New progress of Grey System Theory in the new millennium

Abstract

Purpose – The purpose of this paper is to summarize the progress in grey system research during 2000-2015, so as to present some important new concepts, models, methods and a new framework of grey system theory. Design/methodology/approach – The new thinking, new models and new methods of grey system theory and their applications are presented in this paper. It includes algorithm rules of grey numbers based on the “kernel” and the degree of greyness of grey numbers, the concept of general grey numbers, the synthesis axiom of degree of greyness of grey numbers and their operations; the general form of buffer operators of grey sequence operators; the four basic models of grey model GM(1,1), such as even GM, original difference GM, even difference GM, discrete GM and the suitable sequence type of each basic model, and suitable range of most used grey forecasting models; the similarity degree of grey incidences, the closeness degree of grey incidences and the three-dimensional absolute degree of grey incidence of grey incidence analysis models; the grey cluster model based on center-point and end-point mixed triangular whitenization functions; the multi-attribute intelligent grey target decision model, the two stages decision model with grey synthetic measure of grey decision models; grey game models, grey input-output models of grey combined models; and the problems of robust stability for grey stochastic time-delay systems of neutral type, distributed-delay type and neutral distributed-delay type of grey control, etc. And the new framework of grey system theory is given as well. Findings – The problems which remain for further studying are discussed at the end of each section. The reader could know the general picture of research and developing trend of grey system theory from this paper. Practical implications – A lot of successful practical applications of the new models to solve various problems have been found in many different areas of natural science, social science and engineering, including spaceflight, civil aviation, information, metallurgy, machinery, petroleum, chemical industry, electrical power, electronics, light industries, energy resources, transportation, medicine, health, agriculture, forestry, geography, hydrology, seismology, meteorology, environment protection, architecture, behavioral science, management science, law, education, military science, etc. These practical applications have brought forward definite and noticeable social and economic benefits. It demonstrates a wide range of applicability of grey system theory, especially in the situation where the available information is incomplete and the collected data are inaccurate. Originality/value – The reader is given a general picture of grey systems theory as a new model system and a new framework for studying problems where partial information is known; especially for uncertain systems with few data points and poor information. The problems remaining for further studying are identified at the end of each section.

Forecasting strategies and analyzing the numbers of incoming students: Case in Taiwanese vocational schools

“…To observe and receive an overview about the future value through the past and modern data is what it means by prognostication (Liu et al, 2004). The usage of Grey model is to predict the change of system after examining the combination of clear data and variable information.…”

“…In the second step, a range of equation model established is considered with the aim to discover and gain the rule of sequence, also make a prediction of the future trend of current system. Thus, a giant leap is able to be simply achieved to establish the wonted and energetic differential equation through fixed data source (Liu et al, 2004 andCheng, 2003). All in all, Grey predicting is the most well-known methods to be applied to analyze the consequence of numerical data output from the single time series data (Tang and Feng, 2007).…”

Multilevel Correlation Analysis of Influencing Factors on Grain Total Factor Productivity in Main Grain Producing Provinces of China

“…The corresponding weight vector of each factor has been given in (9), which makes the analysis results more objective compared with the traditional grey correlation analysis.…”

“…The basic idea is to determine whether the relationship between curves is close by determining the similarity between the reference series and the geometric shapes of several comparative series degree [7]. Since the grey correlation analysis model was put forward, many scholars have studied and constructed many grey correlation analysis models [8] [9] [10] [11]. The calculation step of grey correlation analysis can be introduced as follows:…”

Performance Evaluation of Third-party Cold Chain Logistics Enterprise Based on A Comprehensive Evaluation Method

“…It divides the various factors into orderly hierarchies and is a simple, flexible and practical method for quantitative analysis of qualitative problems [4] . Grey theory, mainly through the extraction of some known or unknown information to realize the effective management [5] . Fuzzy comprehensive evaluation method is used to conduct an overall evaluation of objects that are constrained by a variety of factors and is also a widely used method for multi-criteria decision making [6] .…”