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Monitoring hospital adverse events ensures the patient's safety. This study aims to develop a multilevel control chart and to apply fuzzy set theory and warning lines concept to monitor inpatient adverse events. This study uses a u chart to monitor the adverse events relating to falls. This study also considers the severity of fall injuries to develop multilevel control charts, and applies fuzzy set theory to determine the severity of falls. The final analysis of this study is a combination of multilevel control charts, fuzzy set theory, and warning lines concept. The findings of this study show that traditional control charts do not consider the severity of fall injury, whereas multilevel control charts can make up for the deficiencies of traditional control charts through the establishment of fuzzy rules and warning lines, thus reducing the shortcomings of traditional control charts, which cause error and low sensitivity.

How to evaluate an appropriate correlation with fuzzy data is an important topic in the educational and psychological measurement. Especially when the data illustrate uncertain, inconsistent and incomplete type, fuzzy statistical method has some promising features that help resolving the unclear thinking in human logic and recognition. Traditionally, we use Pearson’s Correlation Coefficient to measure the correlation between data with real value. However, when the data are composed of fuzzy numbers, it is not feasible to use such a traditional approach to determine the fuzzy correlation coefficient. This study proposes the calculation of fuzzy correlation with three types of fuzzy data: interval, triangular and trapezoidal. Empirical studies are used to illustrate the application for evaluating fuzzy correlations. More related practical phenomena can be explained by this appropriate definition of fuzzy correlation.