C++ Neural Networks and Fuzzy Logic: Preface

Conditional Probability of a Fuzzy Event

Suppose you, as a shareholder of the XYZ company in the previous example come up with the fuzzy set, we

will call the fuzzy event:

B = {0.8/100, 0.4/85, 0.7/60}

The probability for your fuzzy event is as follows:

     0.8 x 0.3 + 0.4 x 0.5 + 0.7 x 0.2 = 0.58

B_fuzzy_mean and B_fuzzy_variance of the takeover price of XYZ stock work out as 85.17 and 244.35,

respectively. But you want to see how these values change if at all when you take A, the analyst’s fuzzy event,

as a given. You are then asking to determine the conditional probability of your fuzzy event, and your

conditional fuzzy mean and fuzzy variance as well.

C++ Neural Networks and Fuzzy Logic:Preface

Fuzzy Mean and Fuzzy Variance

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The conditional probability of your fuzzy event is calculated as follows:

     (1/0.81) x (0.8 x 0.7 x 0.3 + 0.4 x 1 x 0.5 + 0.7 x 0.5 x 0.2) = 0.54

This value is smaller than the probability you got before when you did not take the analyst’s fuzzy event as

given. The a priori probability of fuzzy event B is 0.58, while the a posteriori probability of fuzzy event B

given the fuzzy event A is 0.54.