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If we can find a mapping from data to real numbers, ranking the data can be solved by ranking the real numbers. This mapping is called [[utility function]]. For label ranking the mapping is a function <math>f: X \times Y \rightarrow \mathbb{R}\,\!</math> such that <math>y_i \succ_x y_j \Rightarrow f(x,y_i) > f(x,y_j)\,\!</math>. For instance ranking and object ranking, the mapping is a function <math>f: X \rightarrow \mathbb{R}\,\!</math>.
Finding the utility function is a [[Regression analysis|regression]] learning problem{{citation needed}} which is well developed in machine learning.
===Preference relations===
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