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These upper and lower thresholds determine region inclusion for elements. This model is unique and powerful since the thresholds themselves are calculated from a set of six loss functions representing classification risks. Game-theoretic rough sets (GTRS) is a game theory-based extension of rough set that was introduced by Herbert and Yao (2011 ...
One method of arranging a double-elimination tournament is to break the competitors into two sets of brackets, the winners' bracket and losers' bracket (W and L brackets for short; also referred to as championship bracket and elimination bracket, [1] upper bracket and lower bracket, or main bracket and repechage) after the first round. The ...
Bilevel optimization is a special kind of optimization where one problem is embedded (nested) within another. The outer optimization task is commonly referred to as the upper-level optimization task, and the inner optimization task is commonly referred to as the lower-level optimization task.
The corresponding scoresheet, like the parent game, has an Upper and Lower Section. In the Upper Section, points are scored and marked for two- to six-letter words, with each word determined by the point values of its letters. The player is awarded 35 points if the total score in the Upper Section is at least 45.
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If is continuous (i.e. both upper and lower hemicontinuous) at , then the value function is continuous, and the set of maximizers is upper-hemicontinuous with nonempty and compact values. As a consequence, the sup {\displaystyle \sup } may be replaced by max {\displaystyle \max } .
q has a lower adjoint q * if and only if all binary joins in X exist. Conversely, the join operation : X × X → X can always provide the (necessarily unique) lower adjoint for q. Dually, q allows for an upper adjoint if and only if X has all binary meets.