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The purpose of this paper is to focus on the adjustment of the GM(1, 2) errors for financial data series that measures changes in the public sector financial indicators, taking into account that the errors in grey models remain a key problem in reconstructing the original data series.

Adjusting the errors in grey models must follow some rules that most often cannot be determined based on the chaotic trends they register in reconstructing data series. In order to ensure the adjustment of these errors, for improving the robustness of GM(1, 2), was constructed an adaptive fuzzy controller which is based on two input variables and one output variable. The input variables in the adaptive fuzzy controller are: the absolute error ε i 0 ( k ) [ % ] of GM(1, 2), and the distance between two values x i 0 ( k ) [ % ] , while the output variable is the error adjustment A ε i 0 ( k ) [ % ] determined with the help of the above-mentioned input variables.

The adaptive fuzzy controller has the advantage that sets the values for error adjustments by the intensity (size) of the errors, in this way being possible to determine the value adjustments for each element of the reconstructed financial data series.

To ensure a robust process of planning the financial resources, the available financial data are used for long periods of time, in order to notice the trend of the financial indicators that need to be planned. In this context, the financial data series could be reconstituted using grey models that are based on sequences of financial data that best describe the status of the analyzed indicators and the status of the relevant factors of influence. In this context, the present study proposes the construction of a fuzzy adaptive controller that with the help of the output variable will ensure the error’s adjustment in the reconstituted data series with GM(1, 2).

The purpose of this paper is to review the current literature in the field of tourism demand forecasting.

Published papers in the high quality journals are studied and categorized based their used forecasting method.

There is no forecasting method which can develop the best forecasts for all of the problems. Combined forecasting methods are providing better forecasts in comparison to the traditional forecasting methods.

This paper reviews the available literature from 2007 to 2017. There is not such a review available in the literature.

The purpose of this paper is to test the effectiveness of fuzzy time series (FTS) forecasting system in a supply chain experiencing disruptions and also to examine the changes in performance as the authors move across different tiers.

A discrete event simulation based on the popular beer game model is used for these tests. A popular ordering management system is used to emulate the behavior of the system when the game is played with human players.

FTS is tested against some other well-known forecasting systems and it proves to be the best of the lot. It is also shown that it is better to go for higher order FTS for higher tiers, to match auto regressive integrated moving average.

This study fills an important research gap by proving that FTS forecasting system is the best for a supply chain during disruption scenarios. This is important because the forecasting performance deteriorates significantly and the effect is more pronounced in the upstream tiers because of bullwhip effect.

Having a system which works best in all scenarios and also across the tiers in a chain simplifies things for the practitioners. The costs related to acquiring and training comes down significantly.

This study contributes by suggesting a forecasting system which works best for all the tiers and also for every scenario tested and simultaneously significantly improves on the previous studies available in this area.

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.

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.

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.

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.

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.

In order to overcome the uncertainty and improve the accuracy of spectral estimation, this paper aims to establish a grey fuzzy prediction model of soil organic matter content by using grey theory and fuzzy theory.

Based on the data of 121 soil samples from Zhangqiu district and Jiyang district of Jinan City, Shandong Province, firstly, the soil spectral data are transformed by spectral transformation methods, and the spectral estimation factors are selected according to the principle of maximum correlation. Then, the generalized greyness of interval grey number is used to modify the estimation factors of modeling samples and test samples to improve the correlation. Finally, the hyper-spectral prediction model of soil organic matter is established by using the fuzzy recognition theory, and the model is optimized by adjusting the fuzzy classification number, and the estimation accuracy of the model is evaluated using the mean relative error and the determination coefficient.

The results show that the generalized greyness of interval grey number can effectively improve the correlation between soil organic matter content and estimation factors, and the accuracy of the proposed model and test samples are significantly improved, where the determination coefficient R² = 0.9213 and the mean relative error (MRE) = 6.3630% of 20 test samples. The research shows that the grey fuzzy prediction model proposed in this paper is feasible and effective, and provides a new way for hyper-spectral estimation of soil organic matter content.

The research shows that the grey fuzzy prediction model proposed in this paper can not only effectively deal with the three types of uncertainties in spectral estimation, but also realize the correction of estimation factors, which is helpful to improve the accuracy of modeling estimation. The research result enriches the theory and method of soil spectral estimation, and it also provides a new idea to deal with the three kinds of uncertainty in the prediction problem by using the three kinds of uncertainty theory.

The paper succeeds in realizing both the grey fuzzy prediction model for hyper-spectral estimating soil organic matter content and effectively dealing with the randomness, fuzziness and grey uncertainty in spectral estimation.

The purpose of this paper is to evaluate the forecasting performance of grey prediction models on educational attainment vis-à-vis that of exponential smoothing combined with multiple linear regression employed by the National Center for Education Statistics (NCES).

An out-of-sample forecasting experiment was carried out to compare the forecasting performances on educational attainments among GM(1,1), GM(1,1) rolling, FGM(1,1) derived from the grey system theory and exponential smoothing prediction combined with multivariate regression. The predictive power of each model was measured based on MAD, MAPE, RMSE and simple F-test of equal variance.

The forecasting efficiency evaluated by MAD, MAPE, RMSE and simple F-test of equal variance revealed that the GM(1,1) rolling model displays promise for use in forecasting educational attainment.

Since the possible inadequacy of MAD, MAPE, RMSE and F-type test of equal variance was documented in the literature, further large-scale forecasting comparison studies may be done to test the prediction powers of grey prediction and its competing out-of-sample forecasts by other alternative measures of accuracy.

The findings of this study would be useful for NCES and professional forecasters who are expected to provide government authorities and education policy makers with accurate information for planning future policy directions and optimizing decision-making.

