e q u i r e m O b j I n f o 5 E E q u a t i o n N a t i v e F _ 1 3 6 5 4 9 2 0 3 7 8 F O l e
J e n t s P l a n n e d r e q u i r e m e n t s "1 0 0
F Microsoft Equation 3.0 DS Equation Equation.3 9q j i/ 1
R C R = 2 8 3 4 "1 0 0 % = 8 2 . 3 5 C o m p O b j 7 9 K f O b j I n f o : M E q u a t i o n N a t i v e N _ 1 3 6 4 7 1 3 8 9 0 E = F %
F Microsoft Equation 3.0 DS Equation Equation.3 9q / 1
x 1
( 1 ) , x 1
( 2 ) , . . . . . x 1
( n ) x 2
( 1 ) O l e
Q C o m p O b j < > R f O b j I n f o ? T E q u a t i o n N a t i v e U , x 2
( 2 ) , . . . . x 2
( n ) . . . . . . . . x m
( 1 ) , x m
( 2 ) , . . . . x m
( n ) [ ]
F Microsoft Equation 3.0 DS Equation Equation.3 9q _ 1 3 6 3 0 1 6 2 2 3 B F O l e
\ C o m p O b j A C ] f O b j I n f o D _ E q u a t i o n N a t i v e ` C _ 1 3 6 4 7 1 4 4 0 4 ^ G F O l e
b C o m p O b j F H c f n'
x i
( k )
F Microsoft Equation 3.0 DS Equation Equation.3 9q p-0 1
x i
( k ) = x i
( k ) "m i n x O b j I n f o I e E q u a t i o n N a t i v e f _ 1 3 8 5 5 5 7 5 4 4 L F O l e
j i
( k ) m a x x i
( k ) "m i n x i
( k )
F Microsoft Equation 3.0 DS Equation Equation.3 9q
x i
( k ) = m a x x i
( k ) "x C o m p O b j K M k f O b j I n f o N m E q u a t i o n N a t i v e n _ 1 3 8 5 5 5 7 3 9 0 c J Q F i
( k ) m a x x i
( k ) "m i n x i
( k )
F Microsoft Equation 3.0 DS Equation Equation.3 9q D
x i
( k ) = x i
( k ) "x 0 O l e
r C o m p O b j P R s f O b j I n f o S u E q u a t i o n N a t i v e v
( k ) m a x x i
( k ) "x 0
( k )
F Microsoft Equation 3.0 DS Equation Equation.3 9q z~ {Y V
x i
( k ) = x 0
( k ) "x i _ 1 3 6 5 4 3 5 7 8 8 ; V F O l e
z C o m p O b j U W { f O b j I n f o X } E q u a t i o n N a t i v e ~ _ 1 3 6 4 3 1 5 0 3 1 [ F O l e
C o m p O b j Z \ f
V X ! " # $ % & ' ( ) * + , - . / 0 1 2 3 4 5 6 7 8 9 : ; < = > ? @ A B C D E F G H I J K L M N O P Q R S T U \ W Y [ Z ] ^ _ ` a b c d e f g h j k l m p q r s t u v w x y z { | } ~
( k )
F Microsoft Equation 3.0 DS Equation Equation.3 9q i
F Microsoft Equation 3.0 DS Eq O b j I n f o ] E q u a t i o n N a t i v e ) _ 1 3 6 4 7 1 4 6 7 6 ` F O l e
C o m p O b j _ a f O b j I n f o b E q u a t i o n N a t i v e _ 1 3 6 6 0 4 4 3 5 6 e F uation Equation.3 9q a0 <;0
i
( k ) = m i n + p m a x x i
( k ) + p m a x
F Microsoft Equation 3.0 DS Equation Equation.3 9q O l e
C o m p O b j d f f O b j I n f o g E q u a t i o n N a t i v e y $] Hg Le
r i
= w ( k ) ( k ) [ ]
"
F Microsoft Equation 3.0 DS Equation Equation.3 9q
1 _ 1 3 6 3 2 7 0 1 1 5 @ m j F O l e
C o m p O b j i k f O b j I n f o l E q u a t i o n N a t i v e 6 _ 1 3 6 3 2 7 0 1 4 5 o F O l e
C o m p O b j n p f
F Microsoft Equation 3.0 DS Equation Equation.3 9q "
2
F Microsoft Equation 3.0 DS Equation Equation.3 9q O b j I n f o q E q u a t i o n N a t i v e 6 _ 1 3 6 3 2 7 0 1 8 1 h | t F O l e
C o m p O b j s u f O b j I n f o v E q u a t i o n N a t i v e 6 _ 1 3 6 3 2 7 0 2 5 7 y F pY D'
3
F Microsoft Equation 3.0 DS Equation Equation.3 9q p
4 O l e
C o m p O b j x z f O b j I n f o { E q u a t i o n N a t i v e 6 _ 1 3 6 3 2 7 0 2 9 3 w ~ F O l e
C o m p O b j } f O b j I n f o
F Microsoft Equation 3.0 DS Equation Equation.3 9q G
5
F Microsoft Equation 3.0 DS Equation Equation.3 9q E q u a t i o n N a t i v e 6 _ 1 3 6 3 2 7 0 3 5 0 F O l e
C o m p O b j f O b j I n f o E q u a t i o n N a t i v e 6 _ 1 3 6 3 2 7 0 4 0 7 r T F O l e
z
6
F Microsoft Equation 3.0 DS Equation Equation.3 9q p}
7
F Microsoft Equation 3.0 DS Eq C o m p O b j f O b j I n f o E q u a t i o n N a t i v e 6 _ 1 3 6 3 2 7 0 4 3 2 F O l e
C o m p O b j f O b j I n f o E q u a t i o n N a t i v e 6 uation Equation.3 9q `s T*
8
F Microsoft Equation 3.0 DS Equation Equation.3 9q Y }
9 c $ A ? ? 3 " ` ? 2 Aړr$Ci `! Aړr$Ci @ xROKQ7 tHAA H+I 6y.
