internal Interval(IntervalSet parent, System.Decimal lowerBoundary, System.Decimal upperBoundary, decimal[] coefficients)
{
_parent = parent;
_lowerBound = lowerBoundary;
_upperBound = upperBoundary;
_coefficients = coefficients;
}
internal override void Operate(BinaryInterval operands, ref IntervalSet output)
{
Polynomial poly1 = Interval.GetPolynomial(operands.Coefficients1);
Polynomial poly2 = Interval.GetPolynomial(operands.Coefficients2);
Polynomial result = poly1 + poly2 - (poly1 * poly2);
output.AddInterval(new Interval(output, operands.LowerBound, operands.UpperBound, result));
}
/// <summary>
/// Constructor do define a linear interval μ = ax + b
/// </summary>
/// <param name="lowerBoundary">lower boundary of the interval</param>
/// <param name="upperBoundary">upper boundary of the interval</param>
/// /// <param name="a">a</param>
/// <param name="b">b</param>
internal Interval(IntervalSet parent, System.Decimal lowerBoundary, System.Decimal upperBoundary, System.Decimal a, System.Decimal b)
{
_parent = parent;
_lowerBound = lowerBoundary;
_upperBound = upperBoundary;
_coefficients = new System.Decimal[] { b, a };
if (_upperBound < _lowerBound) throw new ArgumentOutOfRangeException("Lower boundary cannot be higher than upper boundary.");
}
internal override void Operate(BinaryInterval operands, ref IntervalSet output)
{
Polynomial poly1 = Interval.GetPolynomial(operands.Coefficients1);
Polynomial poly2 = Interval.GetPolynomial(operands.Coefficients2);
Polynomial sum = poly1 + poly2;
BinaryInterval temp = new BinaryInterval(operands.LowerBound, operands.UpperBound, sum.Coefficients, (new Polynomial(1)).Coefficients);
GetMinMax(temp, ref output, true);
}
public IntervalSet Operate(IntervalSet operand1)
{
//Calculate resulting function for each interval
IntervalSet output = new IntervalSet(operand1.Dimension);
foreach (Interval operand in operand1.Intervals)
{
Operate(operand, ref output);
}
return output;
}
public IntervalSet Operate( IntervalSet operand1, IntervalSet operand2 )
{
if (operand1.Dimension != operand2.Dimension) throw new ApplicationException("Dimensions don't match");
//Find all boundaries for both interval sets
decimal[] boundaries = IntervalSet.GetAllBoundaries(operand1, operand2);
List<BinaryInterval> semiproduct = BuildBinaryInterval(operand1, operand2);
//Calculate resulting function for each interval
IntervalSet output = new IntervalSet(operand1.Dimension);
foreach (BinaryInterval operands in semiproduct)
{
Operate(operands, ref output );
}
return output;
}
internal override void Operate(BinaryInterval operands, ref IntervalSet output)
{
Polynomial poly1 = Interval.GetPolynomial(operands.Coefficients1);
Polynomial poly2 = Interval.GetPolynomial(operands.Coefficients2);
Polynomial multipl = (Operand1Power ? poly1^2 : poly1) + (Operand2Power ? poly2^2 : poly2);
if (this.FinalDivision)
multipl = multipl / RssDescendantCount;
output.AddInterval(new Interval(output, operands.LowerBound, operands.UpperBound, multipl));
}
/// <summary>
/// Constructor to define a singleton - fixed membership degree in a single point
/// </summary>
/// <param name="memberValue">x</param>
/// <param name="membershipDegree">μ</param>
internal Interval(IntervalSet parent, System.Decimal memberValue, double membershipDegree)
{
_parent = parent;
_lowerBound = _upperBound = memberValue;
_coefficients = new System.Decimal[] { (System.Decimal)membershipDegree };
}
internal override void Operate(BinaryInterval operands, ref IntervalSet output)
{
GetMinMax(operands, ref output, true);
}
public DiscreteSet(IDiscreteDimension dimension, IntervalSet intervals)
: base(dimension)
{
_intervals = intervals;
}
/// <summary>
/// Creates fuzzy set for the specified dimension and explicit set of memebership function, each one for a distinct interval.
