fuzzy applications by w. silvert, ipimar, portugal
TRANSCRIPT
Fuzzy Applications
byW. Silvert, IPIMAR, Portugal
Application to NAFO model
The NAFO model presented by Bill Brodie in his talk uses the following simplified scheme:
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0 20 40 60 80 100 120 140 160 180
Stock biomass
Fish
ing
mor
talit
y
BtrBbuf
Overfishingzone
F-Targetzone
Collapse Recovery zoneDanger
zoneRecovered zone
Fbuf
F-bufferzone
4 3 2
1
We can make a fuzzy representation of this as follows:
Region 1
Region 1 can be described as follows:
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0 20 40 60 80 100 120 140 160 180
Stock biomass
Fish
ing
mor
talit
y
BtrBbuf
Overfishingzone
F-Targetzone
Collapse Recovery zoneDanger
zoneRecovered zone
Fbuf
F-bufferzone
4 3 2
1
If F is low and B is high
Region 2
Region 2 can be described as follows:
0
0.1
0.2
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0.5
0.6
0.7
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0 20 40 60 80 100 120 140 160 180
Stock biomass
Fish
ing
mor
talit
y
BtrBbuf
Overfishingzone
F-Targetzone
Collapse Recovery zoneDanger
zoneRecovered zone
Fbuf
F-bufferzone
4 3 2
1
If F is high and B is high
Region 3
Region 3 can be described as follows:
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 20 40 60 80 100 120 140 160 180
Stock biomass
Fish
ing
mor
talit
y
BtrBbuf
Overfishingzone
F-Targetzone
Collapse Recovery zoneDanger
zoneRecovered zone
Fbuf
F-bufferzone
4 3 2
1
If F is high and B is low
Region 4
Region 4 can be described as follows:
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
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0 20 40 60 80 100 120 140 160 180
Stock biomass
Fish
ing
mor
talit
y
BtrBbuf
Overfishingzone
F-Targetzone
Collapse Recovery zoneDanger
zoneRecovered zone
Fbuf
F-bufferzone
4 3 2
1
If B is very low
Quantification
We quantify the model by saying that:F is 100% low if F < 0.1F is 100% high if F > 0.2For 0.1 < F < 0.2 interpolate
For example F=0.15 is 50% high, 50% low
We do the same for biomassNow let us take a look at the more
complex figure from the written documentation Brodie submitted ...
More Detailed Analysis
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0 20 40 60 80 100 120 140 160 180
Stock biomass
Fis
hin
g m
ort
alit
y
BtrBbuf
Overfishingzone
F-Targetzone
Collapse Recovery zoneDanger
zone Recovered zone
Blim
Flim
Fbuf
F-bufferzone
Fuzzy Zones
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0 20 40 60 80 100 120 140 160 180
Stock biomass
Fis
hin
g m
ort
ali
ty
BtrBbuf
Overfishingzone
F-Targetzone
Collapse Recovery zoneDanger
zone Recovered zone
Blim
Flim
Fbuf
F-bufferzone
The regions between Blim and Bbuf, and between Flim and Fbuf, are fuzzy zones.
These are the zones where B and F are in both HIGH and LOW sets
Rules for Action
Typical rules are:IF B high and F low (#1) THEN continueIF B high and F high (#2) THEN reduce Fetc.Corresponding fuzzy rules areIF B high and F low (#1) THEN continueIF B high and F high (#2) THEN reduce F
drastically, where we might specify a rate of fishing reduction
Implementation
The fuzzy rules get rid of the sharp line between regions. Assume biomass is high (regions #1 and #2) – then the rules are interpreted as follows:
IF F = 0.1 THEN mortality is 100% low and we continue
IF F = 0.2 THEN mortality is 100% high and we reduce fishing drastically
IF F = 0.15 THEN mortality is 50-50 and we reduce fishing moderately (drastic/2)
More Complexity
We can apply the same reasoning to more complicated ranges, such as in this area:
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0 20 40 60 80 100 120 140 160 180
Stock biomass
Fish
ing
mor
talit
y
BtrBbuf
Overfishingzone
F-Targetzone
Collapse Recovery zoneDanger
zoneRecovered zone
Fbuf
F-bufferzone
4 3 2
1
Here we have biomass and mortality both in the fuzzy area between high and low, and we have a continuous management policy
General Procedure
Identify states of the system for which you want to assign actions.In this case the states are visualised as areas
on the Biomass-Mortality phase diagramsThe areas do not cover the entire diagramFor example, (F<0.1)=LOW and (F>0.2)=HIGH
Interpolate to find fuzzy mixed stateAssign action on basis of memberships
Example: if F=0.15, the state is 50% LOW and 50% high and the action is half-way in between
Summary
In any situation where we have different management regimes associated with the values of various variables (Indicators or Characteristics), we can describe fuzzy sets that give us a continuous and more flexible management policy without sharp cutoffs and discontinuities.