}N C}2Yͼ]#y3PKc
>J-#R/cb 1udߑvC20T ~LL9 " %*h6MZ98߰; !/TV[YNn6 ŮEgcr
Z 1ˆa9cSoQYKFhw j!W
N̰%A FwV{V"Ji5 FaM*ˉ~eQzJNooz} ݷ=<%\ ruҶ䜙=zˮV#yC4!rt>ʤ -xN۶9 wD#m0>pzk D d
h b
c $ A
? ? 3 " ` ? 2 f ,3; >{ B `!: ,3; >{Ȗ @ (+ | xcdd``> $X bbd12 ,(ㆫar`Z"Wcgb q SaP5< %! `3) ,L !
~
Ay " %'50F K ʠ 4 Hq=`Tb?8,5jf? j&#@9W 0\Av|%(|vBcdbR
,.Ie J=.f aYl }H D d
h b
c $ A ? ? 3 " ` ? 2 f 2=[ $X bbd12 ,(ㆫar`r`3H1 g` YKA<@øjx|K2B* RvfR `[YB2sSRsD>J0O+k`*KL4Ah*6z(rH~Ib̆@ LF> F\
.0b`p%ؗa%
M RI)$5>ȭ W1t1 `;@ 'H D d
@ b
c $ A ? ? 3 " ` ? 2 5$;a.b& `! 5$;a.b& 8' v xRJQ=VZ-E(Z9hM5;m
Zp?BHA-{3AЃǼsν D E I
)NH)/R>&~996uLY۷瘲\_V34 YkfwۨW/ 8=LJcCJoe_ ޚױ0 u8_<ҽ e3fԣ1 0c^ ;n̈́$Q y
>-NSNQKz[6x
ٷmrU1Lhʪ GœXڱuq2g#CCNcuʷuXkAmkjJ7mjeYqvKnKA0oVwnQy
.Ҭ,ޕv>P79dW\@.M_)E6 Qx["BKlVi] D d
l b
c $ A ? ? 3 " ` ? 2 Q HTއv䋝E{; - z `!% HTއv䋝E{; ) xSOQ,.Ej1 'ڋQV]BZJxN$ N@8x!6Zg҄@%owۙo7oVv?pyRdOSjQ6;s:J#mq佑- ֎q0].7 M2du Ң&AGl +&>M'5M]x>Q2`qzF~զt$k_GZ N%~Jxyᵦ+: e߫g\bD ,/J`P.Ѭ4j_
QCfkv)xZ%
ӡa.҈>C+ k"b ړ"e@ldZ 9x6kWApguo~_nFqp E'J&;͛~R^/W+ Mc*)V]n^P yCm -/ >[%aF;_՟
|ۄFy]&_B$1.Əo D d
| l b
c $ A ? ? 3 " ` ? 2 +L a: o$ `! +L a: ` h{ xRAKQ7殚b $
$((Ptt/#RJcҿQ9P c+ 3
iřiV$_@lǭ3Bh:PhHq[ Tk.npqַ:fOP6p <
rƘ#@\*[a FM2(O0[q D d
b
c $ A ? ? 3 " ` ? 2 7G_q(nDm ' `! 7G_q(nDm @ ! xR=KA}w~]"j> XXʙZAVш NMh6,l b !9(.ٙ7ogV` 0GERЕ F"B~ah>#d ($tK:
#O6q f51 yc2EX盬F U_SC'"@rZ[`!b$ %9m dL=<@u3nͧ?VۢJ+*¢3[_20G^%LkjKEOe(kP j/.o%#Z&W,BQПir-wdLWcBʉL))(bLv_Aj/u D d
l b
c $ A ? ? 3 " ` ?
2 ?| :70 ) `! ?| :70 R xR=KA}ZZBHB,;-X%@@HeM 6vVOE4.ݼ|3:m `|җ 麮Rb "]kŇH?a &'>lkybIE8OnJ3 y `i 7\2A$^ٮ&6D\eWqs(E`Ca:-fukԱcԱpe'2OUOcv4Y?\a^Xо7x3X=6
",qoQw>/OW3OE+ 8܁m ihw3= -n/I)䪈*}VEZdO܌0x $܇EAgԋc/ OHBt\xBGgqƊ8W+ZƷ s!+
)' T R\
ީ+ mtg&;μ_`.êɷgح<4y5P3W':I8b^ /(|_Iknɫ w?Y*shڒx%t<OdϢΟU&r]keskE^^ sb+ꍼisMkd fğb'r7B\Ɉsw0Dxȥ=۴EIަT ĪēhO
w+TVXaDx6b!If⌑4gM14S_c=M=O~xe[߭ қd=&gIlӐ&cw^,1jGezБ}Ad !'Ȁ] 58^? D d
b
c $ A ? ? 3 " ` ? 2 B?
s69 ; `! B?
