The following plots show how all the hedges modify the fuzzy set warm. Warm is the * and the hedged fuzzy set, such as very warm, is the + sign.
The plus hedge adds a value with every point in the fuzzy set.
Fuzzy Variable: temp
Fuzzy Values: warm(*) warm + 0.5000(+)
1.0000 ++++++++++++++++
0.9500 * *
0.9000 + * * +
0.8500 * *
0.8000 + * * +
0.7500
0.7000 + * * +
0.6500 + +
0.6000 + * * +
0.5500 + +
0.5000+++++++++++++++++++ * * +++
0.4500
0.4000 * *
0.3500
0.3000 * *
0.2500
0.2000 * *
0.1500 * *
0.1000 * *
0.0500 * *
0.0000******************* ***
|----|----|----|----|----|----|----|----|----|----|
0.00 20.00 40.00 60.00 80.00 100.00
Universe of Discourse: From 0.00 to 100.00
The minus hedge subtracts a value with every point in the fuzzy set.
Fuzzy Variable: temp
Fuzzy Values: warm(*) warm - 0.5000(+)
1.0000 **
0.9500 * *
0.9000 * *
0.8500 * *
0.8000 * *
0.7500
0.7000 * *
0.6500
0.6000 * *
0.5500
0.5000 * ++ *
0.4500 + +
0.4000 * + + *
0.3500 + +
0.3000 * + + *
0.2500 + +
0.2000 * + + *
0.1500 * + + *
0.1000 * + + *
0.0500 * + + *
0.0000+++++++++++++++++++++++ +++++++
|----|----|----|----|----|----|----|----|----|----|
0.00 20.00 40.00 60.00 80.00 100.00
Universe of Discourse: From 0.00 to 100.00
The multiply hedge multiplies a value with every point in the fuzzy set, it shrinks the fuzzy set.
Fuzzy Variable: temp
Fuzzy Values: warm(*) warm * 0.5000(+)
1.0000 **
0.9500 * *
0.9000 * *
0.8500 * *
0.8000 * *
0.7500
0.7000 * *
0.6500
0.6000 * *
0.5500
0.5000 * ++ *
0.4500 ++ ++
0.4000 * ++ ++ *
0.3500 + +
0.3000 * + + *
0.2500 + +
0.2000 * + + *
0.1500 * + + *
0.1000 *++ ++*
0.0500 ++ ++
0.0000+++++++++++++++++++ +++
|----|----|----|----|----|----|----|----|----|----|
0.00 20.00 40.00 60.00 80.00 100.00
Universe of Discourse: From 0.00 to 100.00
The division hedge divides the fuzzy set by the value, it scales the fuzzy set.
Fuzzy Variable: temp
Fuzzy Values: warm(*) warm / 2.0000(+)
1.0000 ++++++++++++++++
0.9500 * *
0.9000 * *
0.8500 * *
0.8000 + * * +
0.7500
0.7000 * *
0.6500
0.6000 * *
0.5500 + +
0.5000 * *
0.4500
0.4000 + * * +
0.3500
0.3000 + * * +
0.2500
0.2000 + * * +
0.1500 + * * +
0.1000 * *
0.0500 +* *+
0.0000++++++++++++++++++* *++
|----|----|----|----|----|----|----|----|----|----|
0.00 20.00 40.00 60.00 80.00 100.00
Universe of Discourse: From 0.00 to 100.00
The power hedge raises the fuzzy set values by a power of a value, it is used for hedges such as somewhat and very.
Fuzzy Variable: temp
Fuzzy Values: warm(*) warm ^ 0.5000(+)
1.0000 ++
0.9500 ++ ++
0.9000 ++* *++
0.8500 + * * +
0.8000 * *
0.7500 + +
0.7000 + * * +
0.6500
0.6000 + * * +
0.5500
0.5000 + * * +
0.4500
0.4000 + * * +
0.3500 + +
0.3000 * *
0.2500 + +
0.2000 * *
0.1500 + * * +
0.1000 * *
0.0500 +* *+
0.0000++++++++++++++++++* *++
|----|----|----|----|----|----|----|----|----|----|
0.00 20.00 40.00 60.00 80.00 100.00
Universe of Discourse: From 0.00 to 100.00
The lessthan hedge acts as a cutoff, every value below (but not equal to) a value is set to the value.
