AE4M33RZN, Fuzzy logic: Fuzzy relations

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Crisp relations Definition A binary crisp relation R from X onto Y is a subset of the cartesian product X × Y: R ∈ ℙ(X × Y) (12) Definition The inverse relation R -1 to R is a relation from Y to X s.t. R -1 = {(y, x) ∈ Y × X | (x, y) ∈ R} (13)
Crisp relations: Inverse Definition Let X, Y, Z be sets. Then the compound of relations R ⊆ X × Y, S ⊆ Y × Z is the relation R ○ S = {(x, z) ∈ X × Z | (x, y) ∈ R and (y, z) ∈ S for some y} (14)
Page 1 and 2: AE4M33RZN, Fuzzy logic: Fuzzy relat
Page 3: Fuzzy implication We already know f
Page 13 and 14: Generalized fuzzy inclusion: Exampl
Page 18 and 19: Cutworhiness: Examples • The theo
Page 20 and 21: Google: “probability” Sources:
Page 24 and 25: Crisp relations: Properties The equ
Page 26 and 27: Projection Defintion Let R ∈
Page 28 and 29: Cylindrical extension Can we recons
Page 30 and 31: Composition of fuzzy relations Defi
Page 32 and 33: Properties of fuzzy relations Then
Page 34 and 35: Example on fuzzy relation propertie
Page 36 and 37: Proof of 234. Proving (21) and (22)
Page 38: Extensions: Sometimes it is useful

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