PROGRESS OF GREY SYSTEM MODELS

The progress of grey system models is reviewed, and the general grey numbers, the grey sequence op- erators and several most commonly used grey system models are introduced, such as the absolute degree of grey incidence model, the grey cluster model based on endpoint triangular whitenization functions, the grey cluster model based on center-point triangular whitenization functions, the grey prediction model of the model GM （ 1,1）, and the weighted multi-attribute grey target decision model.

Study and Implementation on the Grey Comprehensive Evaluation Support System of Ecocity

According to basic connotation and design principles of ecocity, a comparatively integrated index system is constructed in the paper. And at the same time using hierarchy grey comprehensive evaluation method, a hierarchy grey comprehensive evaluation model of ecocity is established, then on the basis of the model, a comprehensive evaluation support system is developed, and the theoretical guidance supplied for construction of ecocity is provided.

APPLICATION OF GREY SYSTEM THEORY TO PROCESSING OF MEASURING DATA IN REVERSE ENGINEERING

The processing of measuri ng data plays an important role in reverse engineering. Based on grey system the ory, we first propose some methods to the processing of measuring data in revers e engineering. The measured data usually have some abnormalities. When the abnor mal data are eliminated by filtering, blanks are created. The grey generation an d GM(1,1) are used to create new data for these blanks. For the uneven data sequ en ce created by measuring error, the mean generation is used to smooth it and then the stepwise and smooth generations are used to improve the data sequence.

Study on the Yield Prediction Model of Processing Tomato Based on the Grey System Theory

[Objective] The research aimed to study the yield prediction model of processing tomato based on the grey system theory.[Method] The variation trend of processing tomato yield was studied by using the grey system theory,and GM（1,1）grey model of processing tomato yield prediction was established.The processing tomato yield in Xinjiang during 2001-2009 was as the example to carry out the instance analysis.[Result] The model had the high forecast accuracy and strong generalization ability,and was reliable for the prediction of recent processing tomato yield.[Conclusion] The research provided the reference for the macro-control of tomato industry,the processing and storage of tomato in Xinjiang.

Risk Assessment of Diary Cattle Brucellosis Based on Systematic Multilevel Grey Relation Entropy Method

[Objective] The study was to explore the major factors affecting diary cattle brucellosis risk assessment,as well as their strong-to-weak sequence,so as to provide theoretical basis for assessing diary cattle brucellosis risk level in different regions.[Method] From 4 dimensions of feeding and importing,breeding,housing and polyculture situation,an evaluation index system was set up,and diary cattle brucellosis risk survey was conducted in 3 typical regions.Finally,systematic multilevel grey relation entropy method was applied to perform data analysis.[Result] The strong-to-weak sequence of Level 1 impact factor of diary cattle brucellosis was as follows：feeding and importinghousingpolyculture situationbreeding;the sequence of Level 2 impact factor was U32〉U12〉U11〉U31〉U21〉U42〉U43〉U23〉U22〉U41;the risk level sequence of 3 typical regions was Province A（County A1,A2,A3）Province B（County B1,B2,B3）Province C（County C1,C2,C3）.[Conclusion] According to the weight of Level 1 index strata,administrative departments at all levels and dairy cattle farmers should lay emphasis on the aspects of feeding,importing and housing;viewed from the perspective of Level 2 index strata,dairy cattle farmers should value the siting of cattle field,the brucellosis surveillance before importing and milking modes most.According to the diary cattle brucellosis risk level of 3 typical regions,if administrative departments at all levels strengthen peoples＇ awareness of their personal health and increase investment in this area,with new healthy cultured atmosphere built,the risk level of diary cattle brucellosis will surly decline.

Study on effectiveness evaluation of weapon systems based on grey relational analysis and TOPSIS

To evaluate the effectiveness of weapon systems, the advantages and disadvantages of grey relational analysis and TOPSIS for multiattribute decision-making is pointed out, and an effectiveness evaluation model of weapon systems by combining grey relational analysis and TOPSIS is proposed. The model aggregates the grey relational grade and the distance to a new integrated closeness and reflects not only the trend but also the situation of the alternative. The example illuminates that the model is effective for the effectiveness evaluation of weapon systems.

Grey systems for intelligent sensors and information processing

In a measurement system, new representation methods are necessary to maintain the uncertainty and to supply more powerful ability for reasoning and transformation between numerical system and symbolic system. A grey measurement system is discussed from the point of view of intelligent sensors and incomplete information processing compared with a numerical and symbolized measurement system. The methods of grey representation and information processing are proposed for data collection and reasoning. As a case study, multi-ultrasonic sensor systems are demonstrated to verify the effectiveness of the proposed methods.

Multi-attributed decision making for mining methods based on grey system and interval numbers

In the case of unknown weights, theories of multi-attributed decision making based on interval numbers and grey related analysis were used to optimize mining methods. As the representative of independence for the indicator, the smaller the correlation of indicators is, the greater the weight is. Hence, the weights of interval numbers of indicators were determined by using correlation coefficient. Relative closeness based on positive and negative ideal methods was calculated by introducing distance between interval numbers, which made decision making more rational and comprehensive. A new method of ranking interval numbers based on normal distribution was proposed for the optimization of mining methods, whose basic properties were discussed. Finally, the feasibility and effectiveness of this method were verified by theories and practice.

