AE4M33RZN, Fuzzy logic: Fuzzy relations

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Cutworhiness: Examples • The theorem 214 can be stated as: “Set inclusion is cut-consistent.” Brain teasers • Strong normality of A is defined as A(x) = 1 for some x ∈ Δ. iff every cut strongly normal. iff every its cut is non-empty A is strongly-normal Strong normality is cut-consistent: • Being crisp is cutworthy, but not cut-consistent: Every cut is crisp by definition, therefore cutworthiness. But even non-crisp sets have crisp cuts, therefore the property is not not cut-consistent.
Google: “fuzzy” Sources: M. Taylor's Weblog, M. Taylor's Weblog, Eddie's Trick Shop.
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 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 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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