2. • Introduction
• Fuzzy Set vs. Crisp Set
• Membership Function
• Fuzzification
• Defuzzification
• Working principle
• Conclusion
• References
CONTENTS
2
3. Fuzzy logic is best suited for control applications
The ability to embed imprecise human reasoning and complex
problems is the criterion by which the efficiency of fuzzy logic is
judged.
Fuzziness describes the ambiguity of an event. But not the uncertainty
in the randomness
Introduction
3
4. Fuzzy Set vs. Crisp Set
A classical set is defined by crisp boundaries.
A fuzzy set, on the other hand, is prescribed by ambiguous properties
resulting in ambiguous boundaries
4
5. Membership Function & it’s features
characterizes the fuzziness in a fuzzy set
whether the elements in the set are discrete or continuous - in a
graphical form for eventual use in the mathematical formalisms of
fuzzy set theory.
The core of a membership function (x) =
1.
The support is given by A(x) > 0.
Boundaries are given by 0 < A (x) < 1.
5
6. Fuzzification
Fuzzification is the process of making a crisp quantity fuzzy.
They carry considerable uncertainty.
If the form of uncertainty arises because of imprecision or fuzziness,
it can be represented by a membership function.
institution method is used for fuzzification of the input variables.
6
7. Defuzzification is the conversion of a fuzzy quantity to a precise
quantity.
Defuzzification techniques :
1. Max - Membership Principle:
known as height method is limited to peaked output junctions. Given
by
c (Z*) (Z) for all z C
2. Centroid Method:
also called center of area, center of gravity given by
Z* =
Defuzzification
(Z)dzCμ
(Z).zdzCμ
~
~
7
8. 3. Weighted Average Method:
It’s valid for symmetrical O/P membership function. Given by
Z* = where denotes an algebraic sum.
4. Means-Max Membership: ( middle of maxima )
The MAX membership can be a plateau rather than a single point.
Given by
Z* =
)z(cμ
z).z(cμ
~
~
2
ba
8
9. Obstacle Sensor Unit
• Sensing Distance:
The sensing distance depends upon the speed of the car. speed can be
controlled by gradual anti skid braking system.
Input Membership Function for velocity
9
Fuzzy logic control system
13. Conclusion
An automated accident prevention system is necessary to prevent
accidents.
The fuzzy logic control system can relieve the driver from tension &
prevents accidents.
This fuzzy control unit results in an accident free world.
13
14. References
• Timothy J. Ross “Fuzzy logic for Engineering Applications”, 2nd
edition, Pearson education
• http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?reload=true&punumber
=91
•
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