1. CSNB234 ARTIFICIAL INTELLIGENCE
Chapter 8.1
Introduction to Fuzzy Logic and Fuzzy Rules
Instructor: Alicia Tang Y. C.
UNIVERSITI TENAGA NASIONAL

2. Fuzzy Thinking Fuzzy logic is used to describe fuzziness.
Where fuzzy logic is the theory of fuzzy sets, sets that calibrate vagueness
A fuzzy set can be defined as a set with fuzzy boundaries.
Fuzzy logic is based on the idea that all things admit of “degrees” or “scales”.
Such as: temperature, height, speed, distance, beauty etc.
This is acceptable since experts rely on common sense when they solve problems
How can we represent expert knowledge that uses vague and ambiguous terms in a computer?
By using fuzzy logic in representation!

3. Fuzzy Logic Introduced by Lofti Zadeh (1965)
It is a powerful problem-solving methodology
Builds on a set of user-supplied human language rules
It deals with uncertainty and ambiguous criteria or values
Example: “the weather outside is cold”
but, how cold is actually the coldness you described?
What do you mean by ‘cold’ here?
As you can see a particular temperature is cold to one person but it is not to another
It depends on one’s relative definition of the said term

4. Most natural language is bounded with vague and imprecise concepts
Example:
“He is quite tall”
“The student is intelligent”
“Today is a very hot day”
These statements are difficult to translate into more precise language
Fuzzy logic was introduced to design systems that can demonstrate human-like reasoning capability to understand such vague terms

5. Degree of membership of a “tall” man
Height, cm Crisp value Fuzzy
Extremely
tall
Very
tall
tall
It will just
return a ‘yes’
or a ‘no’
When a numeric
data is given
In fuzzy,
Probability is used

6. Relationships between uncertainty terms and certainty factor (CF)
CF takes value from -1 to 1
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
So, be careful when you use the term “may be”.. It represents only 40%

7. What is not considered as fuzzy logic ?
Classical logic or Boolean logic that has two values are not fuzzy!
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
she is 18 years old
man 1.6m tall
FUZZY LOGIC
Imprecise properties
Partial membership
YES ---> NO
TRUE ---> FALSE
1 ---> 0
Fuzzy Sets
she is about 18 years old
man about 1.6m tall

9. How does Fuzzy Logic resembles Human intelligence?
It can handle at certain level of imprecision and uncertainty
By clustering & classification
dividing the scenario/problems into parts
focusing on each part with rank of importance and alternatives to solve
combining the parts to as an integrated whole
It reflects some forms of the human reasoning process by
Setting hypothetical rules
Performing inferencing
Performing logic reasoning on the rules

10. Boolean Logic (for ‘Temperature’) to
Describe terms such as ‘cold’, ‘hot’
Hot
100.0
Temperature (C º)
0.0
Cold
It is discrete, i.e. based on two values

11. Fuzzy Logic (for ‘Temperature’)
100.0
Extremely Hot
Hot
Quite Hot
Temperature (C º)
Quite Cold
Cold
0.0
Extremely Cold
It’s continuous…

12. Fuzzy Logic can represent vague language naturally
enrich not replace crisps sets
allow flexible engineering design
improve model performance
E.g. save power consumption
E.g. increase lifespan
are simple to implement, and
often work

13. History of Fuzzy Logic 1965 - 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)

14. Embedding Fuzzy Logic in Control Systems
Fuzzy Control used in the subway in Sendai, Japan
fuzzy control system is used to control the train's acceleration, deceleration and braking
& passengers hardly notice when the train is actually changing its velocity
has proven to be superior to both human and conventional automated controllers
reduced the energy consumption been by 10%
The idea of fuzzy controlling technology has been enthusiastically received in Japan

15. Fuzzy Logic Applications
Fuzzy Logic success is mainly due to its introduction into consumer products such as:
temperature controlled electrical shower unit
air conditioner
washing machines
refrigerators
television
rice cooker
brake control of vehicles
Etc.

16. Fuzzy Rule
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

17. What is the difference between classical and fuzzy rules?
Consider the rules in fuzzy form, as follows:
Rule Rule 2
IF driving_speed is fast IF driving_speed is slow
THEN stop_distance is long THEN stop_distance is 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.

18. Example of Fuzzy Rules Also, look at the linguistic values used here 
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
One set
of 3
fuzzy rules
More can be
generated
IF service is excellent
OR food is delicious
THEN tip is generous :
Also, look at the linguistic values used here 

19. Example
Problems:
How to handle the temperature of a room so that it is not too hot/cold
How if too many students or very few students are in the room ?
How to designed an automatic air-conditioner which will be able to set temperature:
warmer when it is too cold, and
colder it is too hot?

20. Fuzzy Logic Methodology
Set the boundaries between two values(cold and hot) which will show the degrees of temperature
A sample set of rules
IF temperature is cold THEN set fan_speed to zero
IF temperature is cool THEN set fan_speed to low
IF temperature is warm THEN set fan_speed to medium
IF temperature is hot THEN set fan_speed to high

21. Exercises

22. 2. Design a set of fuzzy rules for an electrical washing machine
IF Load_Weight is heavy THEN set Water_Amount to maximum
IF Load_Weight is medium THEN set Water_Amount to regular
IF Load_Weight is light THEN set Water_Amount to minimum

23. 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

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

25. FUZZY RULES AND RESOLUTION PROOF (WORKED EXAMPLE)
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.

26. 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.

28. Supplementary slides

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

30. 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

31. 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

32. 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.

33. 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

34. 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

35. Conclusion Fuzzy Logic Decision Making is used in many applications
Implemented using fuzzy sets operation(if_then_else statements & logical operators)
Resembles human decision making with its ability to work from approximate data and find a precise solutions