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This study is going to use the Grey relational analysis (GRA) to analyze the Test of the van Hiele levels of geometrical reasoning. The current results of this study is not only identify the easiest and the most difficult questions for students, but also displays that the proposed GRA provides a novel approach in handling educational test.

Research highlights? Grey relational analysis (GRA) has been one of the most practical analytical tools. ? The values of grey relational grade are computed using current GRA model. ? This implies that the GRA model is capable of managing financial risks. ? According to the definition of the prediction accuracy ratio for crisis banks, 11 out of 13 companies are correctly clustered. ? It is a significant implication for the establishment of early warning models of financial crisis. This study proposes a new approach for analyzing the credit risks of banking industry based on the modeling of grey relational analysis (GRA). In order to construct a financial crisis warning system for banking industry, a GRA approach is developed and applied to the real data set with 111 samples. The results of the current model are compared to those of traditional ones, logistic regression and back-propagation neural network. The results illustrate that in the prediction of financially crisis as well as financially sound banks, the proposed GRA model demonstrates better prediction accuracy than the conventional ones. The results also imply that the financial data set one year before the crisis leads to the best accuracy. It is helpful for the establishment of early warning models of financial crisis for banks. The current results show that the proposed GRA provides a novel approach in handling financial crisis warning tasks.

The purpose of this study is to understand how student behave in the online learning environment Moodle. By using Grey relational analysis to understand and to predict students' grades, researchers are interested in understanding if there is any association between students' interactivities and their final grades in Moodle system. We developed online materials for two-semester elementary calculus for the first-year students in college of management of a general University in Taiwan. The current data are collected from the online activities of the first semester, whose topics cover the introductory review through derivatives of exponential and logarithmic functions. Twelve online quizzes are built up to include all important topics of the coverage. GRA results are obtained from this group, so we can understand which online quiz activity is significantly correlated with students' final grades.

A new hybrid approach based on fuzzy logics and logistic regression analysis is proposed to demonstrate whether supervision has early warning ability of financial crises for Taiwan’s banking industry. First, it extracts significant financial variables, macroeconomic variable and corporate governance variable affecting the occurrence of banking crises from past literature, and then creates financial crisis warning system with data of 5 years, 4 years, 3 years, and 2 years before the occurrence of banking crises and discussed key factors causing banking crises. Extracted key factors are further predicted by a fuzzy logics model. When the fuzzy forecasting model is developed to predict the key variables, satisfactory results are obtained. The current hybrid approach is proved to be robust and accurate.

The grey relational analysis is widely used in many fields, such as education, decision-making in economics, marketing research, medicine, computer science, system modeling, social science, chemistry, management, etc. In this paper, the algorithms between grey relational analysis and fuzzy c-mean are compared. Finally, one real data set was applied to prove that the performance of the Grey Relational Analysis (GRA) is better than those of FCM algorithm.

This study proposes a new approach for analyzing the credit risks of banking industry based the modeling of Grey Relational Analysis (GRA). In order to construct a financial distress warning system for banking industry, a GRA approach is developed and applied to the real data set with 111 samples. The results of the current model are compared to those of traditional ones. The results illustrate that in the prediction of financially distress as well as financially sound banks, the proposed GRA model demonstrates better prediction accuracy than the conventional ones. The results also imply that the financial data set one year before the crisis leads to the best accuracy. It is helpful for the establishment of early warning models of financial crisis. The current results show that the proposed GRA provides a novel approach in handling financial distress warning tasks.

A grey relational analysis (GRA) approach is proposed for analyzing the credit risks of banking industry. To construct a financial distress warning system for banking industry, a GRA approach is developed and applied to the real data set with 34 banking samples for the period 2004—2006. The results of the current model are compared to those of traditional ones. The empirical results show that in the prediction of financially distress as well as financially sound banks, the proposed GRA model demonstrates a good prediction model. The results also imply that the three-year average leads to the best accuracy. It is a significant implication for the establishment of early warning models of financial crisis. The current results show that the proposed GRA provides a new and robust approach in managing financial distress warning tasks.

In view of the model of Song and Chissom (1993), their first-order model is effective to analysis historical data with linguistic variables, but the other membership function effects are still unknown. In this study, authors consider various membership functions, and make the results more accurate. The membership functions include unit step function, linear function, and polynomial function with various degrees. To illustrate the effect of the membership function, the forecasting enrollments at the University of Alabama are carried out. It is found that the second-degree polynomial has the best effect to the first-order model, but the unit step function has the best effect to second and third order models.

This study investigates the forecasting scheme of local region data. In view of the model of Song and Chissom (1993), we find it is robust for large amounts of data. After implementation for local region data, in this study, we find it is not so accurate as expected. Hence, the proposed scheme is tried. This scheme can make the forecasting more accurate. To illustrate the effect of this proposed scheme, the forecasting enrollments of Tainan, a small city in Taiwan, are carried out. It is found that the root mean square error of the forecasting enrollments can be improved from 443.44 for the Song-Chissom method to 45.69 for the proposed model.

This paper studies the influence of a novel scheme. First-order fuzzy time series models embedded with this novel scheme become high-order. To illustrate this high-order model, the forecasting of enrolments is conducted. The results are compared with those of Chen's method and those of the Song-Chissom method. It is found that the root mean square error of the forecast can be improved from 630.86 for Chen's method and 624.23 for the Song-Chissom method to 199.32 for the proposed model.

We study the influence of a novel scheme which can be embedded into the Chen model. The data of historical records of exchange rates between the US Dollar and NT Dollar shown by Wu and Shih (1994) are conducted. The root mean square error of the forecasts can be improved from 0.1872 for Chen's method to 0.0314 for the current model.

A formulation is proposed for the modeling of second-order fuzzy time series. The method of fuzzy time series has been proved an effective tool for a variety of forecasting problems. When the historical data on hand are linguistic values, the traditional time series methodologies fail to work. Due to this situation, the fuzzy time series model has been developed and applied. Although many applications of the fuzzy time series method can be found in the literature, they are based on the first-order fuzzy time series and the accuracy of forecast is quite limited. In order to enhance the accuracy of forecasting results and to keep the simplicity of high-order fuzzy time series models, a new formulation is developed. By taking advantage of the current model, the historical records of population in the Taiwan area are tested. The results are compared with those of the traditional regression method and those of the first-order fuzzy time series. It is found that the accuracy of the second-order model is the best.