AE4M33RZN, Fuzzy logic: Fuzzy relations

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Cylindrical extension Can we reconstruct a fuzzy relation from its projections? There is an unique largest relation with prescribed projections: Definition Let A ∈
Cylindrical extension: Drawing ⎧ ⎪x − 1 x ∈ [1, 2] ⎪ A(x) = ⎨3 − x x ∈ [2, 3] ⎪ ⎪0 otherwise ⎩ ⎧ ⎪x − 3 x ∈ [3, 4] ⎪ B(x) = ⎨5 − x x ∈ [4, 5] ⎪ ⎪0 otherwise ⎩
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 22 and 23: Crisp relations Definition A binary
Page 24 and 25: Crisp relations: Properties The equ
Page 26 and 27: Projection Defintion Let R ∈
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

AE4M33RZN, Fuzzy logic: Fuzzy relations

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