/// </summary>
/// <param name="dimension">Dimenstion of the fuzzy set</param>
/// <param name="intervals">Explicit set of memebership function, each one for a distinct interval.</param>
public FuzzySet(IDimension dimension, IntervalSet intervals)
{
_dimension = dimension;
_intervals = intervals;
}
internal override IntervalSet GetFunction(Dictionary<IDimension, System.Decimal> inputs, IDimension variableInput)
{
if (variableInput == this._dimension)
return _intervals; //we will built the function for this dimension as a variable
else
{
if (variableInput is IContinuousDimension)
{
IntervalSet result = new IntervalSet(variableInput);
result.AddInterval( new Interval(result, ((IContinuousDimension)variableInput).MinValue, ((IContinuousDimension)variableInput).MaxValue, this.IsMember(inputs[_dimension])) );
return result;
}
else
{
IDiscreteDimension dim = (IDiscreteDimension)variableInput;
IntervalSet result = new IntervalSet(dim);
for (uint i = 1; i <= dim.MemberCount; i++)
result.AddInterval( new Interval(result, i, i, this.IsMember(inputs[_dimension])));
return result;
}
}
}
public ContinuousSet(IContinuousDimension dimension, IntervalSet intervals)
: base(dimension, intervals)
{
}
public ContinuousSet(IContinuousDimension dimension, string caption)
: base(dimension, caption)
{
_intervals = new IntervalSet(dimension);
}
internal Interval(IntervalSet parent, System.Decimal lowerBoundary, System.Decimal upperBoundary, Polynomial polynomial)
{
Complex[] cs = polynomial.Coefficients;
List<decimal> r = new List<decimal>();
foreach(Complex c in cs)
if (c.IsReal()) r.Add((decimal)c.Re);
_parent = parent;
_lowerBound = lowerBoundary;
_upperBound = upperBoundary;
_coefficients = r.ToArray();
}
/// <summary>
/// Builds minimum/maximum function for the given interval. The method is used directly in AndM and OrM, and as a part of calculation in other operators.
/// </summary>
/// <param name="operands"></param>
/// <param name="output"></param>
/// <param name="minimum"></param>
internal static void GetMinMax(BinaryInterval operands, ref IntervalSet output, bool minimum)
{
//Find all points where operand1 = operand2 for the given interval
Polynomial poly1 = Interval.GetPolynomial(operands.Coefficients1);
Polynomial poly2 = Interval.GetPolynomial(operands.Coefficients2);
Polynomial difference = poly1 - poly2;
if (Interval.IsEmpty(difference)) //both opearands are equal
output.AddInterval(new Interval(output, operands.LowerBound, operands.UpperBound, poly1));
else
{
decimal[] roots = Interval.RealRoots(difference, operands.LowerBound, operands.UpperBound);
if (roots.Length == 0)
{ //just find out which function is higher for the whole interval
double r1 = poly1.Evaluate(new Complex((double)operands.LowerBound)).Re;
double r2 = poly2.Evaluate(new Complex((double)operands.LowerBound)).Re;
if ((minimum && r1 <= r2) || (!minimum && r1 > r2))
output.AddInterval(new Interval(output, operands.LowerBound, operands.UpperBound, poly1));
else
output.AddInterval(new Interval(output, operands.LowerBound, operands.UpperBound, poly2));
}
else
{
List<decimal> crossPoints = new List<decimal>();
crossPoints.AddRange(roots);
if (! crossPoints.Contains(operands.LowerBound))
crossPoints.Add(operands.LowerBound);
if (!crossPoints.Contains(operands.UpperBound))
crossPoints.Add(operands.UpperBound);
crossPoints.Sort();
//Declares that value of operand1 is higher than the value of operand2 for the given range;
for (int i = 0; i < crossPoints.Count() - 1; i++)
{
bool firstIsPreffered;
if (roots.Contains(crossPoints[i]))
{
double deriv1 = poly1.Differentiate(new Complex((double)crossPoints[i])).Re;
double deriv2 = poly2.Differentiate(new Complex((double)crossPoints[i])).Re;
firstIsPreffered = (minimum && deriv1 < deriv2) || (!minimum && deriv1 > deriv2);
}
else
{ //it must be the second one, then
double deriv1 = poly1.Differentiate(new Complex((double)crossPoints[i + 1])).Re;
double deriv2 = poly2.Differentiate(new Complex((double)crossPoints[i + 1])).Re;
firstIsPreffered = (minimum && deriv2 < deriv1) || (!minimum && deriv2 > deriv1);
}
output.AddInterval(new Interval(output, crossPoints[i], crossPoints[i + 1], firstIsPreffered ? poly1 : poly2));
}
}
}
}
internal virtual void Operate(BinaryInterval operands, ref IntervalSet output )
{
throw new NotImplementedException();
}
/// <summary>
/// True if these intervals includes the intervals to compare. I.e. if they share a common dimension and μthis(x) <= μsetToCompare(x) for each x in <dimension.minValue, dimension.MaxValue>.
/// Note that equalty is a special case of inclusion. To check for proper inclusion, you woud have to evaluate if this.Includes(setToCompare) && ! this.Equals(setToCompare).
