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What Is Fuzzy Logic?

What Is Fuzzy Logic?

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zmf<br />

Purpose<br />

Syntax<br />

Description<br />

Z-shaped built-in membership function<br />

y = zmf(x,[a b])<br />

This spline-based function of x is so named because of its Z-shape. The<br />

parameters a and b locate the extremes of the sloped portion of the<br />

curve as given by.<br />

⎧<br />

1,<br />

⎪<br />

2<br />

⎪ ⎛ x−<br />

a⎞<br />

1−<br />

2⎜<br />

⎟ ,<br />

⎪ ⎝ b−<br />

a⎠<br />

⎨<br />

2<br />

⎪ ⎛ x ⎞<br />

⎪<br />

2⎜b<br />

- ⎟ ,<br />

⎝ b-<br />

a<br />

⎪<br />

⎠<br />

⎩⎪<br />

0,<br />

x ≤ a ⎫<br />

⎪<br />

a+<br />

b⎪<br />

a ≤ x ≤<br />

2 ⎪<br />

⎬<br />

a+ b ≤ x ≤ b⎪<br />

2 ⎪<br />

x ≥ b<br />

⎪<br />

⎭⎪<br />

Examples<br />

x=0:0.1:10;<br />

y=zmf(x,[3 7]);<br />

plot(x,y)<br />

xlabel('zmf, P=[3 7]')<br />

1<br />

0.75<br />

0.5<br />

0.25<br />

0<br />

0 2 4 6 8 10<br />

zmf, P = [3 7]<br />

4-93

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