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Fuzzy Applications

Fuzzy Applications. by W. Silvert, IPIMAR, Portugal. Application to NAFO model. The NAFO model presented by Bill Brodie in his talk uses the following simplified scheme:. We can make a fuzzy representation of this as follows:. Region 1. Region 1 can be described as follows:.

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Fuzzy Applications

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  1. Fuzzy Applications by W. Silvert, IPIMAR, Portugal

  2. Application to NAFO model • The NAFO model presented by Bill Brodie in his talk uses the following simplified scheme: We can make a fuzzy representation of this as follows:

  3. Region 1 • Region 1 can be described as follows: If F is lowand B is high

  4. Region 2 • Region 2 can be described as follows: If F is highand B is high

  5. Region 3 • Region 3 can be described as follows: If F is highand B is low

  6. Region 4 • Region 4 can be described as follows: If B is very low

  7. Quantification We quantify the model by saying that: • F is 100% low if F < 0.1 • F is 100% high if F > 0.2 • For 0.1 < F < 0.2 interpolate For example F=0.15 is 50% high, 50% low • We do the same for biomass • Now let us take a look at the more complex figure from the written documentation Brodie submitted ...

  8. More Detailed Analysis

  9. Fuzzy Zones 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

  10. Rules for Action Typical rules are: • IF B high and F low (#1) THEN continue • IF B high and F high (#2) THEN reduce F • etc. Corresponding fuzzy rules are • IF B high and F low (#1) THEN continue • IF B high and F high (#2) THEN reduce F drastically, where we might specify a rate of fishing reduction

  11. 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)

  12. More Complexity • We can apply the same reasoning to more complicated ranges, such as in this area: Here we have biomass and mortality both in the fuzzy area between high and low, and we have a continuous management policy

  13. 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 diagrams • The areas do not cover the entire diagram • For example, (F<0.1)=LOW and (F>0.2)=HIGH • Interpolate to find fuzzy mixed state • Assign 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

  14. 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.

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