Fuzzy logic functions

Fuzzy logic is a form of many-valued logic. In contrast with traditional binary logic that deals only with true or false, fuzzy logic functions have a truth value that ranges in degree between 1 and 0, from 'completely true' over 'almost true' to 'completely false'. Trade signals derived with fuzzy logic are often less susceptible to random noise in the price data, especially with complex logic expressions.

The following functions return a fuzzy truth value:

equalF (var v1, var v2): var

aboveF (var val, var border): var

belowF (var val, var border): var

Fuzzy comparison, equivalent to the binary ==, > and < operators.

betweenF (var val, var lower, var upper): var

Fuzzy between function.

peakF (vars Data): var

valleyF (vars Data): var

Fuzzy peak and valley functions.

risingF (vars Data): var

fallingF (vars Data): var

Fuzzy rising and falling functions.

crossOverF (vars Data1, vars Data2): var

crossUnderF (vars Data1, vars Data2): var

crossOverF (vars Data, var border): var

crossUnderF (vars Data, var border): var

Fuzzy crossOver and crossUnder functions.

andF (var a, var b): var

orF (var a, var b): var

notF (var a, var b): var

Fuzzy logic functions, equivalent to the &&, ||, and ! operators.

Parameters:

a, b Fuzzy truth values, 0.0 .. 1.0
Data, Data1, Data2 Data series.
val, v1, v2 Values to compare.
lower, upper, border Comparison borders.

Returns

Fuzzy truth, from 0.0 (completely false) to 1.0 (completely true)
 

fuzzy (var a): bool

Defuzzyfication, converts a fuzzy truth value to binary true or false. Use this function to convert the result of a fuzzy logic expression back to binary logic.

eq (var v1, var v2): bool

Fuzzy comparison, returns true when the parameters differ less than FuzzyRange, otherwise false.

 

Parameters:

a Fuzzy truth value, 0.0 .. 1.0

Returns

Boolean true or false
 

The following system variables affect the fuzzy logic calculation:

FuzzyRange

Determines the 'fuzziness' range of the input data (default: 0 = no fuzziness). When comparing two variables, the truth value goes from 0 to 1 within that range. Set this to a small fraction of the price volatility, or f.i. to 0.1*PIP for comparing moving averages, or to 0.1 for comparing percentage values. The smaller this value, the 'less fuzzy' is the logic. At the default value 0 the logic is binary. The FuzzyRange variable is also used for classifying signal patterns for price action trading.

FuzzyLevel

Determines the level above which fuzzy true becomes binary true (default: 0.5); used by the fuzzy function.
 

Remarks:

Example:

// Fuzzy version of a Workshop 4 variant ///////////////////
function run()
{
  vars Price = series(price());
  vars Trend = series(LowPass(Price,1000));
  vars Signals = series(0)
 
  Stop = 4*ATR(100);
  FuzzyRange = 0.001*ATR(100);

  var Valley = valleyF(Trend),
    Peak = peakF(Trend);
  Signals[0] = orF(Valley,Peak); // store the signal
  if(fuzzy(Valley))
    exitShort();
  if(fuzzy(andF(Valley,notF(Sum(Signals+1,3)))))
    enterLong();
  if(fuzzy(Peak))
    exitLong();
  if(fuzzy(andF(Peak,notF(Sum(Signals+1,3)))))
    enterShort();  
}

// Binary version for comparison  
function run()
{
  vars Price = series(price());
  vars Trend = series(LowPass(Price,1000));
  vars Signals = series(0);
 
  Stop = 4*ATR(100);
  bool Valley = valley(Trend),
    Peak = peak(Trend);
  if(Valley or Peak)
    Signals[0] = 1; // store the signal
  if(Valley)
    exitShort();
  if(Valley and Sum(Signals+1,3) == 0)
    enterLong();
  if(Peak)
    exitLong();
  if(Peak and Sum(Signals+1,3) == 0)
    enterShort();  
}

See also:

crossOver, crossUnder, rising, falling, peak, valley, comparisons

 

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