Chap2 Fuzzy logic and ANN: Introduction¶

Fuzzy logic: Introduction¶

Introduction¶

The fuzzy logic(FL) is an extension of the binary logic( 二元逻辑 ).

The crucial step towards the application of fuzzy logic to technical systems: to allow variables with linguistic(qualitative, fuzzy) values, to map them onto a numerical(quatitative) range( 将语言变量映射到数字范围 ) and to process them at the numberical level automatically( 自动数值计算 ).

Fuzzy logic¶

Use and map well-defined words(linguisitics parameters) that describe the existing interdependencies in a for humans natural way

This makes it possible to incorporate empirical process knowledge( 经验性知识 ) that is available in a linguistic form into numeric control strategies

The major premise of fuzzy theory is the(for a human natural) incompatibility of high complexity and high precision( 高复杂性和高精度的不可兼容性 )。Striving for high precision if often even counterproductive!( 适得其反 )

The fuzzy concept is predestined for the control of complex processes, which cannot be described mathematically(or only extremely resourced-consuming effort) and therefore cannot be controlled using the the classical control theory

Understanding of fuzziness¶

The fuzziness of information provided in colloquial(common) or technical language is characterized by a gradual representation( 渐变表示 ) of the truth values

This fuzziness in the statements in natural language allows a certain flexbility in the decision-making process and thus enables intelligent system behavior

A combination of fuzzy statements is a relatively precise description of the system behaviour and reflects the existing expert knowledge(in form of IF-THEN rules)

Key concepts of fuzzy logic¶

FL describes logical systems in the mathmatical sense, with the aim of implementing models representing human decision making(IF-THEN rule base)

In a fuzzy set, a so-called membership function( 隶属度函数 ) assigns a numerical value to each element to the set, which is the degree of belonging to the set

Fuzzy set theory is a generalization( 一般化 ) of a classical set theory

Membership degree and probablity are different in nature and have absolutely no correlation

Operation of a fuzzy controller¶

The behaviour of a fuzzy controller is determined by a set of IF-THEN rules(fuzzy rules) that form a so-called rule base( 规则库 )

In addition, fuzzy inference( 模糊推理 ) based on fuzzy mathematics for the numberical processing( 数值处理 ) of these fuzzy rules(which are **linguistic statements** 语言性陈述 ) must be also be defined to convert the (numberical) input values of the controller into a (numeric) output value of the controller

Each element of the codomain( 上域 / 陪域 ) belongs to the membership degree that varies between 0(no belonging) and 1(full belonging)

Fuzzification( 模糊化 ) of input signals ¶

Fuzzification: the transformation of a numeric input signal into a set of membership degrees for all values(fuzzy sets) of the linguistic input variable

If the linguistic input variable is described by n fuzzy sets, then the fuzzification step results in an n-dimensional vector with the elements \(\mu_i(x)\in [0,1], i=1,..n\) which is called a fuzzified input signal or a belonging vector to the fuzzy sets

Fuzzy-logic reasoning(inference)¶

When the controller receives numeric input signals, the fuzzy rule base will be processed by a given inference method to calculate a fuzzy output value

Defuzzification( 解模糊 ) ¶

The numeric output signal of the FC has to be determined by defuzzificationof this fuzzy output value

Neural Networks: Introduction¶

History¶

Artificial neural networks(ANN, NN)¶

Generalization¶

Ability to draw conclusions about unknown things on the condition that given unknown information is different from the existing information, but is similar to

Advantage: Ability to discover complex dependences （依赖性）between input/output that are difficult to describe by mathematical formulas or linguistic rules

In associative learning, which provides a learning model for the supervised trained( 有监督训练 ) artificial NN, a new response becomes associated with a particular stimulus

• instrumental conditioning learning the relationship between a stimulus(event) and a reaction
• classical conditioning learning the relationships between two different events

Structure and connnetion strengths(weights) of an ANN determine its behavior and represent the degrees of freedom during optimization.

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