C++ Neural Networks and Fuzzy Logic: Preface

p

 clearly suggest fuzziness. The

entry {10, 11}

p

, is a possibility distribution, suggesting that the number of visits outside the United States

made by Roberto is either 10 or 11. Similarly, Raj’s citizenship is India or United States, but not dual

citizenship in both. Andre’s citizenship and Alan’s number of visits outside the United States are not known,

and they can have any values. The possibilities cannot be narrowed down as in the case of Raj’s citizenship

and Roberto’s frequency of visits outside the United States The entry undefined is used for Alan because he

always traveled alone, he never took a companion.

James’ number of visits is fuzzy. He traveled many times. A fuzzy set for many will provide the possibility

distribution. It can be defined, for example, as:

    many = {0.2/6, 0.5/7, 0.8/8, 1/9, 1/10, ...}

The name of the companion on James’ latest visit outside the United States is entered as null because we do

not know on the one hand whether he never took a companion, in which case we could have used undefined

as in Alan’s case, and on the other whom he took as a companion if he did take one, in which case we could

have used unknown. Simply put, we use null when we do not know enough to use either unknown or

undefined.

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C++ Neural Networks and Fuzzy Logic:Preface

Possibility Distributions

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