// Testing basic functionality of fuzzy sets
private void runFuzzySetTestButton_Click(object sender, EventArgs e)
{
ClearDataSeries();
// create 2 fuzzy sets to represent the Cool and Warm temperatures
FuzzySet fsCool = new FuzzySet("Cool", new TrapezoidalFunction(13, 18, 23, 28));
FuzzySet fsWarm = new FuzzySet("Warm", new TrapezoidalFunction(23, 28, 33, 38));
// get membership of some points to the cool fuzzy set
double[,] coolValues = new double[20, 2];
for (int i = 10; i < 30; i++)
{
coolValues[i - 10, 0] = i;
coolValues[i - 10, 1] = fsCool.GetMembership(i);
}
// getting memberships of some points to the warm fuzzy set
double[,] warmValues = new double[20, 2];
for (int i = 20; i < 40; i++)
{
warmValues[i - 20, 0] = i;
warmValues[i - 20, 1] = fsWarm.GetMembership(i);
}
// plot membership to a chart
chart.UpdateDataSeries("COOL", coolValues);
chart.UpdateDataSeries("WARM", warmValues);
}
// Testing basic functionality of linguistic variables
private void runLingVarTestButton_Click(object sender, EventArgs e)
{
ClearDataSeries();
// create a linguistic variable to represent temperature
LinguisticVariable lvTemperature = new LinguisticVariable("Temperature", 0, 80);
// create the linguistic labels (fuzzy sets) that compose the temperature
FuzzySet fsCold = new FuzzySet("Cold", new TrapezoidalFunction(10, 15, TrapezoidalFunction.EdgeType.Right));
FuzzySet fsCool = new FuzzySet("Cool", new TrapezoidalFunction(10, 15, 20, 25));
FuzzySet fsWarm = new FuzzySet("Warm", new TrapezoidalFunction(20, 25, 30, 35));
FuzzySet fsHot = new FuzzySet("Hot", new TrapezoidalFunction(30, 35, TrapezoidalFunction.EdgeType.Left));
// adding labels to the variable
lvTemperature.AddLabel(fsCold);
lvTemperature.AddLabel(fsCool);
lvTemperature.AddLabel(fsWarm);
lvTemperature.AddLabel(fsHot);
// get membership of some points to the cool fuzzy set
double[][,] chartValues = new double[4][,];
for (int i = 0; i < 4; i++)
chartValues[i] = new double[160, 2];
// showing the shape of the linguistic variable - the shape of its labels memberships from start to end
int j = 0;
for (float x = 0; x < 80; x += 0.5f, j++)
{
double y1 = lvTemperature.GetLabelMembership("Cold", x);
double y2 = lvTemperature.GetLabelMembership("Cool", x);
double y3 = lvTemperature.GetLabelMembership("Warm", x);
double y4 = lvTemperature.GetLabelMembership("Hot", x);
chartValues[0][j, 0] = x;
chartValues[0][j, 1] = y1;
chartValues[1][j, 0] = x;
chartValues[1][j, 1] = y2;
chartValues[2][j, 0] = x;
chartValues[2][j, 1] = y3;
chartValues[3][j, 0] = x;
chartValues[3][j, 1] = y4;
}
// plot membership to a chart
chart.UpdateDataSeries("COLD", chartValues[0]);
chart.UpdateDataSeries("COOL", chartValues[1]);
chart.UpdateDataSeries("WARM", chartValues[2]);
chart.UpdateDataSeries("HOT", chartValues[3]);
}
/// <summary>
/// Adds a linguistic label to the variable.
