C++ Neural Networks and Fuzzy Logic: Preface

Union of Fuzzy Sets

Consider a union of two traditional sets and an element that belongs to only one of those sets. Earlier you saw

that if you treat these sets as fuzzy sets, this element has a degree of membership of 1 in one case and 0 in the

other since it belongs to one set and not the other. Yet you are going to put this element in the union. The

criterion you use in this action has to do with degrees of membership. You need to look at the two degrees of

membership, namely, 0 and 1, and pick the higher value of the two, namely, 1. In other words, what you want

for the degree of membership of an element when listed in the union of two fuzzy sets, is the maximum value

of its degrees of membership within the two fuzzy sets forming a union.

If a, b, c, and d have the respective degrees of membership in fuzzy sets A, B as A = (0.9, 0.4, 0.5, 0) and B =

(0.7, 0.6, 0.3, 0.8), then A [cup] B = (0.9, 0.6, 0.5, 0.8).

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C++ Neural Networks and Fuzzy Logic:Preface

Fuzzy Set Operations

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