WELCOME TO THE WORLD OF FUZZY SYSTEMS

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WELCOME TO THE WORLD OF FUZZY SYSTEMS
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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".
  

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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.
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DETERMINISTIC BEHAVIOUR OF FUZZY

• Fuzzy system is totally deterministic. fuzzy
  logic is a logic OF fuzziness, not a logic which
  is ITSELF fuzzy !

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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

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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

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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.

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CLASSICAL CONCEPT

• Boolean logic .
• No partial memberships.
• Sharp boundries of membership functions.
• No uncertainties allowed.

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FUZZY CONCEPT

• Fuzzy logic .
• Partial membership is allowed.
• Membership function varies in the range 0,1.
• Smooth boundries.

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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.

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• PROBABILITY

• POSSIBILITY

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• 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 .

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TERMS REGARDING FUZZY CONCEPT

• Membership functions
• Linguistic variables
• Fuzzy rules

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MEMBERSHIP FUNCTIONS

• These are the functions that maps objects in a
  domain of concern to their membership value in
  the set.

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• A membership function usually takes shape as
  shown below
• TRIANGULAR TRAPEZOIDAL

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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.

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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
• IFltantecedentgt THENltconsequentgt
• EXAMPLE
• IF the annual income is high
• THEN the person is rich

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STEPS OF FUZZY LOGIC

• Fuzzification
• Inferences
• Composition
• Defuzzification

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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.

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INFERENCES

• Under INFERENCE, the truth value for the premise
  of each rule is computed, and applied to the
  conclusion part of each rule.

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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.

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DEFUZZIFICATION

• Finally is the (optional) DEFUZZIFICATION, which
  is used when it is useful to convert the fuzzy
  output set to a crisp number.

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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

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CONCLUSION !
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THANKS
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QUERRIES ?