fuzarith (Fuzzy Logic Toolbox)

Perform fuzzy arithmetic.

Syntax

```
C = fuzarith(X, A, B, operator) 
```

Description

Using interval arithmetic, C = fuzarith(X, A, B, operator) returns a fuzzy set C as the result of applying the function represented by the string, operator, that performs a binary operation on the sampled convex fuzzy sets A and B. The elements of A and B are derived from convex functions of the sampled universe, X:

A, B, and X are vectors of the same dimension.
operator is one of the following strings: 'sum', 'sub', 'prod', and 'div'.
The returned fuzzy set C is a column vector with the same length as X.

Note Fuzzy addition might generate the message "divide by zero" but this will not affect the correctness of this function.

Examples

point_n = 101;% this determines MF's resolution
    min_x = -20; max_x = 20;% universe is [min_x, max_x]
    x = linspace(min_x, max_x, point_n)';
    A = trapmf(x, [-10 -2 1 3]);% trapezoidal fuzzy set A
    B = gaussmf(x, [2 5]);% Gaussian fuzzy set B
    C1 = fuzarith(x, A, B, 'sum');
    subplot(2,1,1);
    plot(x, A, 'b--', x, B, 'm:', x, C1, 'c');
    title('fuzzy addition A+B');
    C2 = fuzarith(x, A, B, 'sub');
    subplot(2,1,2);
    plot(x, A, 'b--', x, B, 'm:', x, C2, 'c');
    title('fuzzy subtraction A-B');
    C3 = fuzarith(x, A, B, 'prod');

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