Response surface method using grey relational analysis for decision making in weapon system selection

A proper weapon system is very important for a na- tional defense system. Generally, it means selecting the optimal weapon system among many alternatives, which is a multiple- attribute decision making （MADM） problem. This paper proposes a new mathematical model based on the response surface method （RSM） and the grey relational analysis （GRA）. RSM is used to obtain the experimental points and analyze the factors that have a significant impact on the selection results. GRA is used to an- alyze the trend relationship between alternatives and reference series. And then an RSM model is obtained, which can be used to calculate all alternatives and obtain ranking results. A real world application is introduced to illustrate the utilization of the model for the weapon selection problem. The results show that this model can be used to help decision-makers to make a quick comparison of alternatives and select a proper weapon system from multiple alternatives, which is an effective and adaptable method for solving the weapon system selection problem.

Forecasting Model of Coal Requirement Quantity Based on Grey System Theory

The generally used methods of forecasting coal requirement quantity include the analogy method, the outside push method and the cause effect analysis method. However, the precision of forecasting results using these methods is lower. This paper uses the grey system theory, and sets up grey forecasting model GM (1, 3) to coal requirement quantity. The forecasting result for the Chinese coal requirement quantity coincides with the actual values, and this shows that the model is reliable. Finally, this model are used to forecast Chinese coal requirement quantity in the future ten years.

Investigation of the Interactive,Intimidating Relation Between Urbanization and the Environment in an Arid Area Based on Grey System Theory

Taking the Hexi Corridor in western China as an example, this paper studies the interactive intimate i relation between urbanization and the environment in add areas based on the grey system theory. The results show that the grey relational degree between urbanization and the environment is low in the agriculture-oriented cities, modest in the tourism-oriented cities and great in the industry-oriented cities. The changing trend of coupling degree between urbanization and the environment does not entirely agree with that of urbanization or the environment. It showed fluctuating trends, which reflects the compactness and properties of the different stages of the coupling states between urbanization and the environment. In order to achieve a harmonious development with the environment in add areas, traditional development ideas about urbanization should be revised and more attention should be paid to the effect of restriction of water resources and the ecological environment on the development of the economy and society.

Study on generation in grey system theory

Grey sequence generation can draw out and develop implied rules of the original data. Different kinds of generation methods were summarized and classified into two types: partial generation and whole generation. The average generation and stepwise ratio generation is disussed , the preference generation is regard as a special case of proportional division based on analysis geometric theory, propose an idea of using concave and convex status of discrete data to determine the generation coefficient. Based on the stepwise and smooth ratio generation, a tendency average generation is proposed and have a comparison using the data provided in papers listed in the references. The comparison proves that the new generation is better than the other two generations and errors are obviously reduced.

Structural damage identification using test static data based on grey system theory

A new structural damage identification method using limited test static displacement based on grey system theory is proposed in this paper. The grey relation coefficient of displacement curvature is defined and used to locate damage in the structure, and an iterative estimation scheme for solving nonlinear optimization programming problems based on the quadratic programming technique is used to identify the damage magnitude. A numerical example of a cantilever beam with single or multiple damages is used to examine the capability of the proposed grey-theory-based method to localize and identify damages. The factors of meas-urement noise and incomplete test data are also discussed. The numerical results showed that the damage in the structure can be localized correctly through using the grey-related coefficient of displacement curvature, and the damage magnitude can be iden-tified with a high degree of accuracy, regardless of the number of measured displacement nodes. This proposed method only requires limited static test data, which is easily available in practice, and has wide applications in structural damage detection.

Predicting changes in Bitcoin price using grey system theory

Bitcoin is currently the leading global provider of cryptocurrency.Cryptocurrency allows users to safely and anonymously use the Internet to perform digital currency transfers and storage.In recent years,the Bitcoin network has attracted investors,businesses,and corporations while facilitating services and product deals.Moreover,Bitcoin has made itself the dominant source of decentralized cryptocurrency.While considerable research has been done concerning Bitcoin network analysis,limited research has been conducted on predicting the Bitcoin price.The purpose of this study is to predict the price of Bitcoin and changes therein using the grey system theory.The first order grey model(GM(1,1))is used for this purpose.It uses a firstorder differential equation to model the trend of time series.The results show that the GM(1,1)model predicts Bitcoin’s price accurately and that one can earn a maximum profit confidence level of approximately 98%by choosing the appropriate time frame and by managing investment assets.

