C++ Neural Networks and Fuzzy Logic: Preface

price

100

85

60

probability

0.3

0.5

0.2

C++ Neural Networks and Fuzzy Logic:Preface

Queries

392

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From standard probability theory, this distribution gives a mean(or expected price) of:

     100 x 0.3 + 85 x 0.5 + 60 x 0.2 = 84.5

and a variance of :

     (100−84.5)

2

 x 0.3 +(85−84.5)

2

 x 0.5 + (60−84.5)

2

 x 0.2 = 124.825

Suppose now that a security analyst specializing in takeover situations feels that the board hates a hostile

takeover but to some extent they cannot resist the price being offered. The analyst also thinks that the board

likes to keep some control over the company, which is possible if they sell the company to their friendly

associate company. The analyst recognizes that the Board is sensitive to the fears and apprehensions of their

loyal employees with whom they built a healthy relationship over the years, and are going to consider the

offer from the employees.

The analyst’s feelings are reflected in the following fuzzy set:

     {0.7/100, 1/85, 0.5/60}

You recall that this notation says, the degree of membership of 100 in this set is 0.7, that of 85 is 1, and the

degree of membership is 0.5 for the value 60.

The fuzzy set obtained in this manner is also called a fuzzy event. A different analyst may define a different

fuzzy event with the takeover price values. You, as a shareholder, may have your own intuition that suggests a

different fuzzy event. Let us stay with the previous fuzzy set that we got from a security analyst, and give it

the name A.