uncertainty and information - wilkes...
TRANSCRIPT
Next
Uncertainty and Information
Develop New Castle News Jul ,-, /0-1
Fuzziness
Previous
("#$" - $'"()Lotfi Zadeh
Evidence:
None. Basically fuzziness deals with linguistic sharplessness and this lack of crispness is not eliminated by gaining evidence.
Fuzzy Set TheoryUncertainty Type: Vagueness
Next
Previous
Fuzzy Set TheoryUncertainty Type: Vagueness
Next
0.0000./000.300-.0000.,00
( -", inf )
-.0000.4000.1000.0000.500
0.6000.5000.0000.500-.000
-.0000.4000.1000.0000.500
0.600---0.,00
A(x) B(x)
Fuzzy Complements ->
Fuzzy T-conorms ->
Fuzzy T-norms ->
standard cA(x)
Yager cA(x)
standard cB(x)
Sugeno cA(x)
lambda omega
0.6000.,00-.0000.,000.000
-
0.6000.,00-.000-.0000.,00
0.6000.110-.000-.0000.,00
0.6000.600-.000-.0000.,00
-.0000.4000.1000.0000.500
0.0000./000.3000.,000.000
0.0000.0300.3000.,000.000
0.0000.0000.3000.,000.000
000.3000.,000
Bounded difference
Standard intersection
Algebraic product
Drastic intersection
Standard union
Algebraic sum
Bounded sum
Drastic union
0
( ', inf )Defined FOR ALL elements of some universal set X.
Previous
Fuzzy Set TheoryUncertainty Type: Vagueness
Next
0.0000./000.300-.0000.,00
/.-00
0.6000.,00-.0000.,070.,1
A(x) B(x)alpha- ->
Scalar Cardinality
strong alpha-cut
A(x)0.6000.,00-.0000.,070.,1
0.,
0.600-.0000.,070.,1
alpha-cutB(x)
strong alpha-cut
B(x)
All alpha-cut sets are CRISP sets !
alpha-cutA(x)
Relative Cardinality
S( A, B )
0.300-.0000.,00
/.117
0.1/0
0.170
-6.000
4.000
Fuzzy Cardinality
S( B, A )
0.35- 0.656
Degree of Subsethood
h(A) h(B)
support(B(x))
support(A(x))
0.300-.000
x-x/x,x1x6
x/x,x1x6
-.000 -.000
alpha-cuts of A(x)
alpha-cuts of B(x)
-.0000.600,-.000
0.,00,0.,07,0.,1,0.600,-.000
-.0000.300,-.000
0.,00,0.300,-.0000./00,0.,00,0.300,-.000
0.000,0./00,0.,00,0.300,-.000
"'.Q'.R
"'.S'.R'.$'.'
Previous Next
Fuzzy Set TheoryUncertainty Type: Vagueness
Temperature around 21
Fuzzy set interpretation of Possibilty Theory