原文: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