The phrase "attainable set" is correct and usable in written English.
It can be used in contexts related to mathematics, optimization, or goal-setting, where it refers to a collection of achievable outcomes or targets.
Example: "In our analysis, we identified the attainable set of solutions that meet the project's constraints."
Alternatives: "achievable set" or "feasible set".
For any set (mathcal{M}subset X), let (mathcal {M}^ z)=C^ z capmathcal{M}-{z}), where (G z,t)={win X|Pi w,t)=z} ) is the attainable set of z at (tin {mathbb {R}}_).
We can define the unconditional attainable set as: varPsi =left{left.left x,yright)in {mathrm{Re}}_^{p+q}right|x mathrm{can} mathrm{produce} yright}, (1 which according to Daraio and Simar (2005; 2007a) can also be characterized as: Ψ = {(x, y)|H X, Y(x, y) > 0} where {H}_{X,Y}left x,yright)=mathrm{Prob}left(Xle x,Yge yright).
For any set (M subset X), let M^ z)=C^ z cap M-{z} quadmbox{and}quad M^ z)=G z cap M-{z}, where G z)=cupbigl{ G z,t)| tin R_bigr} quad mbox{and} quad G z,t)=bigl{ win X| Pi (w,t)=zbigr} is the attainable set of z at (tin R_).
With this scenario, Figure 1 displays the concepts of an SCF f, the set of outcomes P and the set of utilities U K. Let g Sk, s−k) be the attainable set of user k at s−k, i.e., the set of outcomes that user k can induce when the other users select s−k.
Then the attainable set can be defined as ( {varPsi}_t^zsubseteq {varPsi}_tsubset {mathrm{Re}}_^{p+q} ), and its distribution can be characterized as: {H}_{left.X,Yright|Z}^tleft left.x,yright|zright)=mathrm{Prob}left left.Xle x,Yge yright|Z=z,T=tright). (4).
More importantly, as the descendants of 19th century immigrants find it increasingly difficult to outdo their parents, new immigrants, starting from a more easily attainable set of goals, can achieve a "success" in more manageable terms.
The belief that love, as much as gravity, holds galaxies together, may have held some interest for Stephen Hawking, but in a more attainable setting than on a planet beyond the Milky Way.
Exterior trajectories executing ballistic lunar capture are formalized through the definition of special attainable sets.
The attainable sets are used in both cases to handle families of either coast arcs or low-thrust orbits.
Lakshmikantham and Mohapatra [13] presented a theorem to show under what conditions the attainable sets of FDIs are the level sets of a fuzzy map.
In using optimal control for scheduling stage, feedback adaptive control for execution stage, and attainable sets for analysis of the achievement of the planned performance in a real execution environment, we pro-vide a mathematically unified framework for SC scheduling and execution control.