/// </summary>
///
/// <param name="label">A <see cref="FuzzySet"/> that will be a linguistic label of the linguistic variable.</param>
///
/// <remarks>Linguistic labels are fuzzy sets (<see cref="FuzzySet"/>). Each
/// label of the variable must have a unique name. The range of the label
/// (left and right limits) cannot be greater than
/// the linguistic variable range (start/end).</remarks>
///
/// <exception cref="NullReferenceException">The fuzzy set was not initialized.</exception>
/// <exception cref="ArgumentException">The linguistic label name already exists in the linguistic variable.</exception>
/// <exception cref="ArgumentException">The left limit of the fuzzy set can not be lower than the linguistic variable's starting point.</exception>
/// <exception cref="ArgumentException">"The right limit of the fuzzy set can not be greater than the linguistic variable's ending point."</exception>
///
public void AddLabel(FuzzySet label)
{
// checking for existing name
if (this.labels.ContainsKey(label.Name))
{
throw new ArgumentException("The linguistic label name already exists in the linguistic variable.");
}
// checking ranges
if (label.LeftLimit < this.start)
{
throw new ArgumentException("The left limit of the fuzzy set can not be lower than the linguistic variable's starting point.");
}
if (label.RightLimit > this.end)
{
throw new ArgumentException("The right limit of the fuzzy set can not be greater than the linguistic variable's ending point.");
}
// adding label
this.labels.Add(label.Name, label);
}
/// <summary>
/// Adds a linguistic label to the variable.
/// </summary>
///
/// <param name="label">A <see cref="FuzzySet"/> that will be a linguistic label of the linguistic variable.</param>
///
/// <remarks>Linguistic labels are fuzzy sets (<see cref="FuzzySet"/>). Each
/// label of the variable must have a unique name. The range of the label
/// (left and right limits) cannot be greater than
/// the linguistic variable range (start/end).</remarks>
///
/// <exception cref="NullReferenceException">The fuzzy set was not initialized.</exception>
/// <exception cref="ArgumentException">The linguistic label name already exists in the linguistic variable.</exception>
/// <exception cref="ArgumentException">The left limit of the fuzzy set can not be lower than the linguistic variable's starting point.</exception>
/// <exception cref="ArgumentException">"The right limit of the fuzzy set can not be greater than the linguistic variable's ending point."</exception>
///
public void AddLabel( FuzzySet label )
{
// checking for existing name
if ( this.labels.ContainsKey( label.Name ) )
throw new ArgumentException( "The linguistic label name already exists in the linguistic variable." );
// checking ranges
if ( label.LeftLimit < this.start )
throw new ArgumentException( "The left limit of the fuzzy set can not be lower than the linguistic variable's starting point." );
if ( label.RightLimit > this.end )
throw new ArgumentException( "The right limit of the fuzzy set can not be greater than the linguistic variable's ending point." );
// adding label
this.labels.Add( label.Name, label );
}
/// <summary>
/// Converts the Fuzzy Rule to RPN (Reverse Polish Notation). For debug proposes, the string representation of the
/// RPN expression can be acessed by calling <see cref="GetRPNExpression"/> method.
/// </summary>
///
private void ParseRule( )
{
// flag to incicate we are on consequent state
bool consequent = false;
// tokens like IF and THEN will be searched always in upper case
string upRule = rule.ToUpper( );
// the rule must start with IF, and must have a THEN somewhere
if (!upRule.StartsWith("IF"))
{
throw new ArgumentException("A Fuzzy Rule must start with an IF statement.");
}
if (upRule.IndexOf("THEN") < 0)
{
throw new ArgumentException("Missing the consequent (THEN) statement.");
}
