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 Numbers

A fuzzy number is an ordered pair of numbers (a, b) with respect to a reference function L, which gives you

the membership function. Here b has to be a positive number.

Here are the properties of L, the reference function:

1.  It is a function of one variable and is symmetric about 0. That is, L(x) = L(−x).

2.  It has a value of 1 at x = 0. In other words, L(0) = 1.

3.  It is generally decreasing, when x is 0 or a positive number, meaning that its value drops as the

value of its argument is increased. For example, L(2) < L(1). Thus L(x) has its values less than 1 for

positive values of x. It does not make sense to have negative numbers as values of L, and so you

ignore the values of x that cause such values for L.