《人工智能（智能系统指南，第二版）》读书笔记——5、第四章

1. introduction to knowledge-based intelligent systems(summary / questions for review / references)

2. rule-based expert systems

3. uncertainty management in rule-based expert systems

4. fuzzy expert systems

5. frame-based expert systems

6. artificial neural networks

7. evolutionary computation

8. hybrid intelligent systems

9. knowledge engineering and data mining

4. fuzzy expert systems

Fussy logic is a logic that describes fuzziness. As fuzzy logic attempts to model humans' sense of words, decision making and common sense, it is leading to more human intelligent machines.

A fussy set is a set with fuzzy boundaries, such as short, average for man's height. To represent a fuzzy set in a computer, we express it as a function and then map the elements of the set to their degree of membership. Typical membership functions used in fuzzy expert systems are triangles and trapezoids. (Because the two is linear fit function<线性拟合函数>, some other functions<sigmoid, gaussian and pi> will increase the time of computation, so we hardly use those functions.)

In classical set theory, crisp set A of Xis defined as function fa(x) called the characteristic function(特征函数) of A, say fa(x) : X -> 0,1; In the fuzzy theory, fuzzy set A of universe X is defined by function ua(x) called the membership function(隶属函数) of set A, say ua(x) : X -> [0,1].

A linguistic variable(语言变量) is used to describe a term or concept with vague or fuzzy values. These values are represented in fuzzy sets. The statement "John is tall" implies that the linguistic(fuzzy) variable John takes the linguistic(fuzzy) value tall. In fuzzy expert systems, linguistic variables are used in fuzzy rules, for example, IF   wind is strong   THEN   sailing is good.

Hedges(模糊限制语) are fuzzy set qualifiers used to modify the shape of fuzzy sets. They include adverbs such as very, somewhat, quite, more or less and slightly. Hedges perform mathematical operatins of concentration(集中) by reducing the degree of membership of fuzzy elements(e.g. very tall men), dilation(扩散) by increasing the degree of membership(e.g. more or less tall men) and intensification(强化) by increasing the degree of membership above 0.5 and decreasing those below 0.5(e.g. indeed tall men). (p97)

Fuzzy sets can interact. These relations are called operations. The main operatins of fuzzy sets are: complement, containment, intersection and union(补、包含、交、并). Crisp and fuzzy sets have the same properties,frequently used properties of fuzzy sets are: commutativity, associativity, distributivity, idempotency, identity, involution, transitivity, De Morgan's Laws(交换律、结合律、分配率、幂等率、恒等率、自乘率、传递率、德·摩根定律). (p100)

Fuzzy rules are used to capture human knowledge. A fuzzy rule is a conditional statement in the form:

IF           x is A

THEN   y is B

where x and y are linguistic variables and A and B are linguistic values determined by fuzzy sets.

Fuzzy reasoning includes two distinct parts: evaluating the rule antecedent(the IF part of the rule) and implication or applying the result to the consequent(the THEN part of the rule).

Fuzzy inference is aprocess of mapping from a given input to an output by using the theory of fuzzy sets. The fuzzy inference process includes four steps: fuzzification of the input variables, rule evaluation, aggregation of the rule outputs and defuzzification(模糊化输入变量、规则评估、聚集规则的所有模糊输出为【一个】模糊输出、逆模糊化).

The two fuzzy inference techniques are the Mamdani and Sugeno methods. The Mamdani method is widely accepted in fuzzy expert systems for its ability to capture expert knowledge in fuzzy rules. However, Mamdani-type fuzzy inference entails a substantial computational burden.

To improve the computational efficiency of fuzzy inference, Sugeno used a single spike, a singleton, as the membership function of the rule consequent. Instead of a fuzzy set, he used a mathematical function of the input variable. The format of the Sugeno-style fuzzy rule is:

IF           x is A

AND      y is B

THEM   z is f(x,y)

where x, y and z are linguistic variables; A and B are fuzzy sets on universe of discourses X and Y, respecively; and f(x,y) is a mathematical function.

The Sugeno method works well with optimisation and adaptive techniques, which makes it very attractive in control, particularly for dynamic nonlinear systems.

Building a fuzzy expert system is an iterative process that involves the following steps:

1)Specify the problem and define linguistic variables.

2)Determine fuzzy sets.

3)Elicit(抽取) and construct fuzzy rules.

4)Encode the fuzzy sets, fuzzy rules and procedures to perform fuzzy inference into the expert system.

5)Evaluate and tune the system.

And tuning is the most laborious and tedious part in building a fuzzy system. It often involves adjusting existing fuzzy sets and fuzzy rules.