子句判斷、啟動強度和去模糊化--AForge.NET框架的使用（三）

使用AForge.NET進行模糊運算

上一篇說來一些模糊運算的數學問題，用AForge.NET做相關運算就很簡單了。

1.聯集運算中的標准聯集

數學：s (p,q) = max (p,q)

程序：

public class MaximumCoNorm : ICoNorm 
{ 
    public float Evaluate( float membershipA, float membershipB ) 
    { 
        return Math.Max( membershipA, membershipB ); 
    } 
}

2.交集運算中的標准交集

數學：t (p,q) = min (p,q)

程序：

public class MinimumNorm : INorm 
{ 
    public float Evaluate( float membershipA, float membershipB ) 
    { 
        return Math.Min( membershipA, membershipB ); 
    } 
}

3.交集運算中的代數乘積：

數學：t (p,q) = pq

程序：

public class ProductNorm : INorm 
{ 
    public float Evaluate( float membershipA, float membershipB ) 
    { 
        return membershipA * membershipB; 
    } 
}

 

4.邏輯非

數學：t(p)=1-p

程序：

public class NotOperator : IUnaryOperator 
{ 
    public float Evaluate( float membership ) 
    { 
        return ( 1 - membership ); 
    } 
}

我比較好奇AForge.NET沒有實現徹底聯集和徹底交集，只有自己補上了。

子句判斷（Clause）

這個嚴格來說只是一個輔助用的類，它可以判斷特定的子句是否可以構建。

依舊用溫度舉例，語意變量temperature的hot隸屬度0.4，warm隸屬度0.6。那么temperature is hot和temperature is warm都可以構建。

LinguisticVariable lvTemperature = new LinguisticVariable("Temperature", 0, 50);

TrapezoidalFunction function1 = new TrapezoidalFunction(10, 15, TrapezoidalFunction.EdgeType.Right); 
FuzzySet fsCold = new FuzzySet("Cold", function1); 
TrapezoidalFunction function2 = new TrapezoidalFunction(10, 15, 20, 25); 
FuzzySet fsCool = new FuzzySet("Cool", function2); 
TrapezoidalFunction function3 = new TrapezoidalFunction(20, 25, 30, 35); 
FuzzySet fsWarm = new FuzzySet("Warm", function3); 
TrapezoidalFunction function4 = new TrapezoidalFunction(30, 35, TrapezoidalFunction.EdgeType.Left); 
FuzzySet fsHot = new FuzzySet("Hot", function4);

lvTemperature.AddLabel(fsCold); 
lvTemperature.AddLabel(fsCool); 
lvTemperature.AddLabel(fsWarm); 
lvTemperature.AddLabel(fsHot);

Clause fuzzyClause1 = new Clause(lvTemperature, fsHot); 
lvTemperature.NumericInput = 35; 
float result1 = fuzzyClause1.Evaluate(); 
Console.WriteLine("temperature is hot  ====>  {0}", result1.ToString());

Clause fuzzyClause2 = new Clause(lvTemperature, fsCold); 
lvTemperature.NumericInput = 35; 
float result2 = fuzzyClause2.Evaluate(); 
Console.WriteLine("temperature is cold  ====>  {0}", result2.ToString());  

效果：

很明顯在35度時，temperature is hot 可以構建，temperature is cold則不行。

這個類在自己寫東西的時候一般用不上，但是如果要編寫泛用性的或者拿給別人用的系統，那么最后每個子句都檢查一下。

啟動強度（Firing Strength）

啟動強度（Firing Strength）是衡量規則和輸入的匹配度的量。

舉個例子，語意變量Steel為Cold 的隸屬度是0.6，Stove為Hot的隸屬度為0.4。

那么規則R1：IF Steel is Cold and Stove is Hot then Pressure is Low 的Firing Strength=min(x,y)=0.4

規則R2：IF Steel is Cold and not (Stove is Warm or Stove is Hot) then Pressure is Medium"的Firing Strength=0.4

（以上算法只是這里采用的而已，不同的運算規則會有不同結果，比如0.24之類的）

       