// building a list with all the expression (rule) string tokens
string spacedRule = rule.Replace("(", " ( ").Replace(")", " ) ");
// getting the tokens list
string[] tokensList = GetRuleTokens(spacedRule);
// stack to convert to RPN
Stack <string> s = new Stack <string>( );
// storing the last token
string lastToken = "IF";
// linguistic var read, used to build clause
LinguisticVariable lingVar = null;
// verifying each token
for (int i = 0; i < tokensList.Length; i++)
{
// removing spaces
string token = tokensList[i].Trim( );
// getting upper case
string upToken = token.ToUpper( );
// ignoring these tokens
if (upToken == "" || upToken == "IF")
{
continue;
}
// if the THEN is found, the rule is now on consequent
if (upToken == "THEN")
{
lastToken = upToken;
consequent = true;
continue;
}
// if we got a linguistic variable, an IS statement and a label is needed
if (lastToken == "VAR")
{
if (upToken == "IS")
{
lastToken = upToken;
}
else
{
throw new ArgumentException("An IS statement is expected after a linguistic variable.");
}
}
// if we got an IS statement, a label must follow it
else if (lastToken == "IS")
{
try
{
FuzzySet fs = lingVar.GetLabel(token);
Clause c = new Clause(lingVar, fs);
if (consequent)
{
output = c;
}
else
{
rpnTokenList.Add(c);
}
lastToken = "LAB";
}
catch (KeyNotFoundException)
{
throw new ArgumentException("Linguistic label " + token + " was not found on the variable " + lingVar.Name + ".");
}
}
// not VAR and not IS statement
else
{
// openning new scope
if (upToken == "(")
{
// if we are on consequent, only variables can be found
if (consequent)
{
throw new ArgumentException("Linguistic variable expected after a THEN statement.");
}
// if its a (, just push it
s.Push(upToken);
lastToken = upToken;
}
// operators
else if (upToken == "AND" || upToken == "OR" || unaryOperators.IndexOf(upToken) >= 0)
{
// if we are on consequent, only variables can be found
if (consequent)
{
throw new ArgumentException("Linguistic variable expected after a THEN statement.");
}
// pop all the higher priority operators until the stack is empty
while ((s.Count > 0) && (Priority(s.Peek( )) > Priority(upToken)))
{
rpnTokenList.Add(s.Pop( ));
}
// pushing the operator
s.Push(upToken);
lastToken = upToken;
}
// closing the scope
else if (upToken == ")")
{
// if we are on consequent, only variables can be found
if (consequent)
{
throw new ArgumentException("Linguistic variable expected after a THEN statement.");
}
// if there is nothing on the stack, an oppening parenthesis is missing.
if (s.Count == 0)
{
throw new ArgumentException("Openning parenthesis missing.");
}
// pop the tokens and copy to output until openning is found
while (s.Peek( ) != "(")
{
rpnTokenList.Add(s.Pop( ));
if (s.Count == 0)
{
throw new ArgumentException("Openning parenthesis missing.");
}
}
s.Pop( );
// saving last token...
lastToken = upToken;
}
// finally, the token is a variable
else
{
// find the variable
try
{
lingVar = database.GetVariable(token);
lastToken = "VAR";
}
catch (KeyNotFoundException)
{
throw new ArgumentException("Linguistic variable " + token + " was not found on the database.");
}
}
}
}
// popping all operators left in stack
while (s.Count > 0)
{
rpnTokenList.Add(s.Pop( ));
}
}
// Hardcode initializing the Fuzzy Inference System
void InitFuzzyEngine()
{
// Linguistic labels (fuzzy sets) that compose the distances
FuzzySet fsNear = new FuzzySet("Near", new TrapezoidalFunction(15, 50, TrapezoidalFunction.EdgeType.Right));
FuzzySet fsMedium = new FuzzySet("Medium", new TrapezoidalFunction(15, 50, 60, 100));
FuzzySet fsFar = new FuzzySet("Far", new TrapezoidalFunction(60, 100, TrapezoidalFunction.EdgeType.Left));
// Right Distance (Input)
LinguisticVariable lvRight = new LinguisticVariable("RightDistance", 0, 120);
lvRight.AddLabel(fsNear);
lvRight.AddLabel(fsMedium);
lvRight.AddLabel(fsFar);
// Left Distance (Input)
