Motivated defuzzification in totally fuzzy inference

This paper begins with mathematical background and a review of inference using totally fuzzy sets (also called Omega-valued sets) based mainly on the comprehensive work of U. Hohle. Following reference [1] and especially references [5-6], we delineate the process by which fuzzy inference can be performed using "fuzzy partitions". In this context, and adhering strictly to the mathematics, it becomes apparent that commonly used defuzzification techniques are unmotivated. We propose, in the final section, one way this inference "defect" can be remedied, using the notion of a frame nucleus. This nuclear defuzzification is very different from the usual kind, which is applied ad hoc to the inference results, and amounts to a predefuzzification of the entire inference system.