C++ Neural Networks and Fuzzy Logic: Preface

C++ Neural Networks and Fuzzy Logic

by Valluru B. Rao

MTBooks, IDG Books Worldwide, Inc.

ISBN: 1558515526   Pub Date: 06/01/95

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Fuzziness in Neural Networks

There are a number of ways fuzzy logic can be used with neural networks. Perhaps the simplest way is to use

a fuzzifier function to preprocess or post−process data for a neural network. This is shown in Figure 3.1,

where a neural network has a preprocessing fuzzifier that converts data into fuzzy data for application to a

neural network.

Figure 3.1

  A neural network with fuzzy preprocessor.

Let us build a simple fuzzifier based on an application to predict the direction of the stock market. Suppose

that you wish to fuzzify one set of data used in the network, the Federal Reserve’s fiscal policy, in one of four

fuzzy categories: very accommodative, accommodative, tight, or very tight. Let us suppose that the raw data

that we need to fuzzify is the discount rate and the interest rate that the Federal Reserve controls to set the

fiscal policy. Now, a low discount rate usually indicates a loose fiscal policy, but this depends not only on the

observer, but also on the political climate. There is a probability, for a given discount rate that you will find

two people who offer different categories for the Fed fiscal policy. Hence, it is appropriate to fuzzify the data,

so that the data we present to the neural network is like what an observer would see.

Figure 3.2 shows the fuzzy categories for different interest rates. Note that the category tight has the largest

range. At any given interest rate level, you could have one possible category or several. If only one interest

rate is present on the graph, this indicates that membership in that fuzzy set is 1.0. If you have three possible

fuzzy sets, there is a requirement that membership add up to 1.0. For an interest rate of 8%, you have some

chance of finding this in the tight category or the accommodative category. To find out the percentage

probability from the graph, take the height of each curve at a given interest rate and normalize this to a

one−unit length. At 8%, the tight category is about 0.8 unit in height, and accommodative is about 0.3 unit in

height. The total is about 1.1 units, and the probability of the value being tight is then 0.8/1.1 = 0.73, while the

probability of the value being accommodative is 0.27.

Figure 3.2

  Fuzzy categories for Federal Reserve policy based on the Fed discount rate.

C++ Neural Networks and Fuzzy Logic:Preface

Fuzziness in Neural Networks

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