User talk:Khannoorn

Grey Theory The black box is used to indicate a system lacking interior information [W.R. Ashby, 1945]. 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 modelling: 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. This study will adopt all six above-mentioned research steps to develop a vendor evaluation model based on Grey relational analysis, and apply to vendor evaluation and selection. All details will be discussed in the following sections. 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 for the vendor selection. This analytical model magnifies and clarifies the Grey relation among all factors. It also provides data to support quantification and comparison analysis [2]. 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. Some of its defects are: (1) it must have plenty of data; (2) data distribution must be typical; (3) a few factors are allowed and can be expressed functionally. But the Grey relational analysis requires less data and can analyze many factors that can overcome the disadvantages of statistics method. The Grey theory and method are described in the following: 2.1. Influence space, measurement space, and Grey relational space Let P(X) represent the factor set of a specific topics, Q is the influence relation, then {P(X); Q} is influence space. It must have the following properties [3]: 1. Existence of key factors: for example, the key factors of basketball player are height, weight, and rebound. 2. Numbers of factors are limited and countable: for example each of the height, weight, and rebound are countable. 3. Factor independability: each factor must be independent. 4. Factor expandability: For example, besides the height, weight, and rebound, the free throw attempt can be added as a factor. The series formed by P(X) is: where i=0,..., m. k=1,...,n.? N If the following conditions are satisfied: 1. Nondimension: the numeric value for all factors must be nondimension. 2. Scaling: the factor value for various series must be at the same level. 3. Polarization: if the factor value in the series is described as the same direction, the series is comparable. Then the measurement space is expressed as {P(X); xi*(k)}, the Grey relational space formed by the satisfaction of both factor space and comparability is termed by {P(X); Γ}.
 * xi(0)(k)=(xi(0)(1),?,??, xi(0)(k))? X;