Abstract: At first, based on the theory of fuzzy sets and fractal theory, the concepts of fuzzy fractal dimensions has been further introduced, the definitions and methods for determination of fuzzy Hausdorff fractal dimension D0 and fuzzy relative fractal dimension D2 were given, and the relation between fuzzy fractal dimension and usual （clear） fractal dimension was discussed.Then, three results of the applications of the fuzzy fractal dimension in earthquake researches were obtained. They are as follows:1.The characteristics of fuzzy temporal fractal dimension of the activity- of large earthquakes. According to the variation of fuzzy temporal fractal dimension D0（1） with respect to time, the periods of high seismicity of large earthquakes corresponding to the periods of increase of D0（1） can be distinguished. By using the temporal variation curves of fuzzy Hausdorff fractal dimension D0（1） and fuzzy relative fractal dimension D2 the long-medium term precursory anomalous variations in seismicity before large earthquakes may be recognized.2.The characteristics of fuzzy spatial fractal dimension of the activity of strong and moderate earthquakes. According to the temporal and spatial variations of D0（2）, the riskful regions of forthcoming large earthquakes corresponding to the regions of increase or decrease of D0（2） and the anomalous variations of seismicity in several years before large earthquakes may be recognized.3.The characteristics of fuzzy temporal fractal dimension of the earthquake precursors. According to the variation of fuzzy temporal fractal dimension D0（1） of precursors data with respect to time,the short term precursory anomalies before large earthquakes may be discovered.