Tuesday, February 21, 2012

Grey Theory and Grey Relational Analysis - A Brief Introduction

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.

 Wu, H.H., “The Introduction of Grey Analysis,” Gauli Publishing Co., Taipei, 1996.


Grey system theory-based models in time series prediction, 2010 paper in journal Expert Systems With Applications
Combined Grey Relational Analysis and methods for optimization of process parameters in cylindrical grinding
Paper uploaded on academica.edu, 2009

Multi-attribute Decision Making Model by Applying Grey Numbers
Informatica, 2009
(Has good explanation of white, grey and black)
Airline Network Optimization using Grey Theory (2007, Research Paper by IIT Bombay faculty and PG student)

A Novel Prediction Method for Stock Index Applying Grey Theory and Neural Networks, 2008 OR Symposium paper

Grey Information: Theory and Practical Applications, 2006

Implementing Grey Model and Value Analysis aind QFD Proces to improve customer satisfaction
(Application to Juanda International Airport - Surabaya, Indonesia)

Combined Grey Relational Analysis and methods for optimization of process parameters in cylindrical grinding
Paper uploaded on academica.edu
Seminal paper

"The Control Problems of Grey Systems,"  Deng Julong (of China), The Journal of Systems and Control Letters, 1982.
originally posted by me in http://knol.google.com/k/narayana-rao/grey-theory-and-grey-relational/ 2utb2lsm2k7a/ 934

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