White Blue and Lightnings by sdfwerte

VIEWS: 5 PAGES: 36

• pg 1
```									Intelligent Sensor Fusion -
ENG4083M

Fuzzy Logic 1
Overview
•   Background
•   An introductory example
•   Fuzzy vs. non-fuzzy
•   Foundations of fuzzy logic
Background
•   What is fuzzy logic?
•   Why use fuzzy logic?
•   When not to use fuzzy logic
What is fuzzy logic?
“As complexity rises, precise statements lose
meaning and meaningful statements lose
precision.”
Precision v significance
Input – output map
Why use fuzzy logic?
•   Conceptually easy to understand
•   Flexible
•   Tolerant of imprecise data
•   Can model non-linear functions
•   Can be based on the experience of experts
•   Can be blended with conventional techniques
•   Is based on natural language
When not to use fuzzy logic
•   Fuzzy logic is not a cure-all
•   If you find it's not convenient, try
something else
•   If a simpler solution already exists, use it
An introductory example
•   The basic tipping problem:
–    Given a number between 0 and 10 that
represents the quality of service at a
restaurant (where 10 is excellent), what
should the tip be?
•   Extension:
–    Additionally given a number between 0
and 10 that represents the quality of food
at a restaurant (where 10 is excellent),
what should the tip be?
The non-fuzzy approach - 1
•   Derive a simple linear formula based on
typical percentage tip for good food and
service
•   See Toolbox documentation for details
The non-fuzzy approach - 2
The fuzzy approach - 1
•   Choose a set of natural language rules
that describe your basic approach to
tipping e.g.

IF service is poor OR food is
rancid
THEN tip is cheap
The fuzzy approach - 2
IF service is poor OR food is rancid
THEN tip is cheap

IF service is good
THEN tip is average

IF service is excellent OR food is
delicious
THEN tip is generous
The fuzzy approach - 3
Foundations of fuzzy logic
•   Fuzzy sets
•   Membership functions
•   Logical operations
•   If-then rules
Example of a normal set
Example of a fuzzy set
Two valued logic   Multi-valued logic
Membership functions
•   A membership function (MF) is a curve
that defines how each point in the
input space is mapped to a
membership value (or degree of
membership) between 0 and 1
•   The input space is sometimes referred
to as the universe of discourse, a
fancy name for a simple concept
Membership functions
height – crisp membership
Membership functions
height – crisp membership
Membership functions
height – fuzzy membership
Example membership functions

Triangle MF (trimf)
Example membership functions

Trapizoidal MF (trapmf)
Example membership functions

Sigmoid MF (sigmf)
Example membership functions

Double Sigmoid MF (dsigmf)
Summary so far
•   Fuzzy sets describe vague concepts (hot weather,
weekend days)
•   A fuzzy set admits the possibility of partial
membership in it (Friday is sort of a weekend day)
•   The degree an object belongs to a fuzzy set is
denoted by a membership value between 0 and 1.
(Friday is a weekend day to the degree 0.8)
•   A membership function associated with a given
fuzzy set maps an input value to its appropriate
membership value
Logical operations
Fuzzy logic operations are a superset of
normal Boolean logic shown below:
Logical operations
There are a number of possible implementations
but a simple one that is very commonly used is
as shown below:
Logical operations
If-then rules
IF service is good
THEN tip is average

Note that “is” used in two ways this rule means:
IF service == good
THEN tip = average

The rules can be extended by using logical operations in
the IF part
If-then rules
If-then rules
Implication
•   In the previous example the output
membership function is truncated to the
result of the antecedent this is called
minimum implications
•   An alternative method product implication
simply multiplies the output membership
is simply multiplied by the result of the
antecedent
•   The difference is shown in the following
diagram:
Implication
Conclusions
•   This lecture has:
–   Introduced the basic idea of fuzzy logic
and fuzzy control
–   Given some guidelines on when to use
fuzzy control
–   Introduced fuzzy membership
–   Introduced fuzzy rules

```
To top