Fuzzy set modifiers linguistic hedges

1
Fuzzy set modifiers (linguistic hedges)

• Fuzzy set modifiers change the shape of a fuzzy
  set (i.e. they
• modify the membership function).
• They are also described linguistically and play a
  similar
• role the use of adverbs and adjectives in
  language.
• They are heuristic in nature and are associated
  with a
• perceived fit of the modification to a
  psychological goodness' of the resultant set.

2
Fuzzy set modifiers (linguistic hedges)

• Some examples
• where µ(x) represents the membership value of
  reference set element, x in the fuzzy set, µ
• i.e. µ X --gt 0,1

For further examples see table 4.2, p127 course
readings
3
Fuzzy set modifiers (linguistic hedges)

• For continuous fuzzy sets e.g. A set
  representing low temperature

4
Fuzzy set modifiers (linguistic hedges)

• For continuous fuzzy sets e.g. A set
  representing very low temperature

5
Fuzzy set modifiers (linguistic hedges)

• For continuous fuzzy sets e.g. A set
  representing extremely low temperature

6
Fuzzy set modifiers (linguistic hedges)

• What about a somewhat low temperature?

7
Fuzzy logic

• Fuzzy logic permits partial truth of a
  proposition
• In boolean logic
• Tom is a member of the set of tall people and he
  is not a member of the set of average people gt
  that the proposition, tom is a tall person is
  true
• and the proposition, tom is an average person is
  false
• However in fuzzy logic
• Tom exhibits 0.6 membership in the (fuzzy) set
  of tall people and 0.4 membership in the (fuzzy)
  set of average people
• gt that the proposition, tom is a tall person is
  only true to a partial degree (in this case 0.6)
• and that the proposition tom is an average
  person is only true to a partial degree (in this
  case 0.4)

8
Fuzzy logic

• Evaluation of the degree of truth of compound
  propositions uses min (for logical AND), max (for
  logical OR) and 1 - truth value (for logical
  NOT).
• So, the degree of truth of the compound
  proposition, tom is a tall person AND tom is an
  average person would be min(0.6, 0.4) i.e. 0.4
• the degree of truth of the proposition, tom is
  NOT a tall person is also 0.4 (i.e. 1 - 0.6)
• the degree of truth of the proposition, tom is a
  tall person OR tom is an average person would be
  max (0.6, 0.4) i.e. 0.6
• There is also an evaluation function for fuzzy
  implication (gt)
• degree of truth of the implication (proposition A
  -gt proposition B) is evaluated as
• max ( 1 - truth(A), min(truth(A), truth(B))