s69ê
x h xS;LA >(Q4hO!BHb&` )FcOc4c'8w 9̼flo 0lZnx(9v[zQ4r U|P~9 @m ?Ѫ T1j)B .;"t4 ;0 jNc-ҋI ʩbh3{ʫ#|f\^\?Ghxy|8p`g.+>;domV|u\
e?/t^NnLAt@S`=U3~zxa_.>/b gi_r/WyN D IM B91, ~$4bW *p)Ws}jaoߕO8Ԋ
q? Q8qľw5K ص_ D d
@ b
c $ A ? ? 3 " ` ? 2 = ofyT7"ɟʊ. |> `! ofyT7"ɟʊ.: @ x=O=a}3%JDBG. p $+
BBvsB Z7 XK&7o>Bl00ǒJ1Q PTlx + ? :&RPF;45˷I(ix ,{ T[VuE 5C%o)nB: 쨻sOgH! "j07%RF9 D d
b
c $ A ? ? 3 " ` ? 2 E E,nu] ! o@ `! E,nu] @ @ xS1K Qzz{wh T˘B-Sj6d1
Q `#6)ҥTPN т鐔#jqA;8Qՠ8]g?w.J۫&Hmsg;YR|>Bl00ǒJ1Q PTlx + ? :&RPF;45˷I(ix ,{ T[VuE 5C%o)nB: 쨻sOgH! "j07%RF9 $$If !v h5 ~5~55555C5#v ~#v#v#v#vC#v:V l
t 0 6 , 5 ~5555C5yt T kdG $$If T l ִ g
IZk O$~ ~ C
t 0 6 4 4
l a yt T $$If !v h5 ~5~55555C5#v ~#v#v#v#vC#v:V l
t 0 6 5 ~5555C5yt T $$If !v h5 ~5~55555C5#v ~#v#v#v#vC#v:V l
t 0 6 5 ~5555C5yt T $$If !v h5 ~5~55555C5#v ~#v#v#v#vC#v:V l
t 0 6 5 ~5555C5yt T $$If !v h5 ~5~55555C5#v ~#v#v#v#vC#v:V l
t 0 6 5 ~5555C5yt T $$If !v h5 ~5~55555C5#v ~#v#v#v#vC#v:V l
t 0 6 5 ~5555C5yt T $$If !v h5 ~5~55555C5#v ~#v#v#v#vC#v:V l
t 0 6 5 ~5555C5yt T $$If !v h5 ~5~55555C5#v ~#v#v#v#vC#v:V l
t 0 6 5 ~5555C5yt T $$If !v h5 ~5~55555C5#v ~#v#v#v#vC#v:V l
t 0 6 5 ~5555C5yt T $$If !v h5 ~5~55555C5#v ~#v#v#v#vC#v:V l
t 0 6 5 ~5555C5yt T $$If !v h5 ~5~55555C5#v ~#v#v#v#vC#v:V l
t 0 6 5 ~5555C5yt T $$If !v h5 ~5~55555C5#v ~#v#v#v#vC#v:V l
t 0 6 , 5 ~5555C5ytf>a T $$If !v h5 ~5~55555C5#v ~#v#v#v#vC#v:V l
t 0 6 5 ~5555C5ytc T $$If !v h5 ~5~55555C5#v ~#v#v#v#vC#v:V l
t 0 6 5 ~5555C5ytc T $$If !v h5 ~5~55555C5#v ~#v#v#v#vC#v:V l
t 0 6 5 ~5555C5ytc T $$If !v h5 ~5~55555C5#v ~#v#v#v#vC#v:V l
t 0 6 5 ~5555C5ytc T $$If !v h5 ~5~55555C5#v ~#v#v#v#vC#v:V l
t 0 6 5 ~5555C5ytc T $$If !v h5 ~5~55555C5#v ~#v#v#v#vC#v:V l
t 0 6 5 ~5555C5ytc T $$If !v h5 ~5~55555C5#v ~#v#v#v#vC#v:V l
t 0 6 5 ~5555C5ytc T $$If !v h5 ~5~55555C5#v ~#v#v#v#vC#v:V l
t 0 6 5 ~5555C5ytc T $$If !v h5 ~5~55555C5#v ~#v#v#v#vC#v:V l
t 0 6 5 ~5555C5ytc T $$If !v h5 ~5~55555C5#v ~#v#v#v#vC#v:V l
t 0 6 5 ~5555C5ytc T $$If !v h5 ~5~55555C5#v ~#v#v#v#vC#v:V l
t 0 6 5 ~5555C5ytc T I$$If !v
h5 5F5R5S5n5555 5
#v #vF#vR#vS#vn#v#v#v#v #v
:V l
t 0 ,
5 5F5R5S5n5555 5
ytf>a %kd?a $$If l
D/ p#& F R S n
t 0 ( ( ( ( 4 4
l a ytf>a I$$If !v
h5 5F5R5S5n5555 5
#v #vF#vR#vS#vn#v#v#v#v #v
:V l
t 0 ,
5 5F5R5S5n5555 5
ytf>a %kdd $$If l
D/ p#& F R S n
t 0 ( ( ( ( 4 4
l a ytf>a D d
T b
c $ A ? ? 3 " ` ? 2 h ? Z D gh `!< ? Z R XJ
xcdd``> @c112BYL%bpua %kdAj $$If l
D/ p#& F R S n
t 0 ( ( ( ( 4 4
l a ytf>a D d
T b
c $ A ? ? 3 " ` ? 2 h tҵU D m `!< tҵU XJ
xcdd``> @c112BYL%bpua %kdo $$If l
D/ p#& F R S n
t 0 ( ( ( ( 4 4
l a ytf>a D d
h b
c $ A ? ? 3 " ` ? 2 h O dAy D s `!< O dAy @ |
xcdd``> @c112BYL%bpu 1, NI$$If !v
h5 5F5R5S5n5555 5
#v #vF#vR#vS#vn#v#v#v#v #v
:V l
t 0 ,
5 5F5R5S5n5555 5
ytf>a %kdau $$If l
D/ p#& F R S n
t 0 ( ( ( ( 4 4
l a ytf>a D d
T b
c $ A ? ? 3 " ` ? 2 h
mr
З D y `!<
mr
З XJ
xcdd``> @c112BYL%bpua %kdz $$If l
D/ p#& F R S n
t 0 ( ( ( ( 4 4
l a ytf>a D d
h b
c $ A ? ? 3 " ` ? 2 h P GkQcկj D ~ `!< P GkQcկj @ |
xcdd``> @c112BYL%bpua %kd $$If l
D/ p#& F R S n
t 0 ( ( ( ( 4 4
l a ytf>a D d
h b
c $ A ? ? 3 " ` ? 2 g ,){m,QR, C 7 `!; ,){m,QR, @ | xcdd``> @c112BYL%bpua %kd $$If l
D/ p#& F R S n
t 0 ( ( ( ( 4 4
l a ytf>a D d
h b
c $ A ? ? 3 " ` ? 2 h N $1~ D Ɖ `!< N $1~ @ |
xcdd``> @c112BYL%bpu 1, E&N!I$$If !v
h5 5F5R5S5n5555 5
#v #vF#vR#vS#vn#v#v#v#v #v
:V l
t 0 ,
5 5F5R5S5n5555 5
ytf>a %kd $$If l
