1. CCSB354 ARTIFICIAL INTELLIGENCE
Chapter 9.2
Introduction to Fuzzy Logic
(Chapter 9, pp , Textbook)
(Chapter 7, Ref. #1)
Instructor: Alicia Tang Y. C.

2. Fuzzy Logic & Fuzzy Thinking
Fuzzy logic is used to describe fuzziness.
It is not a logic that is fuzzy
Fuzzy logic is the theory of fuzzy sets
sets that calibrate vagueness
Experts rely on common sense when they solve problems
How can we represent expert knowledge that uses vague and ambiguous terms in a computer?

3. What is Fuzzy Logic? It is a powerful problem-solving methodology
Builds on a set of user-supplied human language rules
Fuzzy systems convert these rules to their mathematical equivalents
Introduced by Lofti Zadeh (1965)

4. Fuzzy Logic It deals with uncertainty
It deals with ambiguous criteria or values
Example: “ the girl is tall”
but, how tall is tall?
What do you mean by tall?
is 5’3” tall?
A particular height is tall to one person but is not to another
It depends on one’s relative definition of tall

5. Degree of membership of a “tall” man
Height, cm Crisp Fuzzy
Numeric
data
Just ‘yes’ or ‘no’
In terms
of probability

6. Uncertainty terms and their interpretations
Uncertainty term CF
Definitely not
Almost certainly not -0.8
Probably not
Maybe not
Unknown to +0.2
Maybe
Probably
Almost certainly +0.8
Definitely

7. What is not Fuzzy Logic ?
Classical logic or Boolean logic has two values
Example:
true or false
yes or no
on or off
black or white
start or stop

8. Differences between Fuzzy Logic and Crisp Logic
precise properties
Full membership
YES or NO
TRUE or FALSE
1 or 0
Crisp Sets
Jane is 18 years old
The man is 1.6m tall
Fuzzy Logic
Imprecise properties
Partial membership
YES ---> NO
TRUE ---> FALSE
1 ---> 0
Fuzzy Sets
Jane is about 18 years old
The man is about 1.6m

9. Boolean Logic (for ‘Temperature’)
Boolean logic s discrete…
Hot
100.0
Temperature (C º)
0.0
Cold

10. Fuzzy Logic (for ‘Temperature’)
100.0
Extremely Hot
Hot
Quite Hot
Temperature (C º)
Quite Cold
Cold
0.0
Extremely Cold

11. Why Fuzzy Logic? Fuzzy Logic can: represent vague language naturally
enrich not replace crisps sets
allow flexible engineering design
improve model performance
are simple to implement
they often work!

12. Brief History of Fuzzy Logic
Fuzzy Sets ( Lofti Zadeh, seminar)
Fuzzy Logic ( P. Marinos, Bell Labs)
Fuzzy Measure ( M. Sugeno, TIT)
Fuzzy Logic Control (E.H. Mamdani)
Control of Cement Kiln (F.L. Smidt, Denmatk)
Sendai Subway Train Experiment ( Hitachi)
Stock Trading Expert System (Yamaichi)
LIFE ( Lab for International Fuzzy Eng)

13. Fuzzy Logic Success
Fuzzy Logic success is mainly due to its introduction into consumer products such as:
temperature controlled in showers
air conditioner
washing machines
refrigerators
television
rice cooker
camcorder
heaters
brake control of vehicles

14. Fuzzy logic applied to a subway control system
Fuzzy Control used in the subway in Sendai, Japan
fuzzy control system is used to control the train's acceleration, deceleration and braking
has proven to be superior to both human and conventional automated controllers
reduced the energy consumption been by 10%
passengers hardly notice when the train is actually changing its velocity

15. Fuzzy Rule Example
A fuzzy rule can be defined as a conditional statement in the form:
If x is A
Then y is B
where x and y are linguistic variables;
A and B are linguistic values determined by fuzzy sets
on the universe of discourses x and y, respectively

16. What is the difference between classical and fuzzy rules?
Consider the rules in fuzzy form, as follows:
Rule Rule 2
IF speed is fast IF speed is slow
THEN stop_distance long THEN stop_distance short
In fuzzy rules, the linguistic variable speed can have the range between 0 and 220 km/h, but the range includes fuzzy sets,
such as slow, medium, fast.
Linguistic variable stop_distance can take either value: long or short.
The universe of discourse of the linguistic variable stop_distance can be between 0 and 300m and may include
such fuzzy sets as short, medium, and long.

