70. | C++ Neural Networks and Fuzzy Logic

C++ Neural Networks and Fuzzy Logic
by Valluru B. Rao
M&T Books, IDG Books Worldwide, Inc.
ISBN: 1558515526 Pub Date: 06/01/95

Table of Contents

Output

The illustrative run of the previous program uses the fuzzy sets with fit vectors (0.1, 0.3, 0.2, 0.0, 0.7, 0.5) and (0.4, 0.2, 0.1, 0.0). As you can expect according to the discussion earlier, recall is not perfect in the reverse direction and the fuzzy associated memory consists of the pairs (0.1, 0.3, 0.2, 0.0, 0.4, 0.4) with (0.4, 0.2, 0.1, 0.0) and (0.1, 0.2, 0.2, 0, 0.2, 0.2) with (0.2, 0.2, 0.1, 0). The computer output is in such detail as to be self-explanatory.

 THIS PROGRAM IS FOR A FUZZY ASSOCIATIVE MEMORY NETWORK. THE NETWORK IS SET UP FOR ILLUSTRATION WITH SIX INPUT NEURONS, AND FOUR OUTPUT NEURONS. 1 exemplars are used to encode X vector you gave is: 0.1  0.3  0.2  0  0.7  0.5 Y vector you gave is: 0.4  0.2  0.1  0   weights--input layer to output layer: 0.1  0.1  0.1  0 0.3  0.2  0.1  0 0.2  0.2  0.1  0 0    0    0    0 0.4  0.2  0.1  0 0.4  0.2  0.1  0 weights--output layer to input layer: 0.1  0.3  0.2  0  0.4  0.4 0.1  0.2  0.2  0  0.2  0.2 0.1  0.1  0.1  0  0.1  0.1 0    0    0    0  0    0 Input vector is: 0.1 0.3 0.2 0 0.7 0.5 output layer neuron  0 activation is 0.4 output layer neuron  0 output is 0.4 output layer neuron  1 activation is 0.2 output layer neuron  1 output is 0.2 output layer neuron  2 activation is 0.1 output layer neuron  2 output is 0.1 output layer neuron  3 activation is 0  output layer neuron  3 output is 0 X vector in possible associated pair is: 0.1  0.3  0.2  0  0.7  0.5 Y vector in possible associated pair is: 0.4  0.2  0.1  0 input layer neuron 0 activation is 0.1 input layer neuron  0 output is 0.1 input layer neuron 1 activation is 0.3 input layer neuron  1 output is 0.3 input layer neuron 2 activation is 0.2 input layer neuron  2 output is 0.2 input layer neuron 3 activation is 0 input layer neuron  3 output is 0 input layer neuron 4 activation is 0.4 input layer neuron  4 output is 0.4 input layer neuron 5 activation is 0.4 input layer neuron  5 output is 0.4 output layer neuron  0 activation is 0.4 output layer neuron  0 output is 0.4 output layer neuron  1 activation is 0.2 output layer neuron  1 output is 0.2 output layer neuron  2 activation is 0.1 output layer neuron  2 output is 0.1 output layer neuron  3 activation is 0 output layer neuron  3 output is 0 X vector in possible associated pair is: 0.1  0.3  0.2  0  0.4  0.4 Y vector in possible associated pair is: 0.4  0.2  0.1  0 PATTERNS ASSOCIATED: X vector in the associated pair no. 1 is: 0.1  0.3  0.2  0  0.4  0.4 Y vector in the associated pair no. 1 is: 0.4  0.2  0.1  0 Input vector is: 0.6 0 0.3 0.4 0.1 0.2  output layer neuron  0 activation is 0.2  output layer neuron  0 output is 0.2  output layer neuron  1 activation is 0.2  output layer neuron  1 output is 0.2  output layer neuron  2 activation is 0.1  output layer neuron  2 output is 0.1  output layer neuron  3 activation is 0  output layer neuron  3 output is 0 X vector in possible associated pair is: 0.6  0  0.3  0.4  0.1  0.2 Y vector in possible associated pair is: 0.2  0.2  0.1  0 input layer neuron 0 activation is 0.1  input layer neuron  0 output is 0.1 input layer neuron 1 activation is 0.2  input layer neuron  1 output is 0.2 input layer neuron 2 activation is 0.2  input layer neuron  2 output is 0.2 input layer neuron 3 activation is 0  input layer neuron  3 output is 0 input layer neuron 4 activation is 0.2  input layer neuron  4 output is 0.2 input layer neuron 5 activation is 0.2  input layer neuron  5 output is 0.2  output layer neuron  0 activation is 0.2  output layer neuron  0 output is 0.2  output layer neuron  1 activation is 0.2  output layer neuron  1 output is 0.2  output layer neuron  2 activation is 0.1  output layer neuron  2 output is 0.1  output layer neuron  3 activation is 0  output layer neuron  3 output is 0 X vector in possible associated pair is: 0.1  0.2  0.2  0  0.2  0.2 Y vector in possible associated pair is: 0.2  0.2  0.1  0  output layer neuron  0 activation is 0.2  output layer neuron  0 output is 0.2  output layer neuron  1 activation is 0.2  output layer neuron  1 output is 0.2  output layer neuron  2 activation is 0.1  output layer neuron  2 output is 0.1  output layer neuron  3 activation is 0  output layer neuron  3 output is 0  output layer neuron  0 activation is 0.2  output layer neuron  0 output is 0.2  output layer neuron  1 activation is 0.2  output layer neuron  1 output is 0.2  output layer neuron  2 activation is 0.1  output layer neuron  2 output is 0.1  output layer neuron  3 activation is 0  output layer neuron  3 output is 0 X vector in possible associated pair is: 0.1  0.2  0.2  0  0.2  0.2 Y vector in possible associated pair is: 0.2  0.2  0.1  0 PATTERNS ASSOCIATED: X vector in the associated pair no. 2 is: 0.1  0.2  0.2  0  0.2  0.2 Y vector in the associated pair no. 2 is: 0.2  0.2  0.1  0 THE FOLLOWING ASSOCIATED PAIRS WERE FOUND BY FUZZY AM X vector in the associated pair no. 1 is: 0.1  0.3  0.2  0  0.4  0.4 Y vector in the associated pair no. 1 is: 0.4  0.2  0.1  0 X vector in the associated pair no. 2 is: 0.1  0.2  0.2  0  0.2  0.2 Y vector in the associated pair no. 2 is: 0.2  0.2  0.1  0

Summary

In this chapter, bidirectional associative memories are presented for fuzzy subsets. The development of these is largely due to Kosko. They share the feature of resonance between the two layers in the network with Adaptive Resonance theory. Even though there are connections in both directions between neurons in the two layers, only one weight matrix is involved. You use the transpose of this weight matrix for the connections in the opposite direction. When one input at one end leads to some output at the other, which in turn leads to output same as the previous input, resonance is reached and an associated pair is found. In the case of bidirectional fuzzy associative memories, one pair of fuzzy sets determines one fuzzy associative memory system. Fit vectors are used in max–min composition. Perfect recall in both directions is not the case unless the heights of both fit vectors are equal. Fuzzy associative memories can improve the performance of an expert system by allowing fuzzy rules.

Table of Contents