D/ p#& F R S n
t 0 ( ( ( ( 4 4
l a ytf>a D d
h b
c $ A ? ? 3 " ` ? 2 h f/U_l6V ~N D V `!< f/U_l6V ~_ 1 3 6 3 2 7 0 4 6 2 Y F O l e
C o m p O b j f O b j I n f o E q u a t i o n N a t i v e 6 _ 1 3 6 3 2 7 0 4 8 6 F 0x 0x O l e
C o m p O b j f
F Microsoft Equation 3.0 DS Equation Equation.3 9q 0
1 0
F Microsoft Equation 3.0 DS Equation Equation.3 9q O b j I n f o E q u a t i o n N a t i v e : _ 1 3 6 4 4 8 0 0 4 4 F 0x 0x O l e
C o m p O b j f O b j I n f o E q u a t i o n N a t i v e 1 T a b l e o ; \
r 2
*#r 1
*#r 3
*#r 5
*#r 7
*#r 1 0
*#r 9
*#r 4
*#r 8
*#r 6 Oh +'0
8 D P
\ h p x Nƒ @ |
xcdd``> @c112BYL%bpua %kd0 $$If l
D/ p#& F R S n
t 0 ( ( ( ( 4 4
l a ytf>a D d
h b
c $ A ? ? 3 " ` ? 2 g OΏ5* C `!; OΏ5* @ | xcdd``> @c112BYL%bpu;vv0o8L+KRs2A2 u(2tA4 Ag!!v120e }LI$$If !v
h5 5F5R5S5n5555 5
#v #vF#vR#vS#vn#v#v#v#v #v
:V l
t 0 ,
5 5F5R5S5n5555 5
ytf>a %kd $$If l
D/ p#& F R S n
t 0 ( ( ( ( 4 4
l a ytf>a D d
@h b
c $ A ? ? 3 " ` ? 2 i ES>- E'\. E u `!= ES>- E'\. @ | xcdd``> @c112BYL%bpu 1,
KI$$If !v
h5 5F5R5S5n5555 5
#v #vF#vR#vS#vn#v#v#v#v #v
:V l
t 0 ,
5 5F5R5S5n5555 5
ytf>a %kdP $$If l
D/ p#& F R S n
t 0 ( ( ( ( 4 4
l a ytf>a D d
h b
c $ A ? ? 3 " ` ? 2 AX2r7$F `! AX2r7$F @ p | xڕӽK@ w iCtp~RG l'` ӊ-lA AA (8XgK$]+8p+(D ( ~44(!~D< 3hZfE8 `2߳蚭V ,Z會6Z.8MA`RZ+խ](CS`˲m'q a"Gq,u煗
^>`KSn.jW^Dt* # D
>}_btٓ'!mU"^Ͻ}:v鷙vID~E[4dcϣ/²MU#B<|x3kB#YZ+ِǾU 1/Nzߩ4q $$If !v h5 55555555 5
5
#v #v#v#v #v
#v
:V l
t 0 @ , 5 555 5
5
yt^b T Skdm $$If T l 2j>
/
+
t 0 @ , , , , 4 4
l a yt^b T $$If !v h5 55555555 5
5
#v #v#v#v #v
#v
:V l
t 0 @ , 5 555 5
5
yt^b T Skd $$If T l 2j>
/
+
t 0 @ , , , , 4 4
l a yt^b T 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 i 9 6 6 6 6 6 6 6 6 6 v v v v v v v v v 6 6 6 6 6 6 8 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 h H 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 > @ > N o r m a l 7$ 8$ _HmH sH tH N @ "N {" H e a d i n g 1 $
& F P @&
5:KH J @ "J *_ H e a d i n g 2 $
& F x < @& 5]B @ B H e a d i n g 3 $
& F @& 6]R @ R H e a d i n g 4 $
& F < @& 6CJ ]aJ H @"H X9- H e a d i n g 5
& F V@&^`V 8 @Q 8 0: H e a d i n g 6
& F @& 8 @Q 8 H e a d i n g 7
& F @& N @ N H e a d i n g 8
& F < @& 6CJ ]aJ H @ H H e a d i n g 9
& F < @& CJ aJ D A@ D D e f a u l t P a r a g r a p h F o n t V i@ V T a b l e N o r m a l :V 4 4
l a ( k@ ( N o L i s t L O L A b s t r a c t $ ` a$ 5CJ \aJ V O V A u t h o r s & $@ p#&#$. / a$ CJ aJ F O F
M e m b e r T y p e 6CJ OJ QJ ]^J aJ R >@ R T i t l e " $ $&#$. / a$ CJ0 KH aJ0 L @ 2L
F o o t n o t e T e x t $ ` a$ CJ aJ V O BV
R e f e r e n c e s $
& F h^h`a$ CJ aJ L O L
I n d e x T e r m s $ ` a$ 5CJ \aJ @ &@ a@ F o o t n o t e R e f e r e n c e H* 4 @ r4 % 0 F o o t e r
! < O < # T e x t $ d 1$ ` a$ F O F F i g u r e C a p t i o n $a$ CJ aJ D O D T a b l e T i t l e $a$ :CJ aJ @ O @ R e f e r e n c e H e a d
& F 4 @ 4 H e a d e r
! D O D E q u a t i o n $
d 1$ a$ 6 U@ 6 H y p e r l i n k >*B*ph F V@ F F o l l o w e d H y p e r l i n k >*B* ph P C@ P B o d y T e x t I n d e n t v^v` aJ N O N \ M T E q u a t i o n S e c t i o n <B*CJ aJ ph J O J $ \ M T D i s p l a y E q u a t i o n
"
* O 1* \ T e x t C h a r D O2AD " \ M T D i s p l a y E q u a t i o n C h a r . O Q. g 0 C h a r C h a r 4 H @ bH
' g 0 B a l l o o n T e x t & CJ OJ QJ ^J aJ B O qB & g 0 C h a r C h a r 3 CJ OJ QJ ^J aJ 0 "@ 0 o| 0 C a p t i o n ( 5\V O V -F t a b l e c o l h e a d ) $7$8$a$ 5CJ PJ \aJ L OL -F t a b l e c o l s u b h e a d * 6CJ ]aJ Z OZ -F
