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.

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.

Key indexes identifying approach of weapon equipment system-of-systems effectiveness integrating Bayes method and dynamic grey incidence analysis model

Aiming at the characteristics of multi-stage and(extremely)small samples of the identification problem of key effectiveness indexes of weapon equipment system-of-systems(WESoS),a Bayesian intelligent identification and inference model for system effectiveness assessment indexes based on dynamic grey incidence is proposed.The method uses multi-layer Bayesian techniques,makes full use of historical statistics and empirical information,and determines the Bayesian estima-tion of the incidence degree of indexes,which effectively solves the difficulties of small sample size of effectiveness indexes and difficulty in obtaining incidence rules between indexes.Sec-ondly,The method quantifies the incidence relationship between evaluation indexes and combat effectiveness based on Bayesian posterior grey incidence,and then identifies key system effec-tiveness evaluation indexes.Finally,the proposed method is applied to a case of screening key effectiveness indexes of a missile defensive system,and the analysis results show that the proposed method can fuse multi-moment information and extract multi-stage key indexes,and has good data extraction capability in the case of small samples.

Interval grey number sequence prediction by using non-homogenous exponential discrete grey forecasting model

This paper aims to study a new grey prediction approach and its solution for forecasting the main system variable whose accurate value could not be collected while the potential value set could be defined. Based on the traditional nonhomogenous discrete grey forecasting model（NDGM）, the interval grey number and its algebra operations are redefined and combined with the NDGM model to construct a new interval grey number sequence prediction approach. The solving principle of the model is analyzed, the new accuracy evaluation indices, i.e. mean absolute percentage error of mean value sequence（MAPEM） and mean percent of interval sequence simulating value set covered（MPSVSC）, are defined and, the procedure of the interval grey number sequence based the NDGM（IG-NDGM） is given out. Finally, a numerical case is used to test the modelling accuracy of the proposed model. Results show that the proposed approach could solve the interval grey number sequence prediction problem and it is much better than the traditional DGM（1,1） model and GM（1,1） model.

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.

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.

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.

Grey System Judgment on Reliability of Mechanical Equipment

he Grey system theory -was applied in reliability analysis of mechanical equip-ment. It is a new theory and method in reliability engineering of mechanical engineering of mechanical equipment. Through the Grey forecast of reliability parameters and the reliability forecast of parts and systems, decisions were made in the real operative state of e-quipment in real time. It replaced the old method that required mathematics and physical statistics in a large base of test data to obtain a pre-check , and it was used in a practical problem. Because of applying the data of practical operation state in real time, it could much more approach the real condition of equipment; it-was applied to guide the procedure and had rather considerable economic and social benefits.

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.

Grey relationship analysis and grey forecasting modeling on thermal stability of synthetic single diamond

Through analyzing 7 Ib-type samples of synthetic single diamonds by their DTA and TG in air, we ascertained the extrapolated onset temperature on the curves of DTA as the characteristic temperature of their thermal stabilities. Based on the grey system theory, we analyzed 4 factors influential in the thermal stability by the grey relationship analysis, a quantitative method, and derived the grey relationship sequence, that is, the rank of the influence extent of 4 factors on the thermal stability. Furthermore, we established the grey forecasting model, namely GM(1,5), for predicting the thermal stability of single diamonds with their intrinsic properties, which was then examined by a deviation-probability examination. The results illustrate that it is reasonable to take the Extrapolated Onset Temperature in DTA as the characteristic temperature for thermal stability (TS) of Ib-type synthetic single diamonds. The nitrogen content and grain shape regularity of diamonds are dominating factors. Likewise, grain size and compressive strength are minor factors. In addition, GM(1,5) can be used to predict the thermal stability of Ib-type synthetic single diamonds available. The precision rank of GM(1,5) is ‘GOOD’.

Grey Repairable System Analysis

In this paper, we systematically discuss the basic concepts of grey theory, particularly the grey differential equation and its mathematical foundation, which is essentially unknown in the reliability engineering community. Accordingly, we propose a small-sample based approach to estimate repair improvement effects by partitioning system stopping times into intrinsic functioning times and repair improvement times. An industrial data set is used for illustrative purposes in a stepwise manner.

