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Fuzzy Traffic Light Method - Ciencia Silvert

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									Fuzzy Traffic Light Method

      A Presentation by
     William Silvert, Ph. D.
       Lisbon, Portugal
     Standard Traffic Lights
n   Each Indicator is represented by a
    single traffic light, red, yellow or green.
n   There is no smooth transition, just two
    sharp lines separating red-yellow and
    yellow-green.
n   The meaning of the lights can be very
    sensitive to the location of these cuts.
    Criteria for Improvement
    The objective is to develop a more
    general approach with the following
    characteristics:
n   Resolution
n   Uncertainty
n   Weighting
             Resolution
n   The most serious problem with the
    standard traffic light method is the way
    that the lights change discontinuously
    when the Indicators change smoothly.
n   There is general agreement that there
    must be a more gradual representation
    of the significance of changing
    indicators.
            Uncertainty
n   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:
n   Of varying accuracy
n   Of different relevance
n   Of dubious value
n   New and untested
    Alternative Approaches
n   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.
n   One example is using intermediate
    colours, such as orange between red
    and yellow.
       Fuzzy Traffic Lights
n   Fuzzy Sets offer one way to improve the
    standard traffic light method.
n   With fuzzy traffic lights an Indicator can
    correspond to more than one light.
n   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
n   Fuzzy traffic lights are continuous, we
    can switch between colours gradually to
    achieve higher resolution.
n   Fuzzy traffic lights show uncertainty if
    we illuminate several lights at once.
n   Fuzzy traffic lights can be weighted to
    show relative importance of indicators.
           Memberships
n   The key idea behind Fuzzy Set Theory is
    that something can belong to more
    than one set at a time.
n   When we say that a light is red, that
    means that it belongs to the set “red”.
n   With fuzzy sets we can have a light be
    50% in set red and 50% in yellow.
    Displaying Fuzzy Lights
n   There are several ways to show a fuzzy
    traffic light:
n   Bubble charts, which look a lot like real
    traffic lights
n   Pie charts, which display information
    more quantitatively
n   Stacked bar graphs, which are less
    familiar but very effective
            Bubble Charts
n   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
n   A pie chart looks
    less like a traffic
    light, but it gives a
    more quantitative
    picture of how much
    of each light is lit,
n   The area of each
    slice represents the
    fuzzy membership.
       Stacked Bar Graphs
n   A stacked bar graph
    is somewhat like a
    traffic light with
    rectangular bulbs.
n   The area of each
    part of the bar
    represents the
    membership in the
    corresponding set.
      Choosing the Display
n   The bubble chart resembles traffic lights
    most, but it does not give a good sense
    of the quantitative information about
    memberships.
n   The pie chart and the stacked bar graph
    both represent the relative
    memberships clearly.
      Displaying Weighting
n   The bubble graph does not give a good
    idea of the relative weights of the
    different Indicators.
n   By varying the diameter of the pie
    charts or the width of the bar graphs
    we can show the relative importance of
    different indicators.
Comparison of Pie Charts
Comparison of Bar Graphs

								
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