t a b l e c o p y + $a$# CJ PJ _HaJ mH nH sH tH u P B@ P - g2 B o d y T e x t , $ d 7$8$` a$ @PJ 6 O 6 , g2 C h a r C h a r 2 @PJ b Ob g2 t a b l e f o o t n o t e . $< a$ CJ PJ _HaJ mH sH tH r Or g2
t a b l e h e a d / $
& F d x a$ & :CJ PJ _HaJ mH nH sH tH uH Oa H
H e a d i n g 6 1 0
& F V^`V @ O @
t L i s t P a r a g r a p h
1 ^ D O"D j? N o S p a c i n g , P a r a g r a p h 2 j @ 3j _9c
T a b l e G r i d 7 :V3 0 3 B '@ AB
&A 0 C o m m e n t R e f e r e n c e CJ aJ 4 @ R4
6 &A 0 C o m m e n t T e x t 5 . O a. 5 &A 0 C h a r C h a r 1 @ j@QR@
8 &A 0 C o m m e n t S u b j e c t 7 5\2 Ob2 7 &A 0
C h a r C h a r 5\ E c 5 E c 5 8 [ ^ 2a e @ / F 8 9
Y @ f S g h ! #" Y" Z" " " # # # # # # &# *# +# -# <# ># ?# A# N# U# V# X# k# o# p# r# # # # # # # # # # # # # # # # # # $ $
$ $ $ $ #$ 0$ =$ >$ A$ R$ W$ X$ [$ s$ u$ v$ y$ $ $ $ $ $ % 6% 7% 8% t% {% % % % % % % .& /& 1& @& & & & & "' #' %' F' ' ' ' ' ( ( ( ( J) K) M) k) ) ) * * d+ e+ + , - - ]. 1/ 2/ / 0 0 %1 ,1 1 2 X2 2 2 2 !4 z5 {5 _6 6 J7 7 7 7 38 8 9 9 r: : : ^; < -< < k= = = ? ? ? ? ? @ A /B |B B B C C UC D 7G H 5J K L M M 8N N
O yO O O P QP uP P P Q Q /R XR R R S S WS S T ET T U
U |U U U eV W W eX Y Y Z [ [ \ I\ X\ a\ g\ j\ o\ y\ |\ \ \ \ \ \ \ \ \ \ ] ] ] ] ] #] (] .] 4] :] ;] >] D] H] L] Q] W] ]] c] d] g] m] q] u] z] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ^ ^ ^ ^ ^ ^ ^ ^ $^ *^ 0^ 1^ 4^ :^ >^ B^ G^ M^ S^ Y^ Z^ ]^ c^ g^ k^ p^ v^ |^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ _ _ _ _ _ _ #_ ,_ /_ :_ S_ n_ q_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ` ` `
` ` ` ` ` ` %` '` ,` 1` 6` ;` =` >` A` F` H` M` R` T` Y` [` \` _` d` f` k` p` u` w` |` }` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` a a a a a a a a !a &a +a 0a 1a 2a 3a 4a ca da ma sa va {a a a a a a a a a a a a b -b 2b 3b 8b =b Bb Gb Lb Qb Vb [b ]b ^b _b wb |b b b b b b b b b b b b b b b b b b b b b b c c c c c c "c (c *c +c Cc Hc Mc Rc Wc \c ac fc lc nc oc c c c c c c c c c c c c c c c c c c c c c c
d d d d !d &d +d 0d 6d 8d 9d Qd Vd [d `d ed jd od td zd |d }d d d d d d d d d d d d d d d d d d d d e e e e ^e we xe f f f f f f f f f f f f f f f f f f f f f f f f f f f f f hh .j Uk l n o &r u u w y }{ { W| c} 4~ ~ R k # ԁ S N ҄ n ԇ Չ ։ ؉ ى ۉ ܉ މ ߉ ' ( O Ȋ ' E F s 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 W 0 0 f 0 f 0 f 0 f 0 f 0 f 0 f 0 f 0 0 nu 0 nu 0 nu 0 0 { 0 { 0 { 0 { 0 { 0 { 0 { 0 { 0 { 0 { 0
{ 0 { 0 { 0
{ 0 { 0 {{ 0 {{ 0 {{ 0 {{ 0 {{ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 dEx 0 0 0 0 " 0 0 " 0 " 0 " 0 0 0 0 0u 0 0 0 0 0 0 0u 0 0 0 0 0u 00
O& , 1 H8 << @ F G oK M U \ ^ S` Cc d Uh l 3p nq r s t -~ P X k c x W ߎ K N O P Q R T U W n p q s t u w x z | } Y Y0 1 >1 U1 o1 1 1 1 1 2 2 =2 W2 u2 2 t3 3 4 "5 5 6 J7 7 : E M 7U Q^ Eb i k :k ;k ck dk k k k k k k l l 0l 1l Yl Zl l l l l m m m m m m n n =n >n [n \n |n }n n n n n n n o o 0o 1o 3p p fq
r r t t R L S V X Y Z [ \ ] ^ _ ` a b c d e f g h i j k l m o r v y { ~ M - - - - - - '. ;. =. 0 0 0 _6 s6 u6 7 8 8 9 9 9 r: : : < )< +< = = = ? ? ? N N N O $O &O uP P P Q Q Q /R CR ER R R R S S S CU WU YU |U U U U U U wV V V _b sb ub b b b b b b +c ?c Ac oc c c c c c c d d 9d Md Od }d d d d d d ^e re te :::::::::::::_::::::::::::::::::: @ @ 2
(
W ^
3 "0 ? `
c $ X 9 9 ?