Fuzzy Variable: temp
Fuzzy Values: warm(*) warm < 0.5000(+)
1.0000 ++
0.9500 + +
0.9000 + +
0.8500 + +
0.8000 + +
0.7500 + +
0.7000 +* *+
0.6500 + +
0.6000 + * * +
0.5500 + +
0.5000+++++++++++++++++++++++ * * +++++++
0.4500
0.4000 * *
0.3500
0.3000 * *
0.2500
0.2000 * *
0.1500 * *
0.1000 * *
0.0500 * *
0.0000******************* ***
|----|----|----|----|----|----|----|----|----|----|
0.00 20.00 40.00 60.00 80.00 100.00
Universe of Discourse: From 0.00 to 100.00
The lessthanequal hedge acts as a cutoff, every value below or equal to a value is set to the value.
Fuzzy Variable: temp
Fuzzy Values: warm(*) warm <= 0.5000(+)
1.0000 ++
0.9500 + +
0.9000 + +
0.8500 + +
0.8000 + +
0.7500 + +
0.7000 +* *+
0.6500 + +
0.6000 + * * +
0.5500 + +
0.5000+++++++++++++++++++++++ * * +++++++
0.4500
0.4000 * *
0.3500
0.3000 * *
0.2500
0.2000 * *
0.1500 * *
0.1000 * *
0.0500 * *
0.0000******************* ***
|----|----|----|----|----|----|----|----|----|----|
0.00 20.00 40.00 60.00 80.00 100.00
Universe of Discourse: From 0.00 to 100.00
The morethan hedge acts as a cutoff, every value above (but not equal to) a value is set to the value.
Fuzzy Variable: temp
Fuzzy Values: warm(*) warm > 0.5000(+)
1.0000 **
0.9500 * *
0.9000 * *
0.8500 * *
0.8000 * *
0.7500
0.7000 * *
0.6500
0.6000 * *
0.5500
0.5000 * ++++++++++ *
0.4500 + +
0.4000 * + + *
0.3500 + +
0.3000 *+ +*
0.2500 + +
0.2000 + +
0.1500 + +
0.1000 + +
0.0500 + +
0.0000+++++++++++++++++++ +++
|----|----|----|----|----|----|----|----|----|----|
0.00 20.00 40.00 60.00 80.00 100.00
Universe of Discourse: From 0.00 to 100.00
The morethanequal hedge acts as a cutoff, every value above or equal to a value is set to the value.
Fuzzy Variable: temp
Fuzzy Values: warm(*) warm >= 0.5000(+)
1.0000 **
0.9500 * *
0.9000 * *
0.8500 * *
0.8000 * *
0.7500
0.7000 * *
0.6500
0.6000 * *
0.5500
0.5000 * ++++++++++ *
0.4500 + +
0.4000 * + + *
0.3500 + +
0.3000 *+ +*
0.2500 + +
0.2000 + +
0.1500 + +
0.1000 + +
0.0500 + +
0.0000+++++++++++++++++++ +++
|----|----|----|----|----|----|----|----|----|----|
0.00 20.00 40.00 60.00 80.00 100.00
Universe of Discourse: From 0.00 to 100.00
The not hedge inverts the fuzzy set.
Fuzzy Variable: temp
Fuzzy Values: warm(*) not warm(+)
1.0000+++++++++++++++++++ ** +++
0.9500 + * * +
0.9000 + * * +
0.8500 + * * +
0.8000 + * * +
0.7500
0.7000 + * * +
0.6500
0.6000 + * * +
0.5500
0.5000 + +
0.4500
0.4000 * + + *
0.3500
0.3000 * + + *
0.2500
0.2000 * + + *
0.1500 * + + *
0.1000 * + + *
0.0500 * + + *
0.0000******************* ++ ***
|----|----|----|----|----|----|----|----|----|----|
0.00 20.00 40.00 60.00 80.00 100.00
Universe of Discourse: From 0.00 to 100.00
The somewhat hedge tends to raise the fuzzy set, to increase the degree of membership for values in the fuzzy set.
Fuzzy Variable: temp
Fuzzy Values: warm(*) somewhat warm(+)
1.0000 ++++
0.9500 +++* *+++
0.9000 + * * +
0.8500 + * * +
0.8000 * *
0.7500 + +
0.7000 + * * +
0.6500 + +
0.6000 * *
0.5500 + +
0.5000 * *
0.4500
0.4000 + * * +
0.3500
0.3000 + * * +
0.2500
0.2000 + * * +
0.1500 * *
0.1000 * *
0.0500 +* *+
0.0000++++++++++++++++++* *++
|----|----|----|----|----|----|----|----|----|----|
0.00 20.00 40.00 60.00 80.00 100.00
Universe of Discourse: From 0.00 to 100.00
The moreorless hedge also tends to raise the fuzzy set, though less than somewhat, to increase the degree of membership for values in the fuzzy set.
