R.K. Brouwer (Canada) and W. Pedrycz (Canada, Poland)

Fuzzy sets, Multilayer perceptrons, Multivaluedmappings, Feed forward networks, Membership functions

Multilayer perceptrons (MLP) or feed forward neural networks (FFNN) are generally used to represent many to-one (m-o) mappings or functions from n to codomain m . Input units distribute real values to hidden layer units and individual output units produce values in . Thus MLP's represent or simulate the mappings of functions where the range consists of vectors. However it is also useful to represent mappings where the range consists of elements that are sets or collections (bags) of vectors of real values. Representing mappings from vectors to sets of real numbers or vectors of real numbers has a useful application that is of interest since a one-to-many (o-m) mapping from n to codomain m is equivalent to a m-o mapping from n to codomain P(m ) where P(m ) is the power set of m . The paper describes a modified training algorithm that successfully stores a one-to-many mapping on a feed-forward network requiring a relatively small number of training epochs.

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