W ^ T
# !
7 =
Z B
S D g = h ] T
# G ]
T
#
Z B
S D j m T
# 5
Z B
S D f g
B
S ? H 0 (
P - t Z Tp Z q Z < $ Z = *urn:schemas-microsoft-com:office:smarttags PlaceName = *urn:schemas-microsoft-com:office:smarttags PlaceType 8 *urn:schemas-microsoft-com:office:smarttagsCity 9 *urn:schemas-microsoft-com:office:smarttagsplace w ) + , - 1 2 8 9 ? A K T a k q z / r v w { ) * 0 1 8 9 A C J K N O V W \ ` b c l m x y # % , 0 7 8 = > E L S T Z ^ c d j k o p y z
& ' 3 4 8 9 D F M N T U [ \ a b h i p q z { 7 9 @ A G I _ ` s t ; @ 1 &# (# ,1 11 1 1 2 2 X2 ^2 2 2 E E N N N N CO DO Y Y Y Y Y Z
Z 6Z [ [ [ [ [ [ 4a ;a =a [a e
e e e "e He Re \e ue ve xe |e e e e e e e e e e f f
f f f (f 4f =f Jf Tf f f f f f f f f f f f f f f f f f f f f f f f f f f f f f { { | | g} k} u} z} } } ` e π Հ * 1 ׁ ہ 6 8 R Ղ ݂ Q V Մ ڄ ܅ J Q Y _ ؉ ؉ ى ى ۉ ܉ މ ߉ & ( F O ̊ ϊ ܊ ފ % ( 8 < C F S X s ߋ / r B C G E 7 2 ! ! '" -" " " 8% @% - - %1 *1 6 6 8 8 38 88 : : B B
C C E E N N
O O QP XP P P T T U U Y 6Z Z Z [ [ [ [ \ \ ^ ^ 4a ba e ]e ue we xe f f f f f f f f f f f f f f f f f f f f f f f f f f f f f { { 7 : ؉ ؉ ى ى ۉ ܉ މ ߉ & ( N O NJ Ȋ & ( D F r ȋ 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 _ \ K
$ # Y @ e d { 2 #" X" " " # # # *# +# ># ?# U# V# o# p# # # # # # # # # # # $ $ $ $ =$ >$ W$ X$ u$ v$ $ % 8% ) e+ N- - - #. ]. 2/ / 0 ,1 1 2 X2 2 l3 3 4 {5 M6 _6 7 7 8 38 8 8 9 9 <: q: : : ^; ; ; -< O< = = ? ? ? C C zK K N
O EQ R R WS S T |U eV W (W X Y fZ Z \ \ I\ f\ g\ \ \ ^ ^ ^ ^ _ _ S_ q_ 1a 4a =a da ra sa a a _b wb b b b b +c Cc oc c c c c
d 9d Qd }d d d d e ^e xe f f f f n 1o u u Hv v y y }{ { { l ԁ ҄ n ։ ؉ ؉ ى ى ۉ ܉ މ ߉ Ȋ ' D 0 0 _6 v6 7 8 9 9 r: : < ,< = = ? ? U U -j Tk r )s =t @t Qt Zt t t %z z ։ ؉ ؉ ى ى ۉ ܉ މ ߉ ' ( E F F ua( R f k!nq 4oJJ L'% M#- #/ d}:] :: /3GȎH Y M#BJ 6cU 08E^`\0 l ic^
k -lpd/ ;)m: ?@sN nPSuXΈ u/ w h
h^h`h H . @ . @ ) @ 0^`0 ) @ P0^P`0 ( ) @
0^
`0 ( ) @ 0^ `0 ( ) @ 0^`0 ( ) @ 0^`0 ( ) ^`o( )
^`h H .
pL p^p`Lh H .
@ @ ^@ `h H .
^`h H .
L ^`Lh H .
^`h H .
^`h H .
PL P^P`Lh H .
P^`Po( h H
@^@`o( h H .
0^`0o( h H . .
`^``o( h H . . .
^`o( h H . . . .
^`o( h H . . . . .
^`o( h H
. . . . . .
`^``o( h H . . . . . . .
0^0`o( h H . . . . . . . . @ ^
h
h^h`o( h H
A P P E N D I X h
^`h H . h
pL^p`Lh H . h
@ ^@ `h H . h
^`h H . h
L^`Lh H . h
^`h H . h
^`h H . h
PL^P`Lh H .
h
^`o( h H
A P P E N D I X h
^`h H . h
pL^p`Lh H . h
@ ^@ `h H . h
^`h H . h
L^`Lh H . h
^`h H . h
^`h H . h
PL^P`Lh H . ) )^)`o( .
^`h H .
L ^ `Lh H .
^ `h H .
i i^i`h H .
9L 9^9`Lh H .
^ `h H .
^`h H .
