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Let ξ be an uncertain set.
Theorem 2 Let ξ be an uncertain set, and f be a nonnegative function.
Let ξ be an uncertain set with finite expected value e.
Let ξ be an uncertain set with a finite expected value E.
Let ξ be an uncertain set with a membership function μ.
Let ( Γ, L, M ) be an uncertainty space, and ξ be an uncertain set on ( Γ, L, M ).
Similar(53)
If f ( x, y ) is monotone increasing with respect to x and y, then τ = f is an uncertain set with a regular membership function λ where λ l − 1 = f ( μ l − 1 , ν l − 1 , λ r − 1 = f ( μ r − 1 , ν r − 1 . Definition 6 (Liu [14]).
Note that μ l − 1 is increasing and μ r − 1 is decreasing with respect to α. Example 2 The word 'young' may be regarded as an uncertain set ξ with a membership function μ ( x ) = { ( x − 15 ) / 5, if 15 ≤ x ≤ 20, 1, if 20 < x < 30, ( 35 − x ) / 5, if 30 ≤ x ≤ 35, 0, otherwise.
A close reading of the Finch Report reveals that the headline estimate of a £50m-60m excess transitional cost is predicated on an uncertain set of assumptions.
Let ξ be a nonempty uncertain set.
An uncertain set is a measurable function ξ from an uncertainty space ( Γ, L, M ) to a collection of sets of real numbers, i.e., for any Borel set B of real numbers, the following two sets: { ξ ⊂ B } = { γ ∈ Γ ∣ ξ ⊂ B }, { B ⊂ ξ } = { γ ∈ Γ ∣ B ⊂ ξ }. are events.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com