@@ -918,7 +918,7 @@ membership value to each pixel, using a Gaussian membership function.
918918Membership values range from 0 to 1.
919919In the fuzzified raster, a value of 0 implies no membership of the
920920defined fuzzy set, whereas a value of 1 means full membership.
921- The gaussian membership function is defined as | gaussian_formula | ,
921+ The gaussian membership function is defined as :math: ` \mu (x)=e^{−f_ 1 *(x−f_ 2 )^ 2 }` ,
922922where *f1 * is the spread and *f2 * the midpoint.
923923
924924.. figure :: img/gaussianimage.png
@@ -1067,7 +1067,7 @@ membership value to each pixel, using a Large membership function.
10671067Membership values range from 0 to 1.
10681068In the fuzzified raster, a value of 0 implies no membership of the
10691069defined fuzzy set, whereas a value of 1 means full membership.
1070- The large membership function is defined as | fuzzy_large_formula |,
1070+ The large membership function is defined as :math: ` \mu (x)={ 1 }/({ 1 +{(x/f_ 2 )}^{-f_ 1 }})`
10711071where *f1 * is the spread and *f2 * the midpoint.
10721072
10731073.. seealso :: :ref:`qgisfuzzifyrastergaussianmembership`,
@@ -1210,9 +1210,9 @@ Transforms an input raster to a fuzzified raster by assigning a
12101210membership value to each pixel, using a Linear membership function.
12111211Membership values range from 0 to 1. In the fuzzified raster, a value
12121212of 0 implies no membership of the defined fuzzy set, whereas a value
1213- of 1 means full membership.
1214- The linear function is defined as | fuzzy_linear_formula |, where * a *
1215- is the low bound and *b * the high bound. This equation assigns
1213+ of 1 means full membership. The linear function is defined as
1214+ :math: ` \mu (x)= \begin {cases} 0 & \text {x≤a}\ \( x-a)/(b-a)& \text {a<x<b} \\ 1 & \text {x≥b} \end {cases}`,
1215+ where * a * is the low bound and *b * the high bound. This equation assigns
12161216membership values using a linear transformation for pixel values
12171217between the low and high bounds.
12181218Pixels values smaller than the low bound are given 0 membership
@@ -1359,8 +1359,8 @@ membership value to each pixel, using a Near membership function.
13591359Membership values range from 0 to 1.
13601360In the fuzzified raster, a value of 0 implies no membership of the
13611361defined fuzzy set, whereas a value of 1 means full membership.
1362- The near membership function is defined as | near_formula |, where
1363- *f1 * is the spread and *f2 * the midpoint.
1362+ The near membership function is defined as :math: ` \mu (x)={ 1 }/( 1 +f_ 1 *({x-f_ 2 })²)`,
1363+ where *f1 * is the spread and *f2 * the midpoint.
13641364
13651365.. seealso :: :ref:`qgisfuzzifyrastergaussianmembership`,
13661366 :ref: `qgisfuzzifyrasterlargemembership `,
@@ -1502,8 +1502,9 @@ membership value to each pixel, using a Power membership function.
15021502Membership values range from 0 to 1.
15031503In the fuzzified raster, a value of 0 implies no membership of the
15041504defined fuzzy set, whereas a value of 1 means full membership.
1505- The power function is defined as |power_formula |, where *a * is the
1506- low bound, *b * is the high bound, and *f1 * the exponent.
1505+ The power function is defined as
1506+ :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}`,
1507+ where *a * is the low bound, *b * is the high bound, and *f1 * the exponent.
15071508This equation assigns membership values using the power transformation
15081509for pixel values between the low and high bounds.
15091510Pixels values smaller than the low bound are given 0 membership
@@ -1654,11 +1655,11 @@ membership value to each pixel, using a Small membership function.
16541655Membership values range from 0 to 1.
16551656In the fuzzified raster, a value of 0 implies no membership of the
16561657defined fuzzy set, whereas a value of 1 means full membership.
1657- The small membership function is defined as | small_formula |, where
1658- *f1 * is the spread and *f2 * the midpoint.
1658+ The small membership function is defined as :math: ` \mu (x)= 1 /({ 1 +{(x/f_ 2 )}^{f_ 1 }})`,
1659+ where *f1 * is the spread and *f2 * the midpoint.
16591660
16601661.. seealso :: :ref:`qgisfuzzifyrastergaussianmembership`,
1661- :ref: `qgisfuzzifyrasterlargemembership `
1662+ :ref: `qgisfuzzifyrasterlargemembership `,
16621663 :ref: `qgisfuzzifyrasterlinearmembership `,
16631664 :ref: `qgisfuzzifyrasternearmembership `,
16641665 :ref: `qgisfuzzifyrasterpowermembership `
@@ -4649,18 +4650,6 @@ Python code
46494650
46504651
46514652.. |344 | replace :: ``NEW in 3.44 ``
4652- .. |gaussian_formula | image :: img/fuzzy_gaussian_formula.png
4653- :height: 1.5em
4654- .. |fuzzy_large_formula | image :: img/fuzzy_large_formula.png
4655- :height: 3.2em
4656- .. |fuzzy_linear_formula | image :: img/fuzzy_linear_formula.png
4657- :height: 3.8em
4658- .. |near_formula | image :: img/fuzzy_near_formula.png
4659- :height: 2.5em
4660- .. |power_formula | image :: img/fuzzy_power_formula.png
4661- :height: 4.4em
4662- .. |small_formula | image :: img/fuzzy_small_formula.png
4663- :height: 3.2em
46644653
46654654
46664655.. Substitutions definitions - AVOID EDITING PAST THIS LINE
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