 TrapezoidalFunction function1 = new TrapezoidalFunction( 
10, 15, TrapezoidalFunction.EdgeType.Right); 
        FuzzySet fsCold = new FuzzySet("Cold", function1); 
        TrapezoidalFunction function2 = new TrapezoidalFunction(10, 15, 20, 25); 
        FuzzySet fsCool = new FuzzySet("Cool", function2); 
        TrapezoidalFunction function3 = new TrapezoidalFunction(20, 25, 30, 35); 
        FuzzySet fsWarm = new FuzzySet("Warm", function3); 
        TrapezoidalFunction function4 = new TrapezoidalFunction( 
            30, 35, TrapezoidalFunction.EdgeType.Left); 
        FuzzySet fsHot = new FuzzySet("Hot", function4);

        LinguisticVariable lvSteel = new LinguisticVariable("Steel", 0, 80);

        lvSteel.AddLabel(fsCold); 
        lvSteel.AddLabel(fsCool); 
        lvSteel.AddLabel(fsWarm); 
        lvSteel.AddLabel(fsHot);

        LinguisticVariable lvStove = new LinguisticVariable("Stove", 0, 80); 
       
        lvStove.AddLabel(fsCold); 
        lvStove.AddLabel(fsCool); 
        lvStove.AddLabel(fsWarm); 
        lvStove.AddLabel(fsHot); 
        
        TrapezoidalFunction function5 = new TrapezoidalFunction( 
            20, 40, TrapezoidalFunction.EdgeType.Right); 
        FuzzySet fsLow = new FuzzySet("Low", function5); 
        TrapezoidalFunction function6 = new TrapezoidalFunction(20, 40, 60, 80); 
        FuzzySet fsMedium = new FuzzySet("Medium", function6); 
        TrapezoidalFunction function7 = new TrapezoidalFunction( 
            60, 80, TrapezoidalFunction.EdgeType.Left); 
        FuzzySet fsHigh = new FuzzySet("High", function7); 
       
        LinguisticVariable lvPressure = new LinguisticVariable("Pressure", 0, 100); 
        
        lvPressure.AddLabel(fsLow); 
        lvPressure.AddLabel(fsMedium); 
        lvPressure.AddLabel(fsHigh);

        Database db = new Database(); 
        db.AddVariable(lvSteel); 
        db.AddVariable(lvStove); 
        db.AddVariable(lvPressure);

        Rule r1 = new Rule(db, "R1", "IF Steel is Cold and Stove is Hot then Pressure is Low"); 
        Rule r2 = new Rule(db, "R2", "IF Steel is Cold and not (Stove is Warm or Stove is Hot) then Pressure is Medium"); 
        Rule r3 = new Rule(db, "R3", "IF Steel is Cold and Stove is Warm or Stove is Hot then Pressure is High");

        lvSteel.NumericInput = 12; 
        lvStove.NumericInput = 32;

        float result1 = lvSteel.GetLabelMembership("Cold", lvSteel.NumericInput); 
        Console.WriteLine("membership of Cold  ===>   {0}", result1); 
        float result2 = lvStove.GetLabelMembership("Hot", lvStove.NumericInput); 
        Console.WriteLine("membership of Hot  ===>  {0}", result2); 
        float result3 = r1.EvaluateFiringStrength(); 
        Console.WriteLine(r1.GetRPNExpression()); 
        Console.WriteLine("firing strength of R1  ===>  {0}",result3); 
        float result4 = r2.EvaluateFiringStrength(); 
        Console.WriteLine(r2.GetRPNExpression()); 
        Console.WriteLine("firing strength of R2  ===>  {0}", result4); 

 

 

去模糊化（defuzzification ）

這可以說是模糊系統的最后一步，將經過模糊推理之后產生的結論，轉換為一明確數值，稱之為“去模糊化”。

至於這一步驟的必要性，一般有兩個原因：

1.不同的模糊規則產生的結果不一致，有的是集合，有的是具體的數據，需要一個統一。

2.模糊系統一般不單獨使用，它和其他系統（如神經網絡）等搭配時，輸出值必須是數值。

去模糊化常用方法有最大隸屬度法、取中位數法和重心法。

AForge.Net的實現是CentroidDefuzzifier，即重心法。

當論域為連續時：

當論域為離散時：

InferenceSystem IS = new InferenceSystem( fuzzyDB, new CentroidDefuzzifier( 1000 ) );

至此大部分知識准備就完成了，下一篇會給出一個完整一些的示例。

最后找到一個有關模糊集合的PPT，大家可以參考一下：
http://www.ctdisk.com/file/4496068