The Study on Agricultural Economy Forecasting using Grey Relationship Model

Thinking of grey group model is the improvement on the traditional grey model. It does not merely use a grey model as the ultimate basis, but takes full account of the traditional GM （1,1） model and the GM （1, n） model and join two predictions to form a prediction interval. So, the results are more reasonable and more realistic requirements and have strong guidance and reference. The farther the forecast period is, the worse the forecast is. The forecasts in the forecast period of 1-3 Years are the best, but the results of long-term are only as a reference value and the guidance data. Therefore, as the forecast period goes on, rolling grey model is used to increase accuracy.

A new grey forecasting model based on BP neural network and Markov chain

A new grey forecasting model based on BP neural network and Markov chain was proposed. In order to combine the grey forecasting model with neural network, an important theorem that the grey differential equation is equivalent to the time response model, was proved by analyzing the features of grey forecasting model（GM（1,1））. Based on this, the differential equation parameters were included in the network when the BP neural network was constructed, and the neural network was trained by extracting samples from grey system＇s known data. When BP network was converged, the whitened grey differential equation parameters were extracted and then the grey neural network forecasting model （GNNM（1,1）） was built. In order to reduce stochastic phenomenon in GNNM（1,1）, the state transition probability between two states was defined and the Markov transition matrix was established by building the residual sequences between grey forecasting and actual value. Thus, the new grey forecasting model（MNNGM（1,1）） was proposed by combining Markov chain with GNNM（1,1）. Based on the above discussion, three different approaches were put forward for forecasting China electricity demands. By comparing GM（1, 1） and GNNM（1,1） with the proposed model, the results indicate that the absolute mean error of MNNGM（1,1） is about 0.4 times of GNNM（1,1） and 0.2 times of GM（I, 1）, and the mean square error of MNNGM（1,1） is about 0.25 times of GNNM（1,1） and 0.1 times of GM（1,1）.

Application of Improved Grey Prediction Model to Petroleum Cost Forecasting

The grey theory is a multidisciplinary and generic theory that deals with systems that lack adequate information and/or have only poor information. In this paper, an improved grey model using step function was proposed. Petroleum cost forecast of the Henan oil field was used as the case study to test the efficiency and accuracy of the proposed method. According to the experimental results, the proposed method obviously could improve the prediction accuracy of the original grey model.

STUDY ON GREY FORECASTING MODEL OF COPPER EXTRACTION RATE WITH BIOLEACHING OF PRIMARY SULFIDE ORE

A model GM （grey model） （1,1） for forecasting the rate of copper extraction during the bioleaching of primary sulphide ore was established on the basis of the mathematical theory and the modeling process of grey system theory. It was used for forecasting the rate of copper extraction from the primary sulfide ore during a laboratory microbial column leaching experiment. The precision of the forecasted results were examined and modified via ＂posterior variance examination＂. The results show that the forecasted values coincide with the experimental values. GM （1,1） model has high forecast accuracy; and it is suitable for simulation control and prediction analysis of the original data series of the processes that have grey characteristics, such as mining, metallurgical and mineral processing, etc. The leaching rate of such copper sulphide ore is low. The grey forecasting result indicates that the rate of copper extraction is approximately 20% even after leaching for six months.

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.

The Application of a Grey Markov Model to Forecasting Annual Maximum Water Levels at Hydrological Stations

Compared with traditional real-time forecasting,this paper proposes a Grey Markov Model(GMM) to forecast the maximum water levels at hydrological stations in the estuary area.The GMM combines the Grey System and Markov theory into a higher precision model.The GMM takes advantage of the Grey System to predict the trend values and uses the Markov theory to forecast fluctuation values,and thus gives forecast results involving two aspects of information.The procedure for forecasting annul maximum water levels with the GMM contains five main steps:1) establish the GM(1,1) model based on the data series;2) estimate the trend values;3) establish a Markov Model based on relative error series;4) modify the relative errors caused in step 2,and then obtain the relative errors of the second order estimation;5) compare the results with measured data and estimate the accuracy.The historical water level records(from 1960 to 1992) at Yuqiao Hydrological Station in the estuary area of the Haihe River near Tianjin,China are utilized to calibrate and verify the proposed model according to the above steps.Every 25 years' data are regarded as a hydro-sequence.Eight groups of simulated results show reasonable agreement between the predicted values and the measured data.The GMM is also applied to the 10 other hydrological stations in the same estuary.The forecast results for all of the hydrological stations are good or acceptable.The feasibility and effectiveness of this new forecasting model have been proved in this paper.

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.

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.