Fuzzy Variable: temp
Fuzzy Values: warm(*) moreorless warm(+)
1.0000 ++
0.9500 ++ ++
0.9000 ++* *++
0.8500 + * * +
0.8000 * *
0.7500 + +
0.7000 + * * +
0.6500
0.6000 + * * +
0.5500
0.5000 + * * +
0.4500
0.4000 + * * +
0.3500 + +
0.3000 * *
0.2500 + +
0.2000 * *
0.1500 + * * +
0.1000 * *
0.0500 +* *+
0.0000++++++++++++++++++* *++
|----|----|----|----|----|----|----|----|----|----|
0.00 20.00 40.00 60.00 80.00 100.00
Universe of Discourse: From 0.00 to 100.00
The greatly hedge also tends to raise the fuzzy set, though less than somewhat, to increase the degree of membership for values in the fuzzy set.
Fuzzy Variable: temp
Fuzzy Values: warm(*) greatly warm(+)
1.0000 ++
0.9500 + +
0.9000 ++ ++
0.8500 +* *+
0.8000 +* *+
0.7500
0.7000 +* *+
0.6500
0.6000 +* *+
0.5500
0.5000 +* *+
0.4500
0.4000 +* *+
0.3500
0.3000 +* *+
0.2500 + +
0.2000 * *
0.1500 +* *+
0.1000 +* *+
0.0500 +* *+
0.0000++++++++++++++++++* *++
|----|----|----|----|----|----|----|----|----|----|
0.00 20.00 40.00 60.00 80.00 100.00
Universe of Discourse: From 0.00 to 100.00
The plus hedge tends to lower the fuzzy set, to decrease the degree of membership for values in the fuzzy set (opposite of greatly).
Fuzzy Variable: temp
Fuzzy Values: warm(*) plus warm(+)
1.0000 **
0.9500 *++*
0.9000 *+ +*
0.8500 *+ +*
0.8000 *+ +*
0.7500 + +
0.7000 * *
0.6500 + +
0.6000 * *
0.5500 + +
0.5000 * *
0.4500 + +
0.4000 * *
0.3500 + +
0.3000 * *
0.2500
0.2000 *+ +*
0.1500 *+ +*
0.1000 ++ ++
0.0500 + +
0.0000+++++++++++++++++++ +++
|----|----|----|----|----|----|----|----|----|----|
0.00 20.00 40.00 60.00 80.00 100.00
Universe of Discourse: From 0.00 to 100.00
The very hedge also tends to lower the fuzzy set, even more than plus, to decrease the degree of membership for values in the fuzzy set (opposite of somewhat).
Fuzzy Variable: temp
Fuzzy Values: warm(*) very warm(+)
1.0000 **
0.9500 *++*
0.9000 *+ +*
0.8500 * *
0.8000 * + + *
0.7500
0.7000 * + + *
0.6500 + +
0.6000 * *
0.5500 + +
0.5000 * *
0.4500 + +
0.4000 * *
0.3500 + +
0.3000 * *
0.2500
0.2000 * + + *
0.1500 * *
0.1000 * + + *
0.0500 * ++ ++ *
0.0000+++++++++++++++++++++ +++++
|----|----|----|----|----|----|----|----|----|----|
0.00 20.00 40.00 60.00 80.00 100.00
Universe of Discourse: From 0.00 to 100.00
The extremely hedge also tends to lower the fuzzy set, even more than very, to decrease the degree of membership for values in the fuzzy set.
Fuzzy Variable: temp
Fuzzy Values: warm(*) extremely warm(+)
1.0000 **
0.9500 *++*
0.9000 * *
0.8500 * + + *
0.8000 * *
0.7500 + +
0.7000 * *
0.6500 + +
0.6000 * *
0.5500
0.5000 * + + *
0.4500
0.4000 * + + *
0.3500 + +
0.3000 * *
0.2500 + +
0.2000 * *
0.1500 * + + *
0.1000 * *
0.0500 * + + *
0.0000+++++++++++++++++++++++ +++++++
|----|----|----|----|----|----|----|----|----|----|
0.00 20.00 40.00 60.00 80.00 100.00
Universe of Discourse: From 0.00 to 100.00
The above hedge moves the membership values for the fuzzy set to the right.
Fuzzy Variable: temp
Fuzzy Values: warm(*) above warm(+)
1.0000 ** +++
0.9500 * * +
0.9000 * * +
0.8500 * * +
0.8000 * * +
0.7500
0.7000 * * +
0.6500
0.6000 * * +
0.5500
0.5000 * +
0.4500
0.4000 * + *
0.3500
0.3000 * + *
0.2500
0.2000 * + *
0.1500 * + *
0.1000 * + *
0.0500 * + *
0.0000++++++++++++++++++++++++++++++++++ ***
|----|----|----|----|----|----|----|----|----|----|
0.00 20.00 40.00 60.00 80.00 100.00
Universe of Discourse: From 0.00 to 100.00
The below hedge moves the membership values for the fuzzy set to the left.