Optimization of green sand mould system using Taguchi based grey relational analysis

The strength of the mould cavity in sand casting is very much significant to attain high-quality castings. Optimization of green sand process parameters plays a vital role in minimizing casting defects. In the present research work, the effect of process parameters such as AFS grain fineness number, water, molasses, bentonite, fly ash, and ramming, and their levels on the resultant mould properties were investigated and optimized using Taguchi based grey relational analysis. The Taguchi L18 orthogonal array and analysis of variance(ANOVA) were used. The quality characteristics viz., green compression strength, permeability, bulk density, mould hardness and shatter index of green sand mould were optimized using grey relational grade, based on the experiments designed using Taguchi's Design of Experiments. ANOVA analysis indicated that water content is the most influential parameter followed by bentonite, and degree of ramming that contributes to the quality characteristics. The results are confirmed by calculating confidence intervals, which lies within the interval limits. Finally, microstructure observations and X-ray diffraction analysis have been performed for the optimal sand parametric combination. Results show that presence of maximum amount of SiO_2, which might be the reason for enhancement of the physical properties of the sand.

The geographical distribution of grey wolves (Canis lupus) in China:a systematic review

The grey wolf （Canis lupus） is one of the most widely distributed terrestrial mammals, and its distribution and ecology in Europe and North America are largely well described. However, the distribution of grey wolves in southern China is still highly controversial. Several well-known western literatures stated that there were no grey wolves in southern China, while the presence of grey wolves across China has been indicated in A Guide to the Mammals of China, published by Princeton University Press. It is essential to solve this discrepancy since dogs may have originated from grey wolves in southern China. Therefore, we systematically investigated Chinese literatures about wild animal surveys and identified more than 100 articles and books that included information of the distribution of grey wolves in China. We also surveyed the collections of three Chinese natural museums and found 26 grey wolf skins specimens collected across China. Moreover, we investigated the fossil records in China and identified 25 archaeological sites with wolf remains including south China. In conclusion, with the comprehensive summary of Chinese literatures, museum specimens and fossil records, we demonstrate that grey wolves do distribute across all parts of the Chinese mainland, including the most southern parts.

Application of Grey System Theory to tree growth prediction

Based on Grey System theory, tree growth prediction models are developed by using 202 temporary plots and 206 stem analysis trees of Dahurian larch (Larix gemlinii Rupr) in 10 forestry bureaus of Yakeshi Forestry Administrative Bureau in Daxing’an Mountains of the Inner Mongolia Autonomous Region. By residual and posterior tests, their precisions are qualified. With several data, tree growth can be predicted using Grey System models. For DBH and volume, the fitting results of Grey System models are better than that of statistical models.

Optimization approach hydroforming car beam billets based grey system theory

Perfect combination of structural size parameters of the hydroforming billets is essential to obtain even wall thicknesses of the car beam. Finite element （ FE ） analysis on hydroforming car beam was carried out, and the results were optimized according to multiple quality objectives by the grey system theory. With bending angle, bending radius and hight difference along the axis direction as variables, orthogonal FE analyses were conducted and the minimum and maximum wall thicknes ses of the billets with different sizes were obtained. Taking the minimum and maximum wall thick nesses as two references, the correlation coefficient between the data for reference and those for comparison by the grey system theory reduced multi objectives to a single quality objective, and the average correlation level of every billet facilitated the optimization of size parameters for hydroform ing car beam. The trial production showed that the optimization approach satisfied the need of hy droforming car beams.

Probability estimation based on grey system theory for simulation evaluation

In the evaluation of some simulation systems, only small samples data are gotten due to the limited conditions. In allusion to the evaluation problem of small sample data, an interval estimation approach with the improved grey confidence degree is proposed.On the basis of the definition of grey distance, three kinds of definition of the grey weight for every sample element in grey estimated value are put forward, and then the improved grey confidence degree is designed. In accordance with the new concept, the grey interval estimation for small sample data is deduced. Furthermore,the bootstrap method is applied for more accurate grey confidence interval. Through resampling of the bootstrap, numerous small samples with the corresponding confidence intervals can be obtained. Then the final confidence interval is calculated from the union of these grey confidence intervals. In the end, the simulation system evaluation using the proposed method is conducted. The simulation results show that the reasonable confidence interval is acquired, which demonstrates the feasibility and effectiveness of the proposed method.

Selecting Suitable Heat Source in Refinery for Multi-effect Distillation Based on Grey System Theory

For dealing with high-salinity wastewater in the refinery, the high cost of driving heat source is the disadvantage of multi-effect distillation (MED) so it is of great importance to evaluate the performance of low-temperature heat source for conducting MED and select the optimal temperature for it. Both the MED and the low-temperature heat sources studied in this paper were from a typical refinery located in northwestern China. Besides, a new methodology to evaluate heat sources as the optimal candidate was proposed for MED based on the grey system theory. Five process units, which included 18 fluids of the refinery, were named as the evaluation projects. Three factors, which included safety effects, total costs and characteristics of low-temperature heat sources were determined as the evaluation indexes, the values of which were established through the analyses. The results obtained through the grey correlation analyses have revealed that the grey correlation degrees of these units were 0.661(AVDU), 0.732 (#1 FCCU), 0.618 (#2 FCCU), 0.535 (#1 DCU), and 0.572 (#2 DCU), respectively. Thus, the optimal heat source was provided from #1 FCCU. Through further analyses of the fluids from #1 FCCU, the grey correlation degrees of the fluids were 0.597 (oil and gas at top of tower), 0.714 (recycle oil and gas), and 0.512 (diesel), respectively. Thus, the optimal heat source was the oil and gas recycle stream.