/// <summary>
/// Maps a binary operation on two fuzzy numbers
/// (Performs the operation over each pair of corresponding alpha-cuts)
/// </summary>
public static FuzzyNumber Map(FuzzyNumber X, FuzzyNumber Y, Func <Interval, Interval, Interval> operation)
{
if (X.AlphaCuts.Count == Y.AlphaCuts.Count)
{
return(new FuzzyNumber(X.AlphaCuts.Zip(Y.AlphaCuts, operation)));
}
throw new NotImplementedException();
}
/// <summary>
/// How much is greater than other fuzzy number?
/// </summary>
/// <param name="other"></param>
/// <returns>A Presumption (0 - 1) that the fuzzy number is greater</returns>
public double GreaterThan(FuzzyNumber other)
{
if (other.AlphaCuts.Count == AlphaCuts.Count)
{
var sum = 0d;
for (var i = 0; i < AlphaCuts.Count; i++)
{
sum += AlphaCuts[i].GreaterThan(other.AlphaCuts[i]);
}
return(sum / AlphaCuts.Count);
}
throw new NotImplementedException();
}
/// <summary>
/// Calculates a cosine of the fuzzy angle.
/// </summary>
/// <param name="X">A fuzzy number represents the angle in radians.</param>
public static FuzzyNumber Cos(FuzzyNumber X)
{
return FuzzyNumber.Map(X, x => Cos(x));
}
/// <summary>
/// Calculates a value of the fuzzy number raised to the specified power.
/// </summary>
/// <param name="X">Base</param>
/// <param name="y">Exponent</param>
public static FuzzyNumber Pow(FuzzyNumber X, double y)
{
return(FuzzyNumber.Map(X, x => Pow(x, y)));
}
/// <summary>
/// Returns the smaller of two fuzzy numbers.
/// </summary>
public static FuzzyNumber Min(FuzzyNumber X, FuzzyNumber Y)
{
return(FuzzyNumber.Map(X, Y, (x, y) => Min(x, y)));
}
public static FuzzyNumber Atan2(FuzzyNumber Y, FuzzyNumber X)
{
var rotated = Y.Support.Contains(0) && !X.Support.Contains(0);
return(FuzzyNumber.Map(Y, X, (y, x) => Atan2(y, x, rotated)));
}
/// <summary>
/// Returns the smaller of two fuzzy numbers.
/// </summary>
public static FuzzyNumber Min(FuzzyNumber X, FuzzyNumber Y)
{
return FuzzyNumber.Map(X, Y, (x, y) => Min(x, y));
}
/// <summary>
/// Calculates a sine of the fuzzy angle.
/// </summary>
/// <param name="X">A fuzzy number represents the angle in radians.</param>
public static FuzzyNumber Sin(FuzzyNumber X)
{
return(FuzzyNumber.Map(X, x => Sin(x)));
}
/// <summary>
/// How much is greater than other fuzzy number?
/// </summary>
/// <param name="other"></param>
/// <returns>A Presumption (0 - 1) that the fuzzy number is greater</returns>
public double GreaterThan(FuzzyNumber other)
{
if (other.AlphaCuts.Count == AlphaCuts.Count)
{
var sum = 0d;
for (var i = 0; i < AlphaCuts.Count; i++)
{
sum += AlphaCuts[i].GreaterThan(other.AlphaCuts[i]);
}
return sum / AlphaCuts.Count;
}
throw new NotImplementedException();
}
/// <summary>
/// Calculates e raised to the specified fuzzy number.
/// </summary>
/// <param name="X">Exponent</param>
public static FuzzyNumber Exp(FuzzyNumber X)
{
return FuzzyNumber.Map(X, x => Exp(x));
}
/// <summary>
/// Maps an unary operation on a fuzzy number
/// </summary>
public static FuzzyNumber Map(FuzzyNumber X, Func <Interval, Interval> operation)
{
return(new FuzzyNumber(X.AlphaCuts.Select(operation)));
}
/// <summary>
/// Calculates a value of the fuzzy number raised to the specified power.
/// </summary>
/// <param name="X">Base</param>
/// <param name="y">Exponent</param>
public static FuzzyNumber Pow(FuzzyNumber X, double y)
{
return FuzzyNumber.Map(X, x => Pow(x, y));
}
/// <summary>
/// Maps a binary operation on two fuzzy numbers
/// (Performs the operation over each pair of corresponding alpha-cuts)
/// </summary>
public static FuzzyNumber Map(FuzzyNumber X, FuzzyNumber Y, Func<Interval, Interval, Interval> operation)
{
if (X.AlphaCuts.Count == Y.AlphaCuts.Count)
{
return new FuzzyNumber(X.AlphaCuts.Zip(Y.AlphaCuts, operation));
}
throw new NotImplementedException();
}
/// <summary>
/// Maps an unary operation on a fuzzy number
/// </summary>
public static FuzzyNumber Map(FuzzyNumber X, Func<Interval, Interval> operation)
{
return new FuzzyNumber(X.AlphaCuts.Select(operation));
}
/// <summary>
/// Calculates a cosine of the fuzzy angle.
/// </summary>
/// <param name="X">A fuzzy number represents the angle in radians.</param>
public static FuzzyNumber Cos(FuzzyNumber X)
{
return(FuzzyNumber.Map(X, x => Cos(x)));
}
/// <summary>
/// Calculates e raised to the specified fuzzy number.
/// </summary>
/// <param name="X">Exponent</param>
public static FuzzyNumber Exp(FuzzyNumber X)
{
return(FuzzyNumber.Map(X, x => Exp(x)));
}
/// <summary>
/// Calculates a sine of the fuzzy angle.
/// </summary>
/// <param name="X">A fuzzy number represents the angle in radians.</param>
public static FuzzyNumber Sin(FuzzyNumber X)
{
return FuzzyNumber.Map(X, x => Sin(x));
}
public static FuzzyNumber Atan2(FuzzyNumber Y, FuzzyNumber X)
{
var rotated = Y.Support.Contains(0) && !X.Support.Contains(0);
return FuzzyNumber.Map(Y, X, (y, x) => Atan2(y, x, rotated));
}