01-01-2011, 12:17 PM
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INTRODUCTION
Grey analysis uses a specific concept of information. It defines situations with no information as black, and those with perfect information as white. However, neither of these idealized situations ever occurs in real world problems. In fact, situations between these extremes are described as being grey, hazy or fuzzy. Therefore, a grey system means that a system in which part of information is known and part of information is unknown. With this definition, information quantity and quality form a continuum from a total lack of information to complete information – from black through grey to white. Since uncertainty always exists, one is always somewhere in the middle, somewhere between the extremes, somewhere in the grey area.
Grey analysis then comes to a clear set of statements about system solutions. At one extreme, no solution can be defined for a system with no information. At the other extreme, a system with perfect information has a unique solution. In the middle, grey systems will give a variety of available solutions. Grey analysis does not attempt to find the best solution, but does provide techniques for determining a good solution, an appropriate solution for real world problems.
The proposition of Grey theory occurring in the 1990 to 1999 time period resulted in the uses of Grey theory to each field, and the development is still going on. The major advantage of Grey theory is that it can handle both incomplete information and unclear problems very precisely. It serves as an analysis tool especially in cases when there is no enough data. It was recognized that the Grey relational analysis in Grey theory had been largely applied to project selection, prediction analysis, performance evaluation, and factor effect evaluation due to the Grey relational analysis software development. Recently, this technique has also applied to the field of sport and physical education.
LITERATURE REVIEW
Until recently many researchers have shown interest in the field of Grey Relational Analysis. They have carried out numerous laboratory experiments and field observations to illuminate the darkness of this field. Their findings and suggestions are reviewed here.
The “Grey Systems” approach, advocated by Deng (1982), emphasizes a clear message to resolve the questions. To explore the essence of the system, the partial message was processed by the system from grey to white message. (Shih et al., 1994)
Grey relational analysis (GRA) proposed by Deng Julong is very useful to analyze medical data. The essential thought of GRA is to find a grey relational order, which can be used to describe the relation between the related factors based on data series. The two-grade difference is a traditional method of GRA and the three-grade difference is an improved one. The basic steps and formulae of GRA are introduced and GRA is used to analyze the experiment medical data, clinical trial data, data of clinical study and ambulatory and grouping medical data
Grey system theory by focusing on resolving problems with uncertainty or systems with incomplete information. The Grey system theory can effectively resolve uncertainties, multivariable or discrete data using system relational analysis, model construction, forecasting, and decision analysis. The Grey relational analysis utilizes discrete measurement methods to evaluate the distance between two sequences and to explore the relational degree for two sequences.
Ching-Liang Chang developed a model investigation conducted on the Decathlon Evaluation. After a result he concludes that Grey relational analysis can be applied in analyzing sport technology, selection of coach, and evaluation of overall performance for decathlon. Through quantitative analysis of Grey relation, it provides more accurate and subjective data.
Chih-Hung Tsai developed a model investigation conducted on Vendor Evaluation. After a result he conclude that In order to seek a proper vendor meeting the requirements of enterprise itself subjectively, GRA is important to develop an accurate evaluation method.
GREY THEORY
The black box is used to indicate a system lacking interior information. Nowadays, the black is represented, as lack of information, but the white is full of information. Thus, the information that is either incomplete or undetermined is called Grey.
A system having incomplete information is called Grey system. The Grey number in Grey system represents a number with less complete information. The Grey element represents an element with incomplete information. The Grey relation is the relation with incomplete information. Those three terms are the typical symbols and features for Grey system and Grey phenomenon. There are several aspects for the theory of Grey system:
1. 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 the whitening of a sequence of numbers.
2. Grey modeling: This is done by step 1 to establish a set of Grey variation equations and Grey differential equations, which is the whitening of the model.
3. Grey prediction: By using the Grey model to conduct a qualitative prediction, this is called the whitening of development.
4. Grey decision: A decision is made under imperfect countermeasure and unclear situation, which is called the whitening of status.
5. Grey relational analysis: Quantify all influences of various factors and their relation, which is called the whitening of factor relation.
6. Grey control: Work on the data of system behavior and look for any rules of behavior development to predict future’s behavior, the prediction value can be fed back into the system in order to control the system.
GREY THEORY
The black box is used to indicate a system lacking interior information. Nowadays, the black is represented, as lack of information, but the white is full of information. Thus, the information that is either incomplete or undetermined is called Grey.
A system having incomplete information is called Grey system. The Grey number in Grey system represents a number with less complete information. The Grey element represents an element with incomplete information. The Grey relation is the relation with incomplete information. Those three terms are the typical symbols and features for Grey system and Grey phenomenon. There are several aspects for the theory of Grey system:
1. 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 the whitening of a sequence of numbers.
2. Grey modeling: This is done by step 1 to establish a set of Grey variation equations and Grey differential equations, which is the whitening of the model.
3. Grey prediction: By using the Grey model to conduct a qualitative prediction, this is called the whitening of development.
4. Grey decision: A decision is made under imperfect countermeasure and unclear situation, which is called the whitening of status.
5. Grey relational analysis: Quantify all influences of various factors and their relation, which is called the whitening of factor relation.
6. Grey control: Work on the data of system behavior and look for any rules of behavior development to predict future’s behavior, the prediction value can be fed back into the system in order to control the system.
The Grey relational analysis uses information from the Grey system to dynamically compare each factor quantitatively. This approach is based on the level of similarity and variability among all factors to establish their relation. The relational analysis suggests how to make prediction and decision, and generate reports that make suggestions. This analytical model magnifies and clarifies the Grey relation among all factors. It also provides data to support quantification and comparison analysis. In other words, the Grey relational analysis is a method to analyze the relational grade for discrete sequences. This is unlike the traditional statistics analysis handling the relation between variables.
GREY RELATIONAL ANALYSIS
The validity of traditional statistical analysis techniques is based on assumptions such as the distribution of population and variances of samples. Nevertheless sample size will also affect the reliability and precision of the results produced by traditional statistical analysis techniques. J. Deng argued that many decision situations in real life do not conform to those assumptions, and may not be financially or pragmatically justified for the required sample size. Making decisions under uncertainty and with insufficient or limited data available for analysis is actually a norm for managers in either public or private sectors. To address this problem, J. Deng developed the grey system theory, which has been widely adopted for data analysis in various fields.