Fuzzy Variable: temp
Fuzzy Values: warm(*) below warm(+)
1.0000+++++++++++++++++++ **
0.9500 + * *
0.9000 + * *
0.8500 + * *
0.8000 + * *
0.7500
0.7000 + * *
0.6500
0.6000 + * *
0.5500
0.5000 + *
0.4500
0.4000 * + *
0.3500
0.3000 * + *
0.2500
0.2000 * + *
0.1500 * + *
0.1000 * + *
0.0500 * + *
0.0000******************* ++++++++++++++++++
|----|----|----|----|----|----|----|----|----|----|
0.00 20.00 40.00 60.00 80.00 100.00
Universe of Discourse: From 0.00 to 100.00
The slightly hedge emphasizes the edges of the fuzzy set.
Fuzzy Variable: temp
Fuzzy Values: warm(*) slightly warm(+)
1.0000 + ** +
0.9500 * *
0.9000 + * * +
0.8500 * *
0.8000 * *
0.7500 + + + +
0.7000 * *
0.6500
0.6000 * + + *
0.5500
0.5000 +* *+
0.4500
0.4000 * + + *
0.3500
0.3000 * *
0.2500 + + + +
0.2000 * *
0.1500 *+ +*
0.1000 *+ ++ +*
0.0500 ++ ++
0.0000+++++++++++++++++++ +++
|----|----|----|----|----|----|----|----|----|----|
0.00 20.00 40.00 60.00 80.00 100.00
Universe of Discourse: From 0.00 to 100.00
The normalize hedge normalizes the fuzzy set; it finds the maximum value of the fuzzy set, and if it is not 1, scales the fuzzy set to make it 1.
Fuzzy Variable: temp
Fuzzy Values: warm * 0.5000(*) normalize [warm * 0.5000](+)
1.0000 ++
0.9500 + +
0.9000 + +
0.8500 + +
0.8000 + +
0.7500
0.7000 + +
0.6500
0.6000 + +
0.5500
0.5000 + ** +
0.4500 ** **
0.4000 + ** ** +
0.3500 * *
0.3000 + * * +
0.2500 * *
0.2000 + * * +
0.1500 + * * +
0.1000 +** **+
0.0500 +* *+
0.0000+++++++++++++++++++ +++
|----|----|----|----|----|----|----|----|----|----|
0.00 20.00 40.00 60.00 80.00 100.00
Universe of Discourse: From 0.00 to 100.00
The hedges about, vicinity (of), close, near, and neighboring are called approximation hedges. They are excellent hedges for modify scalar values, e.g., about 50 degrees.
Fuzzy Variable: temp
Fuzzy Values: about 50(+) 50(*)
1.0000 *
0.9500
0.9000 + +
0.8500
0.8000
0.7500
0.7000
0.6500 + +
0.6000
0.5500
0.5000
0.4500 + +
0.4000
0.3500
0.3000 + +
0.2500
0.2000 + +
0.1500 + +
0.1000 +++ +++
0.0500 ++++++ ++++++
0.0000************************* ************************
|----|----|----|----|----|----|----|----|----|----|
0.00 20.00 40.00 60.00 80.00 100.00
Universe of Discourse: From 0.00 to 100.00
Fuzzy Variable: temp
Fuzzy Values: vicinity 50(+) 50(*)
1.0000 *
0.9500 + +
0.9000
0.8500
0.8000
0.7500
0.7000 + +
0.6500
0.6000
0.5500
0.5000
0.4500
0.4000
0.3500 + +
0.3000
0.2500
0.2000
0.1500 + +
0.1000
0.0500 ++ ++
0.0000************************* ************************
|----|----|----|----|----|----|----|----|----|----|
0.00 20.00 40.00 60.00 80.00 100.00
Universe of Discourse: From 0.00 to 100.00
Fuzzy Variable: temp
Fuzzy Values: close 50(+) 50(*)
1.0000 *
0.9500
0.9000
0.8500 + +
0.8000
0.7500
0.7000
0.6500 + +
0.6000
0.5500
0.5000 + +
0.4500
0.4000 + +
0.3500 + +
0.3000 + +
0.2500 ++ ++
0.2000 ++ ++
0.1500 ++++ ++++
0.1000 ++++++++ ++++++++
0.0500+++ ++
0.0000************************* ************************
|----|----|----|----|----|----|----|----|----|----|
