C++ Neural Networks and Fuzzy Logic: Preface

(i)

U o W = V if and only if height (U) e height (V).

(ii)

V o W

T

 = U if and only if height (V) e height (U).

Also note that if X and Y are arbitrary fit vectors with the same dimensions as U and V, then:

(iii)

X o W 4 V.

(iv)

Y o W

T

 4 U.

A 4 B is the notation to say A is a subset of B.

C++ Neural Networks and Fuzzy Logic:Preface

Example of Encoding

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In the previous example, height of (0.3, 0.7, 0.4, 0.2) is 0.7, and height of (0.4, 0.3, 0.9) is 0.9. Therefore (0.4,

0.3, 0.9) as input, produced (0.3, 0.7, 0.4, 0.2) as output, but (0.3, 0.7, 0.4, 0.2) as input, produced only a

subset of (0.4, 0.3, 0.9). That both (0.4, 0.3, 0.7) and (0.4, 0.3, 0.9) gave the same output, (0.3, 0.7, 0.4, 0.2) is

in accordance with the corollary to the above, which states that if (X, Y) is a fuzzy associated memory, and if

X is a subset of X’, then (X’, Y) is also a fuzzy associated memory.