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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Fuzzy Mean and Fuzzy Variance

Our next step is to calculate the fuzzy mean of the takeover price. Let us call it A_fuzzy_mean, to make

reference to the fuzzy event used.

The calculation is as follows:

     A_fuzzy_mean = (1/0.81) x (100 x 0.7 x 0.3 + 85 x 1 x 0.5 + 60 x 0.5 x

0.2) = 85.8

To get the fuzzy variance of the takeover price, you need to use values like (100−85.8)

2

 , which is the square

of the deviation of the takeover price 100 from the fuzzy mean. A simpler way to calculate, which is

mathematically equivalent, is to first take the fuzzy expected value of the square of the takeover price and

then to subtract the square of the fuzzy mean. To make it easier, let us use p as the variable that represents the

takeover price.

The calculations are as below:

     A_fuzzy_expected p

2

 = 1/(0.81) x (100

2

x 0.7 x 0.3 + 85

2

x 1 x 0.5 + 60

2

x

                           0.5 x 0.2) = 7496.91

     A_fuzzy_variance = 7496.91 − 85.8

2

 = 7496.91 − 7361.64 = 135.27

Fuzzy logic is thus introduced into the realm of probability concepts such as events, and statistical concepts

such as mean and variance. Further, you can talk of fuzzy conditional expectations and fuzzy posterior

probabilities, etc. enabling you to use fuzziness in Bayesian concepts, regression analysis, and so on. You will

then be delving into the field of fuzzy quantification theories. In what follows, we continue our discussion

with fuzzy conditional expectations.