`trapezoidal_membership_func`

Syntax


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trapezoidal_membership_func((a, b, c, d), x)

Description


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r = trapezoidal_membership_func((a, b, c, d), x)

This function returns the degree of membership of the state x to a set, whose membership function is trapezoidal. The shape of the trapezoidal membership function is specified by the params, namely (a, b, c, d). It will be triangular if b == c, and rectangular if a == b and c == d.

The membership function is

\begin{matrix} f (x) = {\begin{cases} 0 & x < a \\ \frac{x - a}{c - a} & a ⩽ x < c \\ 1 & c ⩽ x < d \\ \frac{b - x}{b - d} & d ⩽ x < b \\ 1 & b ⩽ x \end{cases} \end{matrix}

Examples


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>>> a = 9.8
>>> c = 9.95
>>> d = 10.05
>>> b = 10.2
>>> x = np.linspace(9.8, 10.2, 10)

>>> f = lambda x: trapezoidal_membership_func((a, b, c, d), x)
# construct the membership function
>>> r = f(x)

[0, 0.29629629629629806, 0.5925925925925961, 0.8888888888888942, 1, 1, 0.8888888888888942, 0.5925925925925961, 0.29629629629629806, -0.0]

Input Arguments

params —— A tuple (a, b, c, d) that specifies the shape of the trapezoidal membership function, and a <= b <= c <= d.

x —— System states, specified as an array of numeric scalars of vectors.

Properties of Arguments

Name of the parameters	Is optional?	Source, dialog or input port?
`params`	No	Dialog
`x`	No	Input port