As a continuing effort to evaluate the forecasting efficiency of grey prediction models, the present study provided accumulated evidence for the predictive power of grey prediction on short-term forecasts of educational statistics.

Many studies have proposed variant fuzzy time series models for uncertain and vague data. The purpose of this paper is to adapt a fuzzy time series combined with genetic algorithm (GA) to forecast tourist arrivals in Taiwan.

Different cases are studied to understand the effect of variation of fuzzy time series order, number of intervals and population size on the fitness function which decreases with increase in fuzzy time series order and number of fuzzy intervals, but do not have marginal effect due to change in population size.

Results based on an example of forecasting Taiwan’s tourism demand was used to verify the efficacy of proposed model and confirmed its superiority to existing models providing solutions for different orders of fuzzy time series, number of intervals and population size with a smaller forecasting error as measured by root mean square error.

This study provides a viable forecasting methodology, adapting a fuzzy time series combined with an evolutionary GA. The proposed hybridized framework of fuzzy time series and GA, where GA is used to calibrate fuzzy interval length, is flexible and replicable to many industrial situations.

The purpose of this paper is to explore new ways and lay a solid foundation to solve the problem of reliability growth analysis of major aerospace equipment with various uncertainty data through propose new concepts of general uncertainty data (GUD) and general uncertainty variable (GUV) and build the operation system of GUVs.

The characteristics of reliability growth data of major aerospace equipment and the limitations of current reliability growth models have been analyzed at first. The most commonly used uncertainty system analysis methods of probability statistics, fuzzy mathematics, grey system theory and rough set theory have been introduced. The concepts of GUD and GUV for reliability growth data analysis of major aerospace equipment are proposed. The simplified form of GUV based on the “kernel” and the degree of uncertainty of GUV is defined. Then an operation system of GUVs is built.

(1) The concept of GUD; (2) the concept of GUV; (3) The novel operation rules of GUVs with simplified form.

The method exposed in this paper can be used to integrate complex reliability growth data of major aerospace equipment. The reliability growth models based on GUV can be built for reliability growth evaluation and forecasting of major aerospace equipment in practice. The reliability evaluation example of a solid rocket motor shows that the concept and idea proposed in this paper are feasible. The research of this paper opens up a new way for the analysis of complex uncertainty data of reliability growth of major aerospace equipment. Moreover, the operation of GUVs could be extended to the case of algebraic equation, differential equation and matrix which including GUVs.

The new concepts of GUD and GUV are given for the first time. The novel operation rules of GUVs with simplified form were constructed.

In the daily energy dispatch process in a power system, accurate short-term electricity load forecasting is a very important tool used by spot market players. It is a critical requirement for optimal generator unit commitment, economic dispatch, system security and stability assessment, contingency and ancillary services management, reserve setting, demand side management, system maintenance and financial planning in power systems. The purpose of this study is to present an improved grey Verhulst electricity load forecasting model.

To test the effectiveness of the proposed model for short-term load forecast, studies made use of Kenya’s load demand data for the period from January 2014 to June 2019.

The convectional grey Verhulst forecasting model yielded a mean absolute percentage error of 7.82 per cent, whereas the improved model yielded much better results with an error of 2.96 per cent.

In the daily energy dispatch process in a power system, accurate short-term load forecasting is a very important tool used by spot market players. It is a critical ingredient for optimal generator unit commitment, economic dispatch, system security and stability assessment, contingency and ancillary services management, reserve setting, demand side management, system maintenance and financial planning in power systems. The fact that the model uses actual Kenya’s utility data confirms its usefulness in the practical world for both economic planning and policy matters.

In terms of generation and transmission investments, proper load forecasting will enable utilities to make economically viable decisions. It forms a critical cog of the strategic plans for power utilities and other market players to avoid a situation of heavy stranded investment that adversely impact the final electricity prices and the other extreme scenario of expensive power shortages.

This research combined the use of natural logarithm and the exponential weighted moving average to improve the forecast accuracy of the grey Verhulst forecasting model.

Because of the high volatility with unstable data patterns in the real world, the ability of forecasting price indices is notoriously embarrassing and represents a major challenge with traditional time series mechanisms; especially, most of the traditional approaches are weak to forecast future predictions in the high volatile and unbalanced frameworks under the global and local financial depressions. The purpose of this paper is to propose a new statistical approach for portfolio selection and stock market forecasting to assist investors as well as stock brokers to predict the future behaviors.

This study mainly takes an attempt to understand the trends, behavioral patterns and predict the future estimations under the new proposed frame for the Colombo Stock Exchange (CSE), Sri Lanka. The methodology of this study is carried out under the two main phases. In the first phase, constructed a new portfolio mechanism based on k-means clustering. In the second stage, proposed a nonlinear forecasting methodology based on grey mechanism for forecasting stock market indices under the high-volatile fluctuations. The autoregressive integrated moving average (ARIMA) predictions are used as comparison mode.

Initially, the k-mean clustering was applied to pick out the profitable sectors running under the CSE and results indicated that BFI is more significant than other 20 sectors. Second, the MAE, MAPE and MAD model comparison results clearly suggested that, the newly proposed nonlinear grey Bernoulli model (NGBM) is more appropriate than traditional ARIMA methods to forecast stock price indices under the non-stationary market conditions.

Because of the flexible nonlinear modeling capability, proposed novel concepts are more suitable for applying in various areas in the field of financial, economic, military, geological and agricultural systems for pattern recognition, classification, time series forecasting, etc.

For the large sample of data forecasting under the normality assumptions, the traditional time series methodologies are more suitable than grey methodologies. However, the NGBM is better both in model building and ex post testing stagers under the s-distributed data patterns with limited data forecastings.