Fuzzy Traffic Light Methods by tKFOwBay

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									Fuzzy Traffic Light Methods

                by
  W. Silvert, IPIMAR, Portugal
               and
    P. Fanning, R. Halliday,
          and R. Mohn
          DFO, Canada
  Why are we doing this?
The first question to be asked about any
 approach is why it is needed.
SGPA Term of Reference D is to revise
 the description of PA concepts to make
 them more intelligible for non-fishery
 users.
The Traffic Light Approach is one of the
 types of descriptions currently under
 investigation to simplify the process of
 management decision-making.
  The Traffic Light Method
The Precautionary Approach (and Risk
 Management in general, not just for
 fisheries) requires that masses of
 complex data be presented clearly to
 managers, fishermen and other
 stakeholders.
The Traffic Light Method is an easily
 understood way of presenting information
 about stock conditions.
  Indicators & Characteristics
We speak of Indicators, which are basic
 properties of the system, and
 Characteristics, which are integrated
 variables representing several Indicators.
Abundance is a typical Characteristic,
 since it represents the result of
 combining several Indicators, such as:
  Research Trawl data
  VPA analysis
  Catch per Unit Effort
  Standard Traffic Lights
Each Indicator or Characteristic is
 represented by a single traffic light, red,
 yellow or green in the standard traffic
 light representation.
There is no smooth transition, just two
 sharp lines separating red-yellow and
 yellow-green.
The meaning of the lights can be very
 sensitive to the location of these cuts.
    Example: 4VsW Cod

A “crisp” traffic light indicator
   sharp transitions between colours make
    positioning the boundaries very critical
   A lot of information is lost
  Criteria for Improvement
 The objective is to develop a more
 general approach with the following
 characteristics:
Resolution
Uncertainty
Weighting
  Resolution
The most serious problem with the
 standard traffic light method is the way
 that the lights change discontinuously
 when the Indicators change smoothly.
There is general agreement that there
 must be a more gradual representation of
 the significance of changing indicators.
  Uncertainty
A less obvious point, but one which is
 clearly relevant to fisheries management,
 is the need to represent the degree of
 uncertainty in the interpretation of
 Indicators, and to provide a mechanism
 for expressing conflicting evidence or
 interpretation.
  Weighting
 It is also clear that not all Indicators are
 equally significant. They can be:
Of varying accuracy
Of different relevance
Of dubious value
New and untested
  Alternative Approaches
Most alternatives to the standard traffic
 light method use some sort of averaging
 to show that an Indicator is on the
 border between red and yellow or
 between yellow and green.
One example is using intermediate
 colours, such as orange between red and
 yellow.
  Fuzzy Traffic Lights
Fuzzy Sets offer one way to improve the
 standard traffic light method.
With fuzzy traffic lights an Indicator
 can correspond to more than one light.
For example, instead of using orange to
 show that an Indicator is on the red-
 yellow boundary, we can simply show both
 red and yellow lights.
  Advantages of Fuzzy
Fuzzy traffic lights are continuous, we
 can switch between colours gradually to
 achieve higher resolution.
Fuzzy traffic lights show uncertainty if
 we illuminate several lights at once.
Fuzzy traffic lights can be weighted to
 show relative importance of indicators.
  Memberships
The key idea behind Fuzzy Set Theory is
 that something can belong to more than
 one set at a time.
When we say that a light is red, that
 means that it belongs to the set “red”.
With fuzzy sets we can have a light that
 is 50% in set red and 50% in yellow.
  Membership Example
Let the amount of each light displayed vary
 with the level of the indicator
  Traffic Light Fuzzy Set
                                               Strict Default Rules
                                        0.6*Mean                      Mean
           1.25


             1


           0.75
  Degree




            0.5


           0.25


             0
                  0   5000   10000   15000    20000      25000        30000   35000
                                        Indicator
    Fuzzy Indicators
Use a combination of colours
  gradual transitions show uncertainty and
   contain more information than solid colour
   bars
  Note that some bars have multiple colours
   Application to Haddock
                                     4TVW Haddock Summer RV #/tow(26-41cm)
                              75


Note how much data is included on this
                              60



 figure, and how easy it is to see a pattern
                              45

                              30

                              15
                                0

                     Abundance
                      Production
                      FishingM
                    Management
                                                                                                  Char   Weight
    Summer RV #/tow(26-41cm)                                                                      Abun    1.0
     Summer RV #/tow(42cm+)                                                                       Abun    1.0
                 Sentinel (kg/set)                                                                Abun    1.0
         Area occupied(30cm+)                                                                     Abun    1.0
                  Density(30cm+)                                                                  Abun    0.5
                        VPA SSB                                                                   Abun    1.0
        Area occupied(1-29cm)                                                                     Prod   1.0
                 Density(1-29cm)                                                                  Prod   0.5
                         VPA Rec                                                                  Prod   1.0
          Summer RV Condition                                                                     Prod   0.5
   Summer RV growth age7(len)                                                                     Prod   1.0
             Spring RV 50% mat                                                                    Prod   1.0
             Spring RV condition                                                                  Prod   0.5
           Misaine Temperature                                                                    Prod   0.5
     Exploitation (%)(ages 5-10)                                                                  Fish   1.0
                 Fraction over 42                                                                 Mana    1.0
                        Cod SSB                                                                   Mana    1.0
                               1970             1975    1980       1985      1990   1995   2000
          C:/1paulf/PA/hadd6c_fuzzy_traffic.txt
 Application to White Hake

