Combining Single Input/Single Output Fuzzy Decision Trees

One widely used technique for modeling large systems entails decomposing the system along logical partitions, modeling each partition with a subsystem, and then linking the subsystems as dictated by the original decomposition. Unfortunately, understanding the overall model is often hindered by the ad hoc nature of the confederated subsystems. However, tightly coupling these subsystems allows them to be viewed at a higher level of abstraction, thus aiding understanding. Unfortunately, combining fuzzy systems is typically an inexact process. However, by employing certain postulates (including, but not limited to, the defuzzification method), fuzzy systems may be combined in a mathematically exact fashion. We propose employing yet another defuzzifier (YAD) and develop the necessary and sufficient theory for combining fuzzy systems.