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Let ξ be an uncertain variable.
Let ξ be an uncertain variable with regular uncertainty distribution (Phi(x)).
Let ξ be an uncertain variable with uncertainty distribution (Phi (x)).
Let ξ be an uncertain variable with regular uncertainty distribution (Phi(t)).
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Assume that the number of customers who prefer to buy the products from newsvendor i is (D_{i}), which is an uncertain variable.
Since ξ is an uncertain variable with regular uncertainty distribution (Phi(t)), its inverse uncertainty distribution (Phi^{-1} alpha)) continuously exists from Definition 4 and Definition 5.
In this paper, the curtailment power ( W_{m,t}^{text{Cur}} ) in the UC model is an uncertain variable defined by a given ratio ( mu_{m,t}^{text{W}} ) of the available wind power as follows.
Note that a constant x is also an uncertain variable with which its inverse distribution is x itself.
The diameter of an uncertain graph is essentially an uncertain variable, which indicates the suitability for investigation of its distribution function.
Similar to stochastic variable defined on a probability space, an uncertain variable is a real-valued function defined on an uncertainty space.
It is easy to know that if an uncertain variable (xisimmathcal {L}(a,b)), i.e., it is subject to a linear uncertainty distribution, then it has an expected value (E[xi]=frac{a+b}{2}). Since the independence between uncertain variables is very important while describing many results, we state it formally.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com