L ^`Lh H . h h^h` ) h h^h` . @ h h^h` . h h^h` [ ] h h^h` [ ] @ h h^h` . @ h h^h` . @ ^
h
h^h`o( h H
A P P E N D I X h ^`3* G5:sH tH _H A . . h
pL^p`Lh H . h
@ ^@ `h H . h
^`h H . h
L^`Lh H . h
^`h H . h
^`h H . h
PL^P`Lh H . h
^`o( h H [ ] h
^`h H . h
pL^p`Lh H . h
@ ^@ `h H . h
^`h H . h
L^`Lh H . h
^`h H . h
^`h H . h
PL^P`Lh H . ) )^)`o( .
^`h H .
L ^ `Lh H .
^ `h H .
i i^i`h H .
9L 9^9`Lh H .
^ `h H .
^`h H .
L ^`Lh H . # 85 6 CJ OJ QJ \ ] ^J aJ o( T A B L E . h h^h` [ ] 80 8^8`0o( )
^`h H .
pL p^p`Lh H .
@ @ ^@ `h H .
^`h H .
L ^`Lh H .
^`h H .
^`h H .
PL P^P`Lh H . ) )^)`o( .
^`h H .
pL^p`Lh H .
@ ^@ `h H .
^`h H .
L^`Lh H .
^`h H .
^`h H .
PL^P`Lh H . ^`OJ PJ QJ ^J o( - ^`OJ QJ ^J o( h H o p p^p`OJ QJ o( h H @ @ ^@ `OJ QJ o( h H ^`OJ QJ ^J o( h H o ^`OJ QJ o( h H ^`OJ QJ o( h H ^`OJ QJ ^J o( h H o P P^P`OJ QJ o( h H @ ^ " #/ #/ XWR #/ WR #/ XR /3G /3G `XR /3G XR /3G YR /3G hYR /3G YR d}: f 6cU Y M w M#- L'% ;)m : R -l 4o k! 08E^ R u l ic R ZR
k nPSu ?@s u dWR @ h h^h` . WR @ h h^h` . XR @ h h^h` . lXR @ h h^h` . XR @ h h^h` . YR @ h h^h` . tYR @ h h^h` . YR @ h h^h` . سk ,8 Ơd 2 $ ƠdJ%: c $ P R $ G =V +\ Gr @ SE ny 3N & mf ' w j . j? 0J u M T T i(! XV$ p$ o( ) ")
z* X9-
/ ($/ uP0 N\0 'X1 l5 X7 8 S8 V8 X : we: = A k,A V WIW _W X e*X a _9c d 'e ?g Eh RVh _qi k`k {um o Bp IUq XPr
t 8t Yrt %%u bbu g{ Hp{ | *| o| ~ X~ r q n ~Q Q bn 6u 7 {b (7 s ? v ]} r# O ^b , pf c^ &`
} \ H / (W
J c H T U. G T zp 8 ? % 2) g2 $ 7 c@ x P IP ; h 3 k! {" B x =n * c, C I ;l a Y -# g 0: PR + z { $ &N 0 R ( &A l o ! u f X - l+ 7l a y 2 '^ i |
gp + kN / A 0 (N `* e* 0n Ts 74 k\ ( " # # # # # # &# *# +# -# <# ># ?# A# N# U# V# X# k# o# p# r# # # # # # # # # # # # # # # # # # $ $
$ $ $ $ #$ 0$ =$ >$ A$ R$ W$ X$ [$ s$ u$ v$ y$ $ $ $ 8% t% {% % % % % % .& /& 1& @& & & & & "' #' %' F' ' ' ' ' ( ( ( ( J) K) M) k) ) ) 6 9 ^; < [ \ I\ X\ j\ |\ \ \ \ \ ] ] ] ] ] #] (] .] 4] :] ;] >] D] H] L] Q] W] ]] c] d] g] m] q] u] z] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ^ ^ ^ ^ ^ ^ ^ ^ $^ *^ 0^ 1^ 4^ :^ >^ B^ G^ M^ S^ Y^ Z^ ]^ c^ g^ k^ p^ v^ |^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ _ _ /_ S_ q_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ` ` `
` ` ` ` ` ` %` '` ,` 1` 6` ;` =` >` A` F` H` M` R` T` Y` [` \` _` d` f` k` p` u` w` |` }` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` a a a a a a a a !a &a +a 0a 1a 4a ca da va a a a a a b -b 2b 3b 8b =b Bb Gb Lb Qb Vb [b ]b ^b _b wb |b b b b b b b b b b b b b b b b b b b b b b c c c c c c "c (c *c +c Cc Hc Mc Rc Wc \c ac fc lc nc oc c c c c c c c c c c c c c c c c c c c c c c
d d d d !d &d +d 0d 6d 8d 9d Qd Vd [d `d ed jd od td zd |d }d d d d d d d d d d d d d d d d d d d d e e e f f f f f f f f f f f f f f f f f f f f f f f f f f ։ )5 )5 9 )5 )5 )5 @HP LaserJet 4200 PCL 6 Ne02: winspool HP LaserJet 4200 PCL 6 H P L a s e r J e t 4 2 0 0 P C L 6 5C
od X X L e t t e r DINU" @|,PrA 8 @ SMTJ 0H P L a s e r J e t 4 2 0 0 P C L 6 InputBin FORMSOURCE RESDLL UniresDLL HPDocUISUI True Resolution 600dpi FastRes True Orientation PORTRAIT HPOrientRotate180 False HPNUseDiffFirstPageChoice TRUE HPPageExceptionsFile HPZPE4wm HPPageExceptionsInterface ShowPageExceptions HPPageExceptionsLowEnd HPPageExceptionsLowEndVer HPPageExceptions CoverInsertion PaperSize LETTER MediaType Auto TextAsBlack False Duplex NONE HPFontInstaller TRUE HPPJLEncoding UTF8 OutputBin Auto Stapling None HPStaplingOpposed False StaplingCmdCallback StaplingCmdCb Collate OFF JRConstraints JRCHDPartial JRHDInstalled JRHDOff JRHDNotInstalled JRHDOff TTAsBitmapsSetting TTModeOutline RETChoice True HPLpiSelection None HPPCL6PassThrough True JRCmdCallback JR HPColorMode