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Fuzzy rank functions

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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Explaining monotonic ranking functions

Proceedings of the VLDB Endowment, 2020
Ranking 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, 1981
Suppose 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, 2020
Summary: 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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