/// </summary>
/// <param name="relationToCompare">Set to compare</param>
/// <returns>True if this set is a subset of setToCompare.</returns>
public bool Includes(IntervalSet setToCompare)
{
IntervalSet isSetToCompare = setToCompare;
if (this.Dimension != isSetToCompare.Dimension) return false;
List<BinaryInterval> binaryInterval = BinaryOperator.BuildBinaryInterval(this, isSetToCompare);
foreach (BinaryInterval operands in binaryInterval)
{
IntervalSet minimum = new IntervalSet(this.Dimension);
BinaryOperator.GetMinMax(operands, ref minimum, true);
//Does the minimum equals operands.Operand2? That is the question
IntervalSet included = new IntervalSet(this.Dimension);
included.AddInterval( new Interval( included, operands.LowerBound, operands.UpperBound, operands.Coefficients2) );
if (this.Dimension is IContinuousDimension)
{
//add empty intervals just to pass the check() method
decimal minVal = ((IContinuousDimension)this.Dimension).MinValue;
decimal maxVal = ((IContinuousDimension)this.Dimension).MaxValue;
if (minVal < operands.LowerBound)
{
minimum.AddInterval(new Interval(minimum, minVal, operands.LowerBound, 0));
included.AddInterval(new Interval(included, minVal, operands.LowerBound, 0));
}
if (maxVal > operands.UpperBound)
{
minimum.AddInterval(new Interval(minimum, operands.UpperBound, maxVal, 0));
included.AddInterval(new Interval(included, operands.UpperBound, maxVal, 0));
}
}
if (!minimum.Equals( included ) )
return false;
}
return true;
}
/// <summary>
/// Creates common set of intervals for both operands
/// </summary>
/// <param name="operand1"></param>
/// <param name="operand2"></param>
/// <returns></returns>
internal static List<BinaryInterval> BuildBinaryInterval(IntervalSet operand1, IntervalSet operand2)
{
decimal[] boundaries = IntervalSet.GetAllBoundaries(operand1, operand2);
List<BinaryInterval> semiproduct = new List<BinaryInterval>();
for (uint i = 0; i < boundaries.Length; i++)
{
decimal boundary = boundaries[i];
//singleton [boundary, boundary]
Interval? singleton1 = operand1.GetExactInterval(boundary, boundary);
Interval? singleton2 = operand2.GetExactInterval(boundary, boundary);
if (singleton1.HasValue && singleton2.HasValue)
semiproduct.Add(new BinaryInterval(boundary, boundary, singleton1.Value.Coefficients, singleton2.Value.Coefficients));
else if (singleton1.HasValue && i < (boundaries.Length - 1))
{
Interval? range2 = operand2.GetSubinterval(boundary, boundaries[i + 1]);
if (range2.HasValue)
semiproduct.Add(new BinaryInterval(boundary, boundary, singleton1.Value.Coefficients, range2.Value.Coefficients));
}
else if (singleton2.HasValue && i < (boundaries.Length - 1))
{
Interval? range1 = (operand1.GetSubinterval(boundary, boundaries[i + 1]));
semiproduct.Add(new BinaryInterval(boundary, boundary, range1.Value.Coefficients, singleton2.Value.Coefficients));
}
else if (singleton1.HasValue)
{
Interval? range2 = operand2.GetSubinterval(boundary, boundary);
semiproduct.Add(new BinaryInterval(boundary, boundary, singleton1.Value.Coefficients, range2.Value.Coefficients));
}
else if (singleton2.HasValue)
{
Interval? range1 = operand1.GetSubinterval(boundary, boundary);
semiproduct.Add(new BinaryInterval(boundary, boundary, range1.Value.Coefficients, singleton2.Value.Coefficients));
}
////
//range [boundary, boundaries[i+1] ]
if (i < (boundaries.Length - 1))
{
decimal boundary2 = boundaries[i + 1];
Interval? range1 = operand1.GetSubinterval(boundary, boundaries[i + 1]);
Interval? range2 = operand2.GetSubinterval(boundary, boundaries[i + 1]);
if (range1.HasValue && range2.HasValue)
{
semiproduct.Add(new BinaryInterval(boundary, boundary2, range1.Value.Coefficients, range2.Value.Coefficients));
}
else if (range1.HasValue)
{
semiproduct.Add(new BinaryInterval(boundary, boundary2, range1.Value.Coefficients, new decimal[] { 0 }));
}
else if (range2.HasValue)
{
semiproduct.Add(new BinaryInterval(boundary, boundary2, new decimal[] { 0 }, range2.Value.Coefficients));
}
}
////
}
return semiproduct;
}
internal override void Operate(Interval operand1, ref IntervalSet output)
{
Polynomial result = (operand1.Polynomial^2);
output.AddInterval( new Interval(output, operand1.LowerBound, operand1.UpperBound, result) );
}
public DiscreteSet(IDiscreteDimension dimension, string caption)
: base(dimension, caption)
{
_intervals = new IntervalSet(dimension);
}
/// <summary>
/// Constructor to define a singleton - fixed membership degree in a single point
/// </summary>
/// <param name="memberValue">x</param>
/// <param name="membershipDegree">μ</param>
internal Interval(IntervalSet parent, System.Decimal memberValue, double membershipDegree)
{
_parent = parent;
_lowerBound = _upperBound = memberValue;
_coefficients = new System.Decimal[] { (System.Decimal) membershipDegree };
}
