WELCOME TO THE
WORLD OF FUZZY
SYSTEMS
DEFINITION
• Fuzzy logic is a
superset of
conventional
(Boolean) logic that
has been extended to
handle the concept of
partial truth -- truth
values between
"completely true" and
"completely false".
History
1965 The Foundation of the
“Fuzzy Set Theory”
1970 First Application of Fuzzy
Logic in Control Engineering
(Europe)
2000 Fuzzy Logic Becomes a
Standard Technology
Application of Fuzzy Logic in
Business and Finance.
DETERMINISTIC
BEHAVIOUR OF FUZZY
 Fuzzy system is totally deterministic. fuzzy
logic is a logic OF fuzziness, not a logic
which is ITSELF fuzzy …!
IMPORTANCE OF FUZZY
 It overcomes the limitations of conventional
mathematical tools.
 Ease of describing human knowledge
involving vague concepts.
 Cost Effective solution to real world
problems
IMPORTANCE TO ENGINEERS
• Engineers consists largely of recommending
decisions based on insufficient information
and even ignorance on the basis of
subjective acceptance criteria. So fuzzy
provides them ways for treating those
uncertainties
CONCEPTUAL STUDY
• CLASSICAL CONCEPT
This concept is constraintful and has a
limited applications in real world as it uses
the basis of idealism.
• FUZZY CONCEPT
This is a more general typed concept and
can deal nonlinear and ill-understood
problems.
CLASSICAL CONCEPT
• Boolean logic .
• No partial memberships.
• Sharp boundries of membership
functions.
• No uncertainties allowed.
FUZZY CONCEPT
• Fuzzy logic .
• Partial membership is allowed.
• Membership function varies in the range
[0,1].
• Smooth boundries.
POSSIBILITY
VS
PROBABILITY
Possibility is a measure of degree of ease for a
variable to take a value,while probability measures
likelihood for a variable to take a value.
EXAMPLE:
If we are talking about height of say a person :
PROBABILITY VIEW
The height is between 5 and 6 feet .
POSSIBILITY VIEW
The person is somewhat tall.
PROBABILITY
• POSSIBILITY
• HOW TO SOLVE A PROBLEM USING
FUZZY LOGIC ?
We need to follow a 4 step process to
solve a problem using fuzzy logic.
Before that let us discuss important
terms associated .
TERMS REGARDING
FUZZY CONCEPT
• Membership functions
• Linguistic variables
• Fuzzy rules
MEMBERSHIP FUNCTIONS
These are the functions that maps objects in
a domain of concern to their membership
value in the set.
A membership function usually takes shape as
shown below :
TRIANGULAR
TRAPEZOIDAL
LINGUISTIC VARIABLES
A Linguistic variable is like a composition of
symbolic variable and a numeric variable.
EXAMPLE:
Temprature is High.
In the above sentence TEMPRATURE is
linguistic variable.
FUZZY RULES
These are the rules which are the core of the logic
and so are made by the experts of the respective
areas.These have the form:
• IF<antecedent> THEN<consequent>
EXAMPLE:
IF the annual income is high
THEN the person is rich
STEPS OF FUZZY LOGIC
•
•
•
•
Fuzzification
Inferences
Composition
Defuzzification
FUZZIFICATION
• Under FUZZIFICATION, the membership
functions defined on the input variables
are applied to their actual values, to
determine the degree of truth for each rule
premise.
INFERENCES
• Under INFERENCE, the truth value for the
premise of each rule is computed, and
applied to the conclusion part of each rule.
COMPOSITION
• Under COMPOSITION, all of the fuzzy
subsets assigned to each output variable
are combined together to form a single
fuzzy subset for each output variable.
DEFUZZIFICATION
• Finally is the (optional)
DEFUZZIFICATION, which is used when
it is useful to convert the fuzzy output set
to a crisp number.
APPLICATIONS
• Applied in different fields of computer science by
different names.
• e.g.
Fuzzy control ,
Fuzzy arithmetic
artificial intelligence
expert systems
etc.
• Fuzzy neural networks theory
• Fuzzy pattern recognizer.
• About 1100 Successful Fuzzy Logic Applications
CONCLUSION !
THANKS
QUERRIES ?