模糊语意变数、规则和模糊运算--AForge.NET框架的使用(二)

长平狐 发布于 2013/11/25 11:38
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语意变数(Linguistic Variable)

语意变数存储了数个语意量(标签),每个语意量包含一个识别名和模糊集合。在宣告陈述时每个语意量只能和在同一变数中的语意比较。

举个很简单的例子,我们有一个名为temperature的语意变数,它包含4个语意量,名为cold、cool、warm、hot,这也是各自的标签名,同时它们还有各自的隶属度函数。

那么我们就在接下来的系统中使用诸如temperature is hot或者temperature is not hot等等了。



// 语意变数的声明
LinguisticVariable lvTemperature = new LinguisticVariable( " Temperature ", 0, 50);

// 模糊集合和隶属度函数
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);

// 添加标签
lvTemperature.AddLabel(fsCold);
lvTemperature.AddLabel(fsCool);
lvTemperature.AddLabel(fsWarm);
lvTemperature.AddLabel(fsHot);

// 获取隶属度
Console.WriteLine( " Input; Cold; Cool; Warm; Hot ");
for ( float x = 0; x < 50; x += 1f)
{
float y1 = lvTemperature.GetLabelMembership( " Cold ", x);
float y2 = lvTemperature.GetLabelMembership( " Cool ", x);
float y3 = lvTemperature.GetLabelMembership( " Warm ", x);
float y4 = lvTemperature.GetLabelMembership( " Hot ", x);

Console.WriteLine(String.Format( " {0:N}; {1:N}; {2:N}; {3:N}; {4:N} ",x, y1, y2, y3, y4));
}

 

fuzzy2-1

 

模糊规则(Fuzzy Rule)与数据库(Fuzzy Database)

在拥有语意变数后,我们就创建表述(Statement),它是一种表达,可以做成判断,比如什么是什么,什么不是什么。

而规则(Rule)是可以被模糊系统执行的语意指令。如什么是什么时,就怎么。最简单的就是这种:

IF antecedent THEN consequent

前提(antecedent )一般由多个由模糊运算符连接的子句组成。如:

...Clause1 AND (Clause2 OR Clause3) AND NOT Clause4 ...

结果(consequent)一般由赋值子句组成,这里的赋值不光是Variable1 IS Value1,Variable1 IS Not Value1同样支持。

举个例子,再创建一个语意变数,Wind,标签有Strong、BreezeAirless。

那么一下规则就是有效的:

IF Wind IS Strong THEN Temperature IS Cold

IF Wind IS AirlessTHEN Temperature IS NOT Cold

数据库(Fuzzy Database)是一个包含语意变数和相应规则的资料集合,它可以被模糊推理系统(Fuzzy Inference System)使用。

 

// 语意变数的声明
LinguisticVariable lvTemperature = new LinguisticVariable( " Temperature ", 0, 50);

// 模糊集合和隶属度函数
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);

// 添加标签
lvTemperature.AddLabel(fsCold);
lvTemperature.AddLabel(fsCool);
lvTemperature.AddLabel(fsWarm);
lvTemperature.AddLabel(fsHot);

// 语意变数的声明
LinguisticVariable lvWind = new LinguisticVariable( " Wind ", 0, 50);

// 模糊集合和隶属度函数
TrapezoidalFunction functionw1 = new TrapezoidalFunction( 25, 40, TrapezoidalFunction.EdgeType.Right);
FuzzySet fsStrong = new FuzzySet( " Strong ", function1);
TrapezoidalFunction functionw2 = new TrapezoidalFunction( 10, 15, 25, 30);
FuzzySet fsBreeze = new FuzzySet( " Breeze ", function2);
TrapezoidalFunction functionw3 = new TrapezoidalFunction( 5, 10,TrapezoidalFunction.EdgeType.Left);
FuzzySet fsAirless = new FuzzySet( " Airless ", function3);

// 添加标签
lvWind.AddLabel(fsStrong);
lvWind.AddLabel(fsBreeze);
lvWind.AddLabel(fsAirless);

// 创建数据库
Database db = new Database();
db.AddVariable(lvTemperature);
db.AddVariable(lvWind);

// 书写规则
Rule r1 = new Rule(db, " Thinking1 ", " IF Wind IS Strong THEN Temperature IS Cold ");
Rule r2 = new Rule(db, " Thinking2 ", " IF Wind IS AirlessTHEN Temperature IS NOT Cold ");

模糊运算

以下全是数学相关物…不喜者勿入。

模糊运算主要针对模糊集合,有3种:联集(union)、补集(complement)与交集(intersection),而依照不同定义有不同的型态。

1.交集中:

标准交集(standard intersection):t (p,q) = min (p,q)

代数乘积(algebraic product):t (p,q) = pq

有界差异(bounded different):t (p,q) = max (0, p+q-1)

彻底交集(drastic intersection):

fuzzy2-2

2.联集中:

标准联集(standard intersection):s (p,q) = max (p,q)

代数加法(algebraic product): s (p,q) = p + q -pq

有界加法(bounded different): s (p,q) = min (1, p+q)

彻底联集(drastic intersection):

fuzzy2-3

 

本来还想写模糊合成的…但是没找到可以画矩阵的软件,matlab画出来太丑了。

 

写在最后:

1.本文参考了很多文档和资料,特别是相关英文的对应翻译上,主要参考http://www.academia.edu相关讨论和台湾一些院校的研究报告。

2.有个不错的PPT,可以看一下:http://www.ctdisk.com/file/4479740


原文链接:http://www.cnblogs.com/htynkn/archive/2012/02/04/AForge_2.html
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