1. Fuzzy Logic and Fuzzy Sets

2. Sub-topics: Motivation History Fuzzy logic representation
Crisp set Vs Fuzzy set
Membership functions
How Fuzzy logic is applied?
Applications
Conclusion

3. Motivation The term “fuzzy logic” refers to a logic of approximation.
Boolean logic assumes that every fact is either entirely true or false.
Fuzzy logic allows for varying degrees of truth.
Computers can apply this logic to represent vague and imprecise ideas.

4. History
Lotfi Zadeh, at the University of California at Berkeley, first presented fuzzy logic in the mid-1960's.
Zadeh developed fuzzy logic as a way of processing data. Instead of requiring a data element to be either a member or non-member of a set, he introduced the idea of partial set membership.
In 1974 Mamdani and Assilian used fuzzy logic to regulate a steam engine.
In 1985 researchers at Bell laboratories developed the first fuzzy logic chip.

5. WHAT IS FUZZY LOGIC? Definition of fuzzy Definition of fuzzy logic
Fuzzy – “not clear, distinct, or precise; blurred”
Definition of fuzzy logic
A form of knowledge representation suitable for notions that cannot be defined precisely, but which depend upon their contexts.

6. TRADITIONAL REPRESENTATION OF LOGIC
Slow
Fast
Speed = 0
Speed = 1
bool speed;
get the speed
if ( speed == 0) {
// speed is slow }
else {
// speed is fast

7. FUZZY LOGIC REPRESENTATION
Slowest
For every problem must represent in terms of fuzzy sets.
[ 0.0 – 0.25 ]
Slow
[ 0.25 – 0.50 ]
Fast
[ 0.50 – 0.75 ]
Fastest
[ 0.75 – 1.00 ]

8. FUZZY LOGIC REPRESENTATION CONT.
Slowest
Slow
Fast
Fastest
float speed;
get the speed
if ((speed >= 0.0)&&(speed < 0.25)) {
// speed is slowest }
else if ((speed >= 0.25)&&(speed < 0.5)) {
// speed is slow
else if ((speed >= 0.5)&&(speed < 0.75))
// speed is fast
else // speed >= 0.75 && speed < 1.0
// speed is fastest

9. Misconceptions and Controversies
Fuzzy logic is same as “imprecise logic
Fuzzy logic is a new way of expressing probability.
Fuzzy logic will be difficult to scale to larger problems.

10. Sets and Fuzzy Sets
Classical sets – either an element belongs to the set or it does not. Classical sets are also called crisp (sets).
Fuzzy Set Theory: An object is either in a set, not in a set, or partially in a set.
In fuzzy sets, membership is based on a degree between 0 and 1
0 = item not in set
1 = item is in set
If degree is between 0 and 1, then this degree is the degree to which the item is thought to be in the set

11. Membership Functions
To determine what is the membership value of an object in a set, refer to membership functions of the object’s attribute(s).
For example, we may define our membership functions for the three sets Short, Medium and Tall
Attribute is height
1.0
Membership
Short
Medium
Tall
0.5
0.0
Height (meters)
1.55

12. Crisp Logic OperationsB
A and B 1
AND OR
NOT A B
A or B 1 A
not A 1

13. Fuzzy Logic Operations
NOT:
If Fuzzy Statement A is m true, then the statement “Not A” is (1.0 – m) true.
AND:
If Fuzzy Statement A is m true, and Fuzzy Statement B is n true, then the Fuzzy Statement “A and B” is k true, where k = min(m,n).
OR:
If Fuzzy Statement A is m true, and Fuzzy Statement B is n true, then the Fuzzy Statement “A or B” is k true, where k = max(m,n).

14. Rules
Crisp rule:
Example: “If Self is Tall and Enemy is Short, then Attack.”
The Condition of a Rule:
The condition for this rule is: “If Self is Tall and Enemy is Short”
Fuzzy rule:
The condition of the rule once again is: “If Self is Tall and Enemy is Short”
Suppose that Self is 0.3 Tall, and Enemy is 0.6 Short, then this condition is 0.3 True.
So, should we attack?

15. Building Fuzzy Systems
Crisp Input
Fuzzification
Inference
Composition
Defuzzification
Fuzzification
Input
Membership Functions
Fuzzy Input
Rule Evaluation
Rules
Fuzzy Output
Defuzzification
Output
Membership
Functions
Crisp Output

16. Where is Fuzzy Logic used?
Fuzzy logic is used directly in very few applications.
Most applications of fuzzy logic use it as the underlying logic system for decision support systems.

17. Fuzzy System Applications
Cement Kiln - first expert system to use fuzzy logic
Sendai Subway - most celebrated fuzzy logic system
Bullet train between Tokyo and Osaka

18. Applications Cont. ABS Brakes Expert Systems Video Cameras Dishwashers
Washing machines
Bus Time Tables

19. TEMPERATURE CONTROLLER
The problem
Change the speed of a heater fan, based on the room temperature and humidity.
A temperature control system has four settings
Cold, Cool, Warm, and Hot
Humidity can be defined by:
Low, Medium, and High
Using this we can define
the fuzzy set.

20. BENEFITS OF USING FUZZY LOGIC

21. Why Use Fuzzy Logic? 
An Alternative Design Methodology Which Is Simpler, And Faster
Fuzzy Logic reduces the design development cycle
Fuzzy Logic simplifies design complexity
Fuzzy Logic improves control performance
Fuzzy Logic simplifies implementation
Fuzzy Logic reduces hardware costs

22. Limitations of Fuzzy Logic
Stability
Learning
Fuzzy Logic control may not scale well to large or complex problems
Verification and Validation requires extensive testing (as in any expert system).

23. CONCLUSION
Fuzzy logic provides an alternative way to represent linguistic and subjective attributes of the real world in computing.
It is able to be applied to control systems and other applications in order to improve the efficiency and simplicity of the design process.