17. More Fuzzy Rules IF service is excellent OR food is delicious
IF project_duration is short
AND project_staffing is medium
AND project_funding is inadequate
THEN risk is high
IF project_duration is long
AND project_staffing is large
AND project_funding is adequate
THEN risk is low
THEN risk is medium
IF service is excellent
OR food is delicious
THEN tip is generous :

18. Example The temperature of room is too hot/cold…
How to designed an automatic air-conditioner which will be able to set temperature:
Hotter(warm) when it is too cold
Colder(cool) when it is too hot

19. Methodology: Boolean Using Boolean: Problems:
Determine 2 discrete values which is mutually exclusive
E.g. hot or cold
Couldn’t cater for continuous value
Problems:
How if too many students or very few students in the room ?
How hot or how cold the room should be?

20. Bivalent Sets to Characterize the Temperature of a room
Membership
Function 1 ºC
-10 10 20 30
Cold
Cool
Warm
Hot

21. Fuzzy Logic Methodology
Set the boundaries between two values(cold and hot) which will show the degrees of temperature
Use fuzzy set operations to solve the problem:
IF temperature is cold THEN set fan to zero
IF temperature is cool THEN set fan to low
IF temperature is warm THEN set fan to medium
IF temperature is hot THEN set fan to high

22. Expresses the shift of temperature more natural and smooth
Fuzzy Sets to Characterize the Temperature of a room
Membership
Function 1 ºC
-10 10 20 30
Cold
Cool
Warm
Hot
Expresses the shift of temperature more natural and smooth

23. Exercise: A question combining fuzzy rules & truth values and resolution proof

24. FUZZY RULES AND RESOLUTION PROOF
Given the following fuzzy rules and facts with their Truth Values (TV) indicated in brackets:
 Q ( TV = 0.3) TVs for facts
W ( TV = 0.65)
Q   P  S (TV = 1.0)
S  U ( TV = 1.0) TVs for fuzzy rules
W  R ( TV = 0.9)
W  P ( TV = 0.6)
You are required to find (or compute) the Truth Value of U by using the fuzzy refutation and resolution rules.

25. Combining resolution proof and fuzzy refutation
Steps
Convert facts and rules to clausal forms. [in our case, there are 4 rules that need conversion].
By resolution & refutation proof , we negate the goal. [in our case, this is U. assign a TV = 1.0 for it]
For those fuzzy rules, check to see if there is any Truth Value less than 0.5 (i.e. 50%); invert the clause and compute new TV for inverted clause using formula (1 – TV(old-clause)). [we have the clause  Q which is < 0.5, in our example]
Apply resolution proof to reach at NIL (i.e. a direct contradiction).
Each time when two clauses are resolved (combined to yield a resolvent), the minimum of the TVs is taken & assigned it to the new clause.

27. Supplementary slides

28. Applications in Fuzzy logic decision making
The most popular area of applications
fuzzy control
industrial applications in domestic appliances
process control
automotive systems

29. Fuzzy Decision Making in Medicine - I
the increased volume of information available to physicians from new medical technologies
the process of classifying different sets of symptoms under a single name and determining appropriate therapeutic actions becomes increasingly difficult

30. Fuzzy Decision Making in Medicine - II
The past history offered by the patient may be subjective, exaggerated, underestimated or incomplete
In order to understand better and teach this difficult and important process of medical diagnosis, it can be modeled with the use of fuzzy sets

31. Fuzzy Decision Making in Medicine - III
The models attempt to deal with different complicating aspects of medical diagnosis
the relative importance of symptoms
the varied symptom patterns of different disease stages
relations between diseases themselves
the stages of hypothesis formation
preliminary diagnosis
final diagnosis within the diagnostic process itself.

32. Fuzzy Decision Making in Medicine - IV
Its importance emanates from the nature of medical information
highly individualized
often imprecise
context-sensitive
often based on subjective judgment
To deal with this kind of information without fuzzy decision making and approximate reasoning is virtually impossible

33. Fuzzy Decision Making in Information Systems
information retrieval and database management has also benefited from fuzzy set methodology
expression of soft requests that provide an ordering among the items that more or less satisfy the request
allow for the presence of imprecise, uncertain, or vague information in the database