Derivation of Fuzzy Membership Functions using One-Dimensional Self-Organizing Maps

Thomas E. Sandidge
Cihan H. Dagli, Missouri University of Science and Technology

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This paper discusses a system of self-organizing maps that approximate the fuzzy membership function for an arbitrary number of fuzzy classes. This is done through the ordering and clustering properties of one-dimensional self-organizing maps and iterative approximation of conditional probabilities of nodes in one map being the winner given that a node in the other map is the winner. Application of this system reduces fuzzy membership design time to that required to train the system of self-organizing maps.