Apple fruit sorting has been an important postharvest process carried on for the sorting of diseased apple fruits. A fuzzy cluster-based thresholding (FCBT) method for segmenting the region of interest from an apple image has been proposed for sorting apples in this study. As the first step, the acquired RGB colour image of an apple fruit was converted into a greyscale image. Then, five different fuzzy cluster bins with overlapped pixel ranges were taken and greypixel values were binned into them. A cluster with the maximum number of pixels was selected for calculating the threshold value. The region of interest from the apple image was then segmented using the proposed FCBT value. Features extracted from the segmented images were given as input to a fully-connected deep neural network for a classification. The performance of the FCBT method was compared with similar greyscale thresholding methods like Otsu's and Kapur's methods. The visual segmentation accuracy and the execution speed showed that the FCBT outperformed the other methods in segmenting the diseased area. A fully-connected deep neural network model with the FCBT image extracted features as input values gave a 98.33% accuracy rate in sorting the apple images.