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Express fuzzy membership functions as literal string instead of an image substitution
Also fix equations missing the equality operator
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docs/user_manual/processing_algs/qgis/rasteranalysis.rst

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@@ -918,7 +918,7 @@ membership value to each pixel, using a Gaussian membership function.
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Membership values range from 0 to 1.
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In the fuzzified raster, a value of 0 implies no membership of the
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defined fuzzy set, whereas a value of 1 means full membership.
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The gaussian membership function is defined as |gaussian_formula|,
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The gaussian membership function is defined as :math:`\mu(x)=e^{−f_1*(x−f_2)^2}`,
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where *f1* is the spread and *f2* the midpoint.
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.. figure:: img/gaussianimage.png
@@ -1067,7 +1067,7 @@ membership value to each pixel, using a Large membership function.
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Membership values range from 0 to 1.
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In the fuzzified raster, a value of 0 implies no membership of the
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defined fuzzy set, whereas a value of 1 means full membership.
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The large membership function is defined as |fuzzy_large_formula|,
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The large membership function is defined as :math:`\mu(x)={1}/({1+{(x/f_2)}^{-f_1}})`
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where *f1* is the spread and *f2* the midpoint.
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.. seealso:: :ref:`qgisfuzzifyrastergaussianmembership`,
@@ -1210,9 +1210,9 @@ Transforms an input raster to a fuzzified raster by assigning a
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membership value to each pixel, using a Linear membership function.
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Membership values range from 0 to 1. In the fuzzified raster, a value
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of 0 implies no membership of the defined fuzzy set, whereas a value
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of 1 means full membership.
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The linear function is defined as |fuzzy_linear_formula|, where *a*
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is the low bound and *b* the high bound. This equation assigns
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of 1 means full membership. The linear function is defined as
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:math:`\mu(x)=\begin{cases}0&\text{x≤a}\\(x-a)/(b-a)&\text{a<x<b}\\1&\text{x≥b}\end{cases}`,
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where *a* is the low bound and *b* the high bound. This equation assigns
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membership values using a linear transformation for pixel values
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between the low and high bounds.
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Pixels values smaller than the low bound are given 0 membership
@@ -1359,8 +1359,8 @@ membership value to each pixel, using a Near membership function.
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Membership values range from 0 to 1.
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In the fuzzified raster, a value of 0 implies no membership of the
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defined fuzzy set, whereas a value of 1 means full membership.
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The near membership function is defined as |near_formula|, where
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*f1* is the spread and *f2* the midpoint.
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The near membership function is defined as :math:`\mu(x)={1}/(1+f_1*({x-f_2})²)`,
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where *f1* is the spread and *f2* the midpoint.
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.. seealso:: :ref:`qgisfuzzifyrastergaussianmembership`,
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:ref:`qgisfuzzifyrasterlargemembership`,
@@ -1502,8 +1502,9 @@ membership value to each pixel, using a Power membership function.
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Membership values range from 0 to 1.
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In the fuzzified raster, a value of 0 implies no membership of the
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defined fuzzy set, whereas a value of 1 means full membership.
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The power function is defined as |power_formula|, where *a* is the
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low bound, *b* is the high bound, and *f1* the exponent.
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The power function is defined as
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:math:`\mu(x)=\begin{cases}0&\text{x≤a}\\{(({x-a})/({b-a}))}^{f_1}&\text{a<x<b}\\1&\text{x≥b}\end{cases}`,
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where *a* is the low bound, *b* is the high bound, and *f1* the exponent.
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This equation assigns membership values using the power transformation
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for pixel values between the low and high bounds.
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Pixels values smaller than the low bound are given 0 membership
@@ -1654,11 +1655,11 @@ membership value to each pixel, using a Small membership function.
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Membership values range from 0 to 1.
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In the fuzzified raster, a value of 0 implies no membership of the
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defined fuzzy set, whereas a value of 1 means full membership.
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The small membership function is defined as |small_formula|, where
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*f1* is the spread and *f2* the midpoint.
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The small membership function is defined as :math:`\mu(x)=1/({1+{(x/f_2)}^{f_1}})`,
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where *f1* is the spread and *f2* the midpoint.
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.. seealso:: :ref:`qgisfuzzifyrastergaussianmembership`,
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:ref:`qgisfuzzifyrasterlargemembership`
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:ref:`qgisfuzzifyrasterlargemembership`,
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:ref:`qgisfuzzifyrasterlinearmembership`,
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:ref:`qgisfuzzifyrasternearmembership`,
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:ref:`qgisfuzzifyrasterpowermembership`
@@ -4649,18 +4650,6 @@ Python code
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.. |344| replace:: ``NEW in 3.44``
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.. |gaussian_formula| image:: img/fuzzy_gaussian_formula.png
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:height: 1.5em
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.. |fuzzy_large_formula| image:: img/fuzzy_large_formula.png
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:height: 3.2em
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.. |fuzzy_linear_formula| image:: img/fuzzy_linear_formula.png
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:height: 3.8em
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.. |near_formula| image:: img/fuzzy_near_formula.png
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:height: 2.5em
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.. |power_formula| image:: img/fuzzy_power_formula.png
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:height: 4.4em
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.. |small_formula| image:: img/fuzzy_small_formula.png
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:height: 3.2em
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.. Substitutions definitions - AVOID EDITING PAST THIS LINE

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