子句判断、启动强度和去模糊化--AForge.NET框架的使用(三)

长平狐 发布于 2013/11/25 11:38
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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:

fuzzy3-1

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.GetRPNExssion());
Console.WriteLine( " firing strength of R1 ===> {0} ",result3);
float result4 = r2.EvaluateFiringStrength();
Console.WriteLine(r2.GetRPNExssion());
Console.WriteLine( " firing strength of R2 ===> {0} ", result4);

 

 

fuzzy3-2

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:

fuzzy3-3

当论域为离散时:

fuzzy3-4

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


原文链接:http://www.cnblogs.com/htynkn/archive/2012/02/05/AForge_3.html
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