one variable fuzzy algorithm

[Nate]

The following fuzzy algorithm showed up in a paper I'm trying to
understand:

Fuzzy rule 1: if ek is LN then ek' is LN (highest speed).
Fuzzy rule 2: i f ek is SN then ek' is SN (high speed).
Fuzzy rule 3: if ek is ZE then ek' is ZE (normal speed).
Fuzzy rule 4: if ek i s SP then ek' is SP (slow speed).
Fuzzy rule 5: if ek is LP then ek' is LP (lowest speed).

In the fuzzy algorithm, a linguistic rule is used to calculate the
modified error ek'. ek is the predicted error.

What could they mean by ek' is LN. Don't you fuzzify, find
membership, and get a crisp value which you call ek'? What does it
matter that ek' is LN?

[Dmitry A. Kazakov]

Post by Nate
The following fuzzy algorithm showed up in a paper I'm trying to
Fuzzy rule 1: if ek is LN then ek' is LN (highest speed).
Fuzzy rule 2: i f ek is SN then ek' is SN (high speed).
Fuzzy rule 3: if ek is ZE then ek' is ZE (normal speed).
Fuzzy rule 4: if ek i s SP then ek' is SP (slow speed).
Fuzzy rule 5: if ek is LP then ek' is LP (lowest speed).
In the fuzzy algorithm, a linguistic rule is used to calculate the
modified error ek'. ek is the predicted error.
What could they mean by ek' is LN.

ek' = LN ?

Post by Nate
Don't you fuzzify, find
membership, and get a crisp value which you call ek'? What does it
matter that ek' is LN?

It does matter if ek' is defined over another domain than ek, like over the
set of linguistic variables:

ek' : { LN, SN, ZE, SP, LP } -> [0,1] , a fuzzy subset of {LN, SN.. LP}

While ek is defined over the domain of velocities:

ek : ] -oo m/s, +oo m/s [ -> [0,1], a fuzzy subset of velocities

Or maybe ek is crisp velocity:

ek in ] -oo m/s, +oo m/s [

then the above is just fuzzification of speed into a fuzzy subset of
linguistic variables {LN, SN ... LP}. I.e. merely

ek' = fuzzified ek

(In which case I would consider it wasting time to read papers deploying a
notation like above instead of saying that ek' is a fuzzified speed! (:-()

[hagna]

Post by Dmitry A. Kazakov

Post by Nate
The following fuzzy algorithm showed up in a paper I'm trying to
Fuzzy rule 1: if ek is LN then ek' is LN (highest speed).
Fuzzy rule 2: i f ek is SN then ek' is SN (high speed).
Fuzzy rule 3: if ek is ZE then ek' is ZE (normal speed).
Fuzzy rule 4: if ek i s SP then ek' is SP (slow speed).
Fuzzy rule 5: if ek is LP then ek' is LP (lowest speed).
In the fuzzy algorithm, a linguistic rule is used to calculate the
modified error ek'.  ek is the predicted error.
What could they mean by ek' is LN.

ek' = LN ?

Post by Nate
Don't you fuzzify, find
membership, and get a crisp value which you call ek'? What does it
matter that ek' is LN?

It does matter if ek' is defined over another domain than ek, like over the
   ek' : { LN, SN, ZE, SP, LP } -> [0,1] , a fuzzy subset of {LN, SN.. LP}
   ek : ] -oo m/s, +oo m/s [ -> [0,1],  a fuzzy subset of velocities
   ek in ] -oo m/s, +oo m/s [
then the above is just fuzzification of speed into a fuzzy subset of
linguistic variables {LN, SN ... LP}. I.e. merely
   ek' = fuzzified ek
(In which case I would consider it wasting time to read papers deploying a
notation like above instead of saying that ek' is a fuzzified speed! (:-()
--
Regards,
Dmitry A. Kazakovhttp://www.dmitry-kazakov.de

Thank you Dmitry.

Maybe they got paid according to the length of the process.

It seems they really mean ek' is fuzzified then defuzzified value of
ek.