We have no VPA results, but we still
 can present an assessment
    Current Developments
                                 4X/5 white hake July Survey numbers (>45)

                       24000

                       18000

                       12000

                        6000
                             0
                                                                                                  3 year trend
             Abundance
              Production
             Fishing Mortality
             Environment

                                                                                                  Char    Weight
  July Survey numbers (>45)                                                                       Abun     1.0
     ITQ Survey numbers/set                                                                       Abun     1.0
 Halibut Survey numbers/set                                                                       Abun     1.0
July Area Occupied (>45cm)                                                                        Abun     0.5
    July Survey mean weight                                                                       Abun     0.5
                July Survey Z                                                                     Prod    1.0
  July Survey numbers (<45)                                                                       Prod    1.0
July Area Occupied (<45cm)                                                                        Prod    0.5
             Condition Factor                                                                     Prod    0.5
                    Relative F                                                                    Fish    1.0
     Temperature (Area >6C)                                                                       Envi    1.0
                            1970          1975          1980          1985   1990   1995   2000
      C:/1paulf/PA/TLwhhakesimple4x_2.txt
Uncertain Reference Levels
Wide yellow zone reflects uncertainty
                                  4X/5 white hake ITQ Survey numbers/set

                            9.5

                            7.6

                            5.7

                            3.8

                            1.9

                                                                                                   3 year trend
              Abundance
               Production
              Fishing Mortality
              Environment

                                                                                                   Char    Weight
   July Survey numbers (>45)                                                                       Abun     1.0
      ITQ Survey numbers/set                                                                       Abun     1.0
  Halibut Survey numbers/set                                                                       Abun     1.0
 July Area Occupied (>45cm)                                                                        Abun     0.5
     July Survey mean weight                                                                       Abun     0.5
                 July Survey Z                                                                     Prod    1.0
   July Survey numbers (<45)                                                                       Prod    1.0
 July Area Occupied (<45cm)                                                                        Prod    0.5
              Condition Factor                                                                     Prod    0.5
                     Relative F                                                                    Fish    1.0
      Temperature (Area >6C)                                                                       Envi    1.0
                             1970          1975          1980          1985   1990   1995   2000
       C:/1paulf/PA/TLwhhakesimple4x_2.txt
  Fuzzy Rules
The use of Fuzzy Traffic Lights to
 represent stock status means that we
 also use fuzzy rules to make management
 decisions.
Some typical (and familiar) fuzzy rules:
   IF it feels cold THEN light a fire
   IF you are hungry THEN eat something
Fuzzy rules are like crisp rules:
   IF the temperature falls below 14.7º C THEN
    switch on the heater
     Fuzzy Control of Fisheries

Fuzzy rules are of the form:
                   IF (condition) THEN (act)
IF management= green AND production= green AND abundance= green
         THEN tac_increment is large positive
IF production= green AND abundance= green THEN tac_increment is small positive
IF production= green AND abundance=yellow THEN tac_increment is no change
IF production=green AND abundance=red THEN tac_increment is small negative
IF production=yellow AND abundance=green THEN tac_increment is no change
IF production=yellow AND abundance=yellow THEN tac_increment is small negative
IF production=yellow AND abundance=red THEN tac_increment is large negative
IF production=red AND abundance=green THEN tac_increment is small negative
IF production=red AND abundance<>green THEN tac_increment is large negative
  Displaying Fuzzy Lights
There are several ways to show a fuzzy
 traffic light:
Bubble charts, which look a lot like real
 traffic lights
Pie charts, which display information
 more quantitatively
Stacked bar graphs, which are less
 familiar but very effective
   Bubble Charts
A Bubble Chart looks
 like a regular traffic
 light, but the sizes of
 the ”lights” are
 proportional to the
 membership in each
 of the three sets,
 red yellow & green.
   Pie Charts
A pie chart looks less
 like a traffic light,
 but it gives a more
 quantitative picture
 of how much of each
 light is lit,
The area of each
 slice represents the
 fuzzy membership.
  Stacked Bar Graphs
A stacked bar graph
 is somewhat like a
 traffic light with
 rectangular bulbs.
The area of each part
 of the bar represents
 the membership in
 the corresponding
 set.
  Choosing the Display
The bubble chart resembles traffic lights
 most, but it does not give a good sense of
 the quantitative information about
 memberships.
The pie chart and the stacked bar graph
 both represent the relative memberships
 clearly.
  Displaying Weighting
The bubble graph does not give a good
 idea of the relative weights of the
 different Indicators.
By varying the diameter of the pie charts
 or the width of the bar graphs we can
 show the relative importance of different
 indicators.
At present weighting has not been well
 implemented in trial applications and it is
 difficult to achieve agreement on it.
Comparison of Pie Charts
Comparison of Bar Graphs
 Conclusions

Traffic Lights offer a
 clear way to present
 complex fisheries data.
Fuzzy Traffic Lights
 provide more information
 with little loss of clarity.

								
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