LinguisticVariable lvLeft = new LinguisticVariable("LeftDistance", 0, 120);
lvLeft.AddLabel(fsNear);
lvLeft.AddLabel(fsMedium);
lvLeft.AddLabel(fsFar);
// Front Distance (Input)
LinguisticVariable lvFront = new LinguisticVariable("FrontalDistance", 0, 120);
lvFront.AddLabel(fsNear);
lvFront.AddLabel(fsMedium);
lvFront.AddLabel(fsFar);
// Linguistic labels (fuzzy sets) that compose the angle
FuzzySet fsVN = new FuzzySet("VeryNegative", new TrapezoidalFunction(-40, -35, TrapezoidalFunction.EdgeType.Right));
FuzzySet fsN = new FuzzySet("Negative", new TrapezoidalFunction(-40, -35, -25, -20));
FuzzySet fsLN = new FuzzySet("LittleNegative", new TrapezoidalFunction(-25, -20, -10, -5));
FuzzySet fsZero = new FuzzySet("Zero", new TrapezoidalFunction(-10, 5, 5, 10));
FuzzySet fsLP = new FuzzySet("LittlePositive", new TrapezoidalFunction(5, 10, 20, 25));
FuzzySet fsP = new FuzzySet("Positive", new TrapezoidalFunction(20, 25, 35, 40));
FuzzySet fsVP = new FuzzySet("VeryPositive", new TrapezoidalFunction(35, 40, TrapezoidalFunction.EdgeType.Left));
// Angle
LinguisticVariable lvAngle = new LinguisticVariable("Angle", -50, 50);
lvAngle.AddLabel(fsVN);
lvAngle.AddLabel(fsN);
lvAngle.AddLabel(fsLN);
lvAngle.AddLabel(fsZero);
lvAngle.AddLabel(fsLP);
lvAngle.AddLabel(fsP);
lvAngle.AddLabel(fsVP);
// The database
Database fuzzyDB = new Database();
fuzzyDB.AddVariable(lvFront);
fuzzyDB.AddVariable(lvLeft);
fuzzyDB.AddVariable(lvRight);
fuzzyDB.AddVariable(lvAngle);
// Creating the inference system
IS = new InferenceSystem(fuzzyDB, new CentroidDefuzzifier(1000));
// Going Straight
IS.NewRule("Rule 1", "IF FrontalDistance IS Far THEN Angle IS Zero");
// Going Straight (if can go anywhere)
IS.NewRule("Rule 2", "IF FrontalDistance IS Far AND RightDistance IS Far AND LeftDistance IS Far THEN Angle IS Zero");
// Near right wall
IS.NewRule("Rule 3", "IF RightDistance IS Near AND LeftDistance IS Not Near THEN Angle IS LittleNegative");
// Near left wall
IS.NewRule("Rule 4", "IF RightDistance IS Not Near AND LeftDistance IS Near THEN Angle IS LittlePositive");
// Near front wall - room at right
IS.NewRule("Rule 5", "IF RightDistance IS Far AND FrontalDistance IS Near THEN Angle IS Positive");
// Near front wall - room at left
IS.NewRule("Rule 6", "IF LeftDistance IS Far AND FrontalDistance IS Near THEN Angle IS Negative");
// Near front wall - room at both sides - go right
IS.NewRule("Rule 7", "IF RightDistance IS Far AND LeftDistance IS Far AND FrontalDistance IS Near THEN Angle IS Positive");
}
/// <summary>
/// Initializes a new instance of the <see cref="Clause"/> class.
/// </summary>
///
/// <param name="variable">Linguistic variable of the clause. </param>
///
/// <param name="label">Label of the linguistic variable, a fuzzy set used as label into the linguistic variable.</param>
///
/// <exception cref="KeyNotFoundException">The label indicated was not found in the linguistic variable.</exception>
///
public Clause( LinguisticVariable variable, FuzzySet label )
{
// check if label belongs to var.
variable.GetLabel( label.Name );
// initializing attributes
this.label = label;
this.variable = variable;
}
/// <summary>
/// Calculate the membership of a given value to a given label. Used to evaluate linguistics clauses like
/// "X IS A", where X is a value and A is a linguistic label.
/// </summary>
///
/// <param name="labelName">Label (fuzzy set) to evaluate value's membership.</param>
/// <param name="value">Value which label's membership will to be calculated.</param>
///
/// <returns>Degree of membership [0..1] of the value to the label (fuzzy set).</returns>
///
/// <exception cref="KeyNotFoundException">The label indicated in labelName was not found in the linguistic variable.</exception>
///
public float GetLabelMembership(string labelName, float value)
{
FuzzySet fs = labels[labelName];
return(fs.GetMembership(value));
}