A fuzzy system trained by a genetic algorithm offers explainability and transparency in its decision making. Here, an aggregate fuzzy system works towards explainability while greatly reducing the number of rules needed to describe the system. The genetic algorithm, fuzzy logic and aggregate fuzzy tree are the separate parts that make up this system, and have been summarized. This system is trained on the Breast Cancer Wisconsin Data set. Two variations in the training of the system include the genetic algorithm mutation rate and the structure of the aggregate fuzzy tree. The method with the highest accuracy, where the tree structure is fixed and the mutation is varied, is examined closer to illustrate the level of explainability and transparency of such a system. An accuracy of 94.96% and a sensitivity of 98.08% is achieved on the test data, and while slightly lower than accuracy achieved in previous works on this data set, the model trained here works towards explainability, which is of high importance.