1. A formal specification for a fuzzy expert system 1 Information and software technology 2003.05 -Vol 45, No 7, p. 419-29. author ： Chris Matthews speaker ： hsiu chun-chiu (9254610)

2. A formal specification for a fuzzy expert system2 Abstract(1/2) Fuzzy logic toolkit – language Z Provides 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

3. A formal specification for a fuzzy expert system3 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 language This 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)

4. A formal specification for a fuzzy expert system4 Fuzzy expert systems rule based systems incorporate 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)

5. A formal specification for a fuzzy expert system5 Mamdani Model Linguistic rules ： IF x is X i and y is Y i and … THEN o is O i IF x is X i and y is Y i and … THEN o is O i linguistic input variables ： x ， y X i ， Y i possible linguistic values ： X i ， Y i o linguistic output variables ： o

6. A formal specification for a fuzzy expert system6 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 ）

7. A formal specification for a fuzzy expert system7 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)

8. 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

10. 股票交易的決策圖

12. A formal specification for a fuzzy expert system12 Nine fuzzy rules & Cartesian products Three of these lead to a decision to buy shares Four to a decision to hold shares Two lead to a decision to sell shares fuzzy Cartesian products( 笛卡兒乘積 )

13. A formal specification for a fuzzy expert system13 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 heavy THEN decision is buy IF share price is stable and trading volume is heavy THEN decision is hold

14. A formal specification for a fuzzy expert system14 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)

15. A formal specification for a fuzzy expert system15 The initial system is In the initial state all fuzzy sets and fuzzy relations, declared in the schema ruleBase are empty.

16. A formal specification for a fuzzy expert system16 BuildSharePriceis input

17. A formal specification for a fuzzy expert system17 buildTradingVolume written

18. A formal specification for a fuzzy expert system18 Advise(1/2)

19. A formal specification for a fuzzy expert system19 Advise(2/2)

20. A formal specification for a fuzzy expert system20 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