Fuzzy logic is a decision-making methodology that manages vague and imprecise information, offering a degree of truth between completely true and completely false. It is flexible, easy to implement, and used in various applications such as anti-lock brakes and auto transmission systems, but it has limitations related to accuracy and requires careful rule setting. Its advantages include dealing with uncertainty and low-cost sensors, while drawbacks involve challenges in validation, verification, and the potential confusion with probability theory.

1. FUZZY LOGIC
HEMANT GUPTA
MBA/45007/19
VANISHRI KORNU
MBA/45016/19

2. WHAT IS
FUZZY
LOGIC?
Fuzzy Logic resembles the human
decision-making methodology. It deals
with vague and imprecise information.
It is a form of many-valued logic in
which the truth values of variables may
be any real number between 0 and 1
both inclusive. It is employed to handle
the concept of partial truth, where the
truth value may range between
completely true and completely false.

3. TAP WATER
TEMPERATURE
Traditional Logic
COLD HOT
Fuzzy Logic
COLD HOT

4. CHARACTERISTICS
Flexible and easy to implement machine learning
technique.
Helps you to mimic the logic of human thought.
Highly suitable method for approximate reasoning.
Exact reasoning is viewed by fuzzy logic.
Everything is matter of degree.
Knowledge is interpreted as fuzzy constraints.
Any logical system can be fuzzified.

5. FUZZY LOGIC ARCHITECTURE

6. REPRESENTATION OF FUZZY SET

7. MEMBERSHIP FUNCTION
20 30 40 50 60 70 80
Very Slow Slow Medium Fast Very Fast
Speed
Fuzzy membership
functions for typical
automatic breaking
system.
To check the degree of fastness
0, if speed is <=40
Speed-40/30, if speed is between
40-70
1 if speed is >=50
0.17 0.83
0.33 0.67
0.5

8. OPERATIONS ON FUZZY SETS
UNION/OR FUNCTION
Fuzzy Set ~A Fuzzy Set ~B Union of two fuzzy sets

9. INTERSECTION/ AND
FUNCTION
Intersection of two
fuzzy sets
COMPLEMENT/NOT
FUNCTION
Complement of a
fuzzy set
~

10. PROPERTIES
Properties on sets play an important role for
obtaining the solution.
Following are the different properties of classical
sets −
Commutative Property
Associative Property
Distributive Property
Idempotency Property
Identity Property
Transitive Property

11. COMMUTATIVE
PROPERTY
Having two sets A and B, this property states −
A⋃B = B⋃A
A⋂B = B⋂A
ASSOCIATIVE
PROPERTY
Having three sets A,B and C this property states −
A⋃(B⋃C) = (A⋃B)⋃C
A⋂(B⋂C) = (A⋂B)⋂C

12. DISTRIBUTIVE
PROPERTY
IDEMPOTENCY
PROPERTY
Having a set A, this property states −
A⋃A = A
A⋂A = A
Having three sets A,B and C this property states −
A⋃(B⋂C) = (A⋃B)⋂(A⋃C)
A⋂(B⋃C) = (A⋂B)⋃(A⋂C)

13. IDENTITY
PROPERTY
TRANSITIVE
PROPERTY
Having three sets A,B and C this property states −
A⊆B⊆C , then A⊆C
For set A and universal set X, this property
states −
A ∪ φ = A A ∩ X = A
A ∩ φ = φ A ∪ X = X

14. DE MORGAN’S
LAW
For set A and B, this property states −
The complement of the union of two sets A and B is
equal to the intersection of the complement of the
sets A and B.
(A∪B)’= A’∩ B’
The complement of the intersection of two sets A and
B is equal to the union of the complement of the sets
A and B.
(A∩B)’= A’∪ B’
A B
BA

15. FUZZY
LOGIC
V/S
PROBABILITY
Probability is associated with events and
not facts, and those events will either
occur or not occur. There is nothing fuzzy
about it. Where as in fuzzy logic we
basically try to capture the essential
concept of vagueness. Fuzzy Logic is all
about degree of truth.
Probability theory has nothing to reason
about things that are not entirely true or
false. In short, we can say that Fuzzy Logic
captures the meaning of partial truth
whereas Probability theory captures
partial knowledge.

16. ADVANTAGES
. It helps you to deal with the
uncertainty in engineering.
. The structure of Fuzzy Logic
Systems is easy and understandable.
. Fuzzy logic is widely used for
commercial and practical purposes.
. Mathematical concepts within
fuzzy reasoning are very simple.
. Inexpensive sensors can be used
which helps you to keep the overall
system cost and complexity low.
. It provides a most effective
solution to complex issues.

17. DISADVANTAGES
. Fuzzy logic is not always accurate, so
the results are perceived based on
assumption, so it may not be widely
accepted.
. Fuzzy systems don't have the
capability of machine learning as-well-
as neural network type pattern
recognition
. Validation and Verification of a fuzzy
knowledge-based system needs
extensive testing with hardware.
. Setting exact, fuzzy rules and,
membership functions is a difficult task
. Some fuzzy time logic is confused
with probability theory and the terms.

18. APPLICATION
AREAS
OF FUZZY
LOGIC

19. PRODUCT COMPANY FUZZY LOGIC
Anti-lock Brakes Nissan
Use fuzzy logic to controls brakes in hazardous cases depend on car speed,
wheel speed and acceleration.
Auto transmission NOK/Nissan
Fuzzy logic is used to control the fuel injection and ignition based on
throttle setting, cooling water temperature, RPM, etc.
Cruise control
Nissan, Isuzu,
Mitsubishi
Use it to adjusts throttle setting to set car speed and acceleration
Dishwasher Matsushita
Use for adjusting the cleaning cycle, rinse and wash strategies depend
upon the number of dishes and the amount of food served on the dishes.
Elevator control
Fujitech, Mitsubishi
Electric, Toshiba
Use it to reduce waiting for time based on passenger traffic
Fitness management Omron Fuzzy rules implied by them to check the fitness of their employees
Kiln control Nippon steel Mixes cement
Microwave oven Mitsubishi Chemical Sets lunes power and cooking strategy

20. REFERENCES
• https://www.google.com/search?q=de+morgan%27s+
law&source=lmns&bih=587&biw=1226&hl=en&ved=2
ahUKEwjWhZfyl8zpAhWRBysKHWdmD8IQ_AUoAHoEC
AEQAA
• https://www.youtube.com/watch?v=tC3K8RLRIZc&list
=PLIY8eNdw5tW9ZqgI9nfXxr6r-FHnLS90k&index=2
• https://byjus.com/maths/de-morgans-first-law/
• Fuzzy%20Logic%20-
%20Classical%20Set%20Theory%20-
%20Tutorialspoint.pdf
• Fuzzy%20Logic%20-%20Set%20Theory%20-
%20Tutorialspoint.pdf
• Fuzzy%20Logic%20-
%20Membership%20Function%20-
%20Tutorialspoint.pdf

21. THANK YOU