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Fuzzy Sets and Systems, 1991
Taking \(M=(E,I)\) as a crisp matroid two definitions fix the independence of the members of \(I\) and the rank function \(R(A)\) for \(A\in I\). Two theorems, well-known results from matroid theory, are established. Similarly results for fuzzy matroids (\(fm\)) are given in Section 2.
Goetschel, Roy jun., Voxman, William
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Taking \(M=(E,I)\) as a crisp matroid two definitions fix the independence of the members of \(I\) and the rank function \(R(A)\) for \(A\in I\). Two theorems, well-known results from matroid theory, are established. Similarly results for fuzzy matroids (\(fm\)) are given in Section 2.
Goetschel, Roy jun., Voxman, William
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Explaining monotonic ranking functions
Proceedings of the VLDB Endowment, 2020Ranking functions are commonly used to assist in decision-making in a wide variety of applications. As the general public realizes the significant societal impacts of the widespread use of algorithms in decision-making, there has been a push towards explainability and transparency in decision processes and results, as well as demands to ...
Abraham Gale, Amélie Marian
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Rankings and Ranking Functions
Canadian Journal of Mathematics, 1981Suppose that n competitors compete in r races and in each race they are awarded placings l, 2, 3, …, n – 1, n. After the r races each competitor has a result consisting of his r placings. Let such a result be written (αj)1≦j≦r where for convenience the positive integers αj are arranged in ascending order.
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Rank Functions for Stable Diagrams
Siberian Advances in Mathematics, 2020Summary: Let \(D\) be the diagram of a sufficiently homogeneous model. For types that are realized in this model, we introduce certain rank functions and prove the following assertions: (1) If, for each type, the rank is less than \(\infty\) then the diagram is stable; (2) if the diagram \(D\) is stable then the set of non-algebraic types of rank less ...
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Construct Weak Ranking Functions for Learning Linear Ranking Function
2011Many Learning to Rank models, which apply machine learning techniques to fuse weak ranking functions and enhance ranking performances, have been proposed for web search. However, most of the existing approaches only apply the Min --- Max normalization method to construct the weak ranking functions without considering the differences among the ranking ...
Guichun Hua +4 more
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Ranks of differentiable functions
Mathematika, 1986The purpose of this paper is to define and study a natural rank function which associates to each differentiable function (say on the interval [0,1]) a countable ordinal number, which measures the complexity of its derivative. Functions with continuous derivatives have the smallest possible rank 1, a function like \(x^ 2 \sin (x^{-1})\) has rank 2, etc.
Kechris, Alexander S., Woodin, W. Hugh
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2015
The four ranking functions were introduced to T-SQL by Microsoft in 2005. Three of the functions, ROW_NUMBER, RANK, and DENSE_RANK, assign a sequential number to each row in a query's results. The fourth ranking function, NTILE, divides the rows by assigning a bucket number to the each row in the results.
Kathi Kellenberger, Clayton Groom
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The four ranking functions were introduced to T-SQL by Microsoft in 2005. Three of the functions, ROW_NUMBER, RANK, and DENSE_RANK, assign a sequential number to each row in a query's results. The fourth ranking function, NTILE, divides the rows by assigning a bucket number to the each row in the results.
Kathi Kellenberger, Clayton Groom
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Order, 2005
The authors describe the correspondence between closure operators \(\text{cl}: D \to D\) and \(\land\)-subsemilattices \(L \subseteq D\) where \(D\) is a lattice of finite height. They investigate what type of number-valued function \(D \to N\) induces a \(\land\)-subsemilattice \(L\) and, conversely, what type of function \(D \to N\) is induced by ...
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The authors describe the correspondence between closure operators \(\text{cl}: D \to D\) and \(\land\)-subsemilattices \(L \subseteq D\) where \(D\) is a lattice of finite height. They investigate what type of number-valued function \(D \to N\) induces a \(\land\)-subsemilattice \(L\) and, conversely, what type of function \(D \to N\) is induced by ...
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