子句判断、启动强度和去模糊化AForge.NET框架的使用（三）

使用AForge.NET进行模糊运算

上一篇说来一些模糊运算的数学问题，用AForge.NET做相关运算就很简单了。

1.联集运算中的标准联集

数学：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.交集运算中的标准交集

数学：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.交集运算中的代数乘积：

数学：t (p,q) = pq

程序：

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

4.逻辑非

数学：t(p)=1-p

程序：

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

我比较好奇AForge.NET没有实现彻底联集和彻底交集，只有自己补上了。

子句判断（Clause）

这个严格来说只是一个辅助用的类，它可以判断特定的子句是否可以构建。

依旧用温度举例，语意变量temperature的hot隶属度0.4，warm隶属度0.6。那么temperature is hot和temperature is warm都可以构建。

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：

很明显在35度时，temperature is hot 可以构建，temperature is cold则不行。

这个类在自己写东西的时候一般用不上，但是如果要编写泛用性的或者拿给别人用的系统，那么最后每个子句都检查一下。

启动强度（Firing Strength）

启动强度（Firing Strength）是衡量规则和输入的匹配度的量。

举个例子，语意变量Steel为Cold 的隶属度是0.6，Stove为Hot的隶属度为0.4。

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

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

（以上算法只是这里采用的而已，不同的运算规则会有不同结果，比如0.24之类的）

       

 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 ）

这可以说是模糊系统的最后一步，将经过模糊推理之后产生的结论，转换为一明确数值，称之为“去模糊化”。

至于这一步骤的必要性，一般有两个原因：

1.不同的模糊规则产生的结果不一致，有的是集合，有的是具体的数据，需要一个统一。

2.模糊系统一般不单独使用，它和其他系统（如神经网络）等搭配时，输出值必须是数值。

去模糊化常用方法有最大隶属度法、取中位数法和重心法。

AForge.Net的实现是CentroidDefuzzifier，即重心法。

当论域为连续时：

当论域为离散时：

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

至此大部分知识准备就完成了，下一篇会给出一个完整一些的示例。

最后找到一个有关模糊集合的PPT，大家可以参考一下：
http://www.ctdisk.com/file/4496068