MONOCHROME_MODE HPBornOnDate HPBOD HPJobByJobOverride JBJO HPXMLFileUsed hpc42006.xml HPPDLType PDL_PCL6 PrintQualityGroup PQGroup_3 Economode False HPJobAccounting HPJOBACCT_JOBACNT AlternateLetterHead False HPDocPropResourceData hpzhl4wm.cab HPSmartDuplexSinglePageJob True HPSmartDuplexOddPageJob True HPConsumerCustomPaper True HPEnableRAWSpooling True PSAlignmentFile HPZLS4wm PSServicesOption PrnStat_SID_242_BID_270_HID_15521 HPSmartHub_Onlinediagnostictools TRUE HPSmartHub_Supportandtroubleshooting TRUE HPSmartHub_Productmanuals TRUE HPSmartHub_Checkfordriverupdates TRUE HPSmartHub Inet_SID_263_BID_276_HID_265 HPPreAnalysis True HPPaperSizeALMConstraints ENV_10 HPMediaTypeDuplexConstraints CARDSTOCK HPJobAccWoPin True , IUPH d L e t t e r
o [ n o n e ] [ n o n e ] A r i a l 4 P d ? < A u t o m a t i c > 0 R
4 4 C u s t o m P r i n t S e t t i n g s d M i c r o s o f t O f f i c e W o r d N o n e WINWORD.EXE C : \ P R O G R A ~ 1 \ M I C R O S ~ 2 \ O F F I C E 1 1 \ W I N W O R D . E X E IPACDRWDSGATCAPI;F4E8Q;K i݅&E%9xPPBHAERP S u m m a r y I n f o r m a t i o n ( D o c u m e n t S u m m a r y I n f o r m a t i o n 8 C o m p O b j q IEEE Transactions on Magnetics - Normal.dot Alan Jovic 14 Microsoft Office Word @ {=. @ ݶ @ F
@ | Eu ՜. +,D ՜. +,4 h p
IEEE F ' Title 0 z
MTWinEqns MTEquationSection MTEquationNumber2 1 (#E1)
F Microsoft Office Word Document
MSWordDoc Word.Document.8 9q
H P L a s e r J e t 4 2 0 0 P C L 6 5C
od X X L e t t e r DINU" @|,PrA 8 @ SMTJ 0H P L a s e r J e t 4 2 0 0 P C L 6 InputBin FORMSOURCE RESDLL UniresDLL HPDocUISUI True Resolution 600dpi FastRes True Orientation PORTRAIT HPOrientRotate180 False HPNUseDiffFirstPageChoice TRUE HPPageExceptionsFile HPZPE4wm HPPageExceptionsInterface ShowPageExceptions HPPageExceptionsLowEnd HPPageExceptionsLowEndVer HPPageExceptions CoverInsertion PaperSize LETTER MediaType Auto TextAsBlack False Duplex NONE HPFontInstaller TRUE HPPJLEncoding UTF8 OutputBin Auto Stapling None HPStaplingOpposed False StaplingCmdCallback StaplingCmdCb Collate OFF JRConstraints JRCHDPartial JRHDInstalled JRHDOff JRHDNotInstalled JRHDOff TTAsBitmapsSetting TTModeOutline RETChoice True HPLpiSelection None HPPCL6PassThrough True JRCmdCallback JR HPColorMode MONOCHROME_MODE HPBornOnDate HPBOD HPJobByJobOverride JBJO HPXMLFileUsed hpc42006.xml HPPDLType PDL_PCL6 PrintQualityGroup PQGroup_3 Economode False HPJobAccounting HPJOBACCT_JOBACNT AlternateLetterHead False HPDocPropResourceData hpzhl4wm.cab HPSmartDuplexSinglePageJob True HPSmartDuplexOddPageJob True HPConsumerCustomPaper True HPEnableRAWSpooling True PSAlignmentFile HPZLS4wm PSServicesOption PrnStat_SID_242_BID_270_HID_15521 HPSmartHub_Onlinediagnostictools TRUE HPSmartHub_Supportandtroubleshooting TRUE HPSmartHub_Productmanuals TRUE HPSmartHub_Checkfordriverupdates TRUE HPSmartHub Inet_SID_263_BID_276_HID_265 HPPreAnalysis True HPPaperSizeALMConstraints ENV_10 HPMediaTypeDuplexConstraints CARDSTOCK HPJobAccWoPin True , IUPH d L e t t e r
o [ n o n e ] [ n o n e ] A r i a l 4 P d ? < A u t o m a t i c > 0 R
4 4 C u s t o m P r i n t S e t t i n g s d M i c r o s o f t O f f i c e W o r d N o n e WINWORD.EXE C : \ P R O G R A ~ 1 \ M I C R O S ~ 2 \ O F F I C E 1 1 \ W I N W O R D . E X E IPACDRWDSGATCAPI;F4E8Q;K i݅&E%9xPPBHAERP Tk Tk e Tk Tk d
P P @ P P P P P 0 @ P @ U n k n o w n G z T i m e s N e w R o m a n 5 S y m b o l 3& z A r i a l 5& z a T a h o m a W S i m S u n A r i a l U n i c o d e M S ?5 z C o u r i e r N e w ; W i n g d i n g s " h $fjp]f K Eu F Eu F d x 4 d 2q XZ ? =a 2 I E E E T r a n s a c t i o n s o n M a g n e t i c s -
A l a n J o v i c l