Introduction to Fuzzy Logic

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Introduction to Fuzzy Logic

• Supem Samarasiri (060424G)?
• Department of Electronic Telecommunication
  Engineering
• University of Moratuwa

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Types of Logic

• Propositional Logic
• Predicate Logic( First order, second order
  higher order logic)?
• Fuzzy Logic

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Propositional Logic

• Has two states (true/false) or (1/0)?
• Has connectives or and implies not
• Eg x5 can either be true or false

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Limits of Propositional Logic

• Cannot express statements such as for all x P(x)?
• for an infinite domain.

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First Order Logic

• Often called predicate logic this logical system
  introduces quantifiers and has 4 basic quantifier
  rules for deduction

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Limitations in FOL

• Cant express finiteness and countability

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Second order Logic

• To Outcome limitations in FOL we have defined SOL
  and HOL's which can be used to describe
  properties of relations of relations of
  relations.......of relations.

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Fuzzy Logic

• Question
• What is fuzzy?

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Fuzzy Logic

• Fuzzy means vagueness.

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Fuzzy set Theory

• As normal logics are related to normal set theory
  fuzzy logic is related to fuzzy set theory.

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Fuzzy sets

• Unlike normal crisp sets fuzzy sets can express
  whether an element is belonging to a set in a
  range of 0,1. A function so called membership
  function will give the corresponding value
  between 0,1 for each element.

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Fuzzy sets

• A
• Where X is the domain and
• is the membership function.

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Membership Functions

• Membership functions provide the value of
  membership for particular elements. The figure
  above shows the membership functions of
  cold(blue), warm(yellow) and hot(red) fuzzy sets
  of a anti locking brake system. Note that unlike
  crisp predicate logic and set theory for some
  temperature values it can be both cold and warm
  at the same time.

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Fuzzy set operations

• As in crisp set theory the basic union,
  intersection, compliment operations are defined
  in the following manner in Fuzzy set Theory as
  membership corresponding functions

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Fuzzy Logic

• Like in Fuzzy Sets fuzzy propositions have a
  value in the range 0,1. Which is denoted by
  T(p) the truth value of p

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Fuzzy Operations

• Like in predicate logic Fuzzy logic also have the
  following operations
• Negation
• Disjunction
• Conjunction
• Implication

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Fuzzy operations

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