0.00 20.00 40.00 60.00 80.00 100.00
Universe of Discourse: From 0.00 to 100.00
Fuzzy Variable: temp
Fuzzy Values: near 50(+) 50(*)
1.0000 *
0.9500
0.9000
0.8500 + +
0.8000
0.7500
0.7000
0.6500 + +
0.6000
0.5500
0.5000 + +
0.4500
0.4000 + +
0.3500 + +
0.3000 + +
0.2500 ++ ++
0.2000 ++ ++
0.1500 ++++ ++++
0.1000 ++++++++ ++++++++
0.0500+++ ++
0.0000************************* ************************
|----|----|----|----|----|----|----|----|----|----|
0.00 20.00 40.00 60.00 80.00 100.00
Universe of Discourse: From 0.00 to 100.00
Fuzzy Variable: temp
Fuzzy Values: neighboring 50(+) 50(*)
1.0000 *
0.9500
0.9000
0.8500 + +
0.8000
0.7500
0.7000
0.6500 + +
0.6000
0.5500
0.5000 + +
0.4500
0.4000 + +
0.3500 + +
0.3000 + +
0.2500 ++ ++
0.2000 ++ ++
0.1500 ++++ ++++
0.1000 ++++++++ ++++++++
0.0500+++ ++
0.0000************************* ************************
|----|----|----|----|----|----|----|----|----|----|
0.00 20.00 40.00 60.00 80.00 100.00
Universe of Discourse: From 0.00 to 100.00
The hedges positively, absolutely, and definitely are called contrast intensification hedges as they intensify the contrast; all Y values are pushed closer to 0 or 1. The Generally hedge is the opposite, it is a contrast diffusion hedge.
Fuzzy Variable: temp
Fuzzy Values: warm(*) positively warm(+)
1.0000 ++
0.9500 +++ +++
0.9000 + * * +
0.8500 * *
0.8000 +* *+
0.7500
0.7000 * *
0.6500 + +
0.6000 * *
0.5500
0.5000 + +
0.4500
0.4000 * *
0.3500 + +
0.3000 * *
0.2500
0.2000 *+ +*
0.1500 * *
0.1000 * + + *
0.0500 +++ +++
0.0000+++++++++++++++++++ +++
|----|----|----|----|----|----|----|----|----|----|
0.00 20.00 40.00 60.00 80.00 100.00
Universe of Discourse: From 0.00 to 100.00
Fuzzy Variable: temp
Fuzzy Values: warm(*) absolutely warm(+)
1.0000 ++
0.9500 +++ +++
0.9000 + * * +
0.8500 * *
0.8000 +* *+
0.7500
0.7000 * *
0.6500 + +
0.6000 * *
0.5500
0.5000 + +
0.4500
0.4000 * *
0.3500 + +
0.3000 * *
0.2500
0.2000 *+ +*
0.1500 * *
0.1000 * + + *
0.0500 +++ +++
0.0000+++++++++++++++++++ +++
|----|----|----|----|----|----|----|----|----|----|
0.00 20.00 40.00 60.00 80.00 100.00
Universe of Discourse: From 0.00 to 100.00
Fuzzy Variable: temp
Fuzzy Values: warm(*) definitely warm(+)
1.0000 ++
0.9500 +++ +++
0.9000 + * * +
0.8500 * *
0.8000 +* *+
0.7500
0.7000 * *
0.6500 + +
0.6000 * *
0.5500
0.5000 + +
0.4500
0.4000 * *
0.3500 + +
0.3000 * *
0.2500
0.2000 *+ +*
0.1500 * *
0.1000 * + + *
0.0500 +++ +++
0.0000+++++++++++++++++++ +++
|----|----|----|----|----|----|----|----|----|----|
0.00 20.00 40.00 60.00 80.00 100.00
Universe of Discourse: From 0.00 to 100.00
Fuzzy Variable: temp
Fuzzy Values: high(*) generally high(+)
1.0000 +
0.9500 ++
0.9000 *++
0.8500 *++
0.8000 *+++
0.7500 +++++
0.7000 ++++++**
0.6500 ++++ **
0.6000 + ***
0.5500 + **
0.5000 + ***
0.4500 ++**
0.4000 +**
0.3500 *+
0.3000 **++
0.2500 +++++
0.2000 +++*
0.1500 ++*
0.1000 ++*
0.0500 ++
0.0000++
|----|----|----|----|----|----|----|----|----|----|
0.00 20.00 40.00 60.00 80.00 100.00
Universe of Discourse: From 0.00 to 100.00
