Abstract
The paper extends Kosko's fuzzy measure of subsethood (Kosko 1992) to a measure of mutual subsethood or fuzzy equivalence. Gaussian or bell-shaped fuzzy sets then simplify the new measure and allow supervised learning to learn and tune the fuzzy rules. The gaussian sets act as nodes in neural fuzzy control networks and give a simple closed form for the measure of mutual subsethood. The new adaptive subsethood controller (ASC) system uses the network structure to store, learn, and tune fuzzy rules. Simulations show how the ASC system can control a model car, balance an inverted wedge, and control the ball and beam system
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