A formal specification for a fuzzy expert system

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A formal specification for a fuzzy expert system

Information and software technology 2003.05 -Vol 45, No 7,  p. 419-29.

author： Chris Matthews

speaker： hsiu chun-chiu (9254610)

A formal specification for a fuzzy expert system

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Abstract(1/2)

Fuzzy logic toolkit – language ZProvides operators, measures and

modifier for the definition and manipulation of fuzzy sets and relations

A simple fuzzy expert system： use of fuzzy Cartesian product fuzzy set truncation operators offers a generic definition for a centroid

defuzzification function

A formal specification for a fuzzy expert system

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Z is a powerful analytical tool that facilitates system understanding through the development of a series of unambiguous, verifiable mathematical models

Z is a well-established specification languageThis example illustrates how the toolkit can

be used to specify a fuzzy rule base and provide the operators necessary for fuzzy inferencing.

Abstract(2/2)

A formal specification for a fuzzy expert system

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Fuzzy expert systems

rule based systemsincorporate fuzzy set theory and fuzzy

logic in both reasoning and knowledge representation

three major conceptual components A fuzzy rule base A description of the fuzzy set parameters A method for fuzzy inferencing (or reasoning)

A formal specification for a fuzzy expert system

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Mamdani Model

Linguistic rules： IF IF xx is is XXii and and yy is is YYii and … THEN and … THEN oo is is OOii

linguistic input variables ： x ， y

possible linguistic values ： XXii ， ， YYii

linguistic output variables ： oo

A formal specification for a fuzzy expert system

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For example (1/2)

A stock market advisory system

two input： share price and trading volume

linguistic variables

（ stable, decreasing, heavy and moderate）

single output： decision（ buy, sell or hold ）

A formal specification for a fuzzy expert system

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example：IF share price is stable and trading volume is heavy THEN decision is hold

IF share price is decreasing and trading volume is moderate THEN decision is sell

For example (2/2)

取mix

是利用股票價格及交易量來計算應該持有或銷售股票

是利用股票價格及交易量來計算應該持有或銷售股票

股票交易的決策圖

A formal specification for a fuzzy expert system

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Nine fuzzy rules & Cartesian products

Three of these lead to a decision to buy shares

Four to a decision to hold sharesTwo lead to a decision to sell sharesfuzzy Cartesian products( 笛卡兒乘積 )

A formal specification for a fuzzy expert system

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Rule base can be read as follows(1/2)

IF share price is stable and trading volume is light THEN decision is buy IF share price is increasing and trading volume is

moderate THEN decision is buy IF share price is increasing and trading volume is he

avy THEN decision is buy IF share price is stable and trading volume is heavy THEN decision is hold

A formal specification for a fuzzy expert system

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IF share price is stable and trading volume is moderate THEN decision is hold

IF share price is increasing and trading volume is light THEN decision is hold

IF share price is decreasing and trading volume is light THEN decision is hold

IF share price is decreasing and trading volume is

moderate THEN decision is sell

IF share price is decreasing and trading volume is heavy THEN decision is sell

Rule base can be read as follows(2/2)

A formal specification for a fuzzy expert system

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The initial system is

In the initial state all fuzzy sets and fuzzy relations, declared in the schema ruleBase are empty.

A formal specification for a fuzzy expert system

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BuildSharePriceis

input

A formal specification for a fuzzy expert system

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buildTradingVolume

written

A formal specification for a fuzzy expert system

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Advise(1/2)

A formal specification for a fuzzy expert system

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Advise(2/2)

A formal specification for a fuzzy expert system

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Conclusion

This paper illustrates the use of the fuzzy logic toolkit in the specification of a simple fuzzy expert system

The toolkit definitions for fuzzy set union and the fuzzy Cartesian product operators are used to build these relations