Abstract. The problem of penalty-based data aggregation in generic real normed vector spaces is studied. Some existence and uniqueness results are indicated. Moreover, various properties of the aggregation functions are considered.
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* [BACKWARD INCOMPATIBILITY] #335: A fix to #314 (by design) prevented the use of the system ICU if the library had been compiled with `U_CHARSET_IS_UTF8=1`. However, this is the default setting in `libicu`>=61. From now on, in such cases the system ICU is used more eagerly, but `stri_enc_set()` issues a warning stating that the default (UTF-8) encoding cannot be changed. * [NEW FEATURE] #232: All `stri_detect_*` functions now have the `max_count` argument that allows for, e.g., stopping at first pattern occurrence. * [NEW FEATURE] #338: `stri_sub_replace()` is now an alias for `stri_sub<-()` which makes it much more easily pipable (@yutannihilation, @BastienFR). * [NEW FEATURE] #334: Added missing `icudt61b.dat` to support big-endian platforms (thanks to Dimitri John Ledkov @xnox). * [BUGFIX] #296: Out-of-the box build used to fail on CentOS 6, upgraded `./configure` to `--disable-cxx11` more eagerly at an early stage. * [BUGFIX] #341: Fixed possible buffer overflows when calling `strncpy()` from within ICU 61. * [BUGFIX] #325: Made `./configure` more portable so that it works under `/bin/dash` now. * [BUGFIX] #319: Fixed overflow in `stri_rand_shuffle()`. * [BUGFIX] #337: Empty search patters in search functions (e.g., `stri_split_regex()` and `stri_count_fixed()`) used to raise too many warnings on empty search patters.
Abstract. The problem of the piecewise linear approximation of fuzzy numbers giving outputs nearest to the inputs with respect to the Euclidean metric is discussed. The results given in Coroianu et al. (Fuzzy Sets Syst 233:26–51, 2013) for the 1-knot fuzzy numbers are generalized for arbitrary n-knot (n>=2) piecewise linear fuzzy numbers. Some results on the existence and properties of the approximation operator are proved. Then, the stability of some fuzzy number characteristics under approximation as the number of knots tends to infinity is considered. Finally, a simulation study concerning the computer implementations of arithmetic operations on fuzzy numbers is provided. Suggested concepts are illustrated by examples and algorithms ready for the practical use. This way, we throw a bridge between theory and applications as the latter ones are so desired in real-world problems.
Abstract. The problem of learning symmetric capacities (or fuzzy measures) from data is investigated toward applications in data analysis and prediction as well as decision making. Theoretical results regarding the solution minimizing the mean absolute error are exploited to develop an exact branch-refine-and-bound-type algorithm for fitting Sugeno integrals (weighted lattice polynomial functions, max-min operators) with respect to symmetric capacities. The proposed method turns out to be particularly suitable for acting on ordinal data. In addition to providing a model that can be used for the general data regression task, the results can be used, among others, to calibrate generalized h-indices to bibliometric data.
Abstract. The efficacy of different league formats in ranking teams according to their true latent strength is analysed. To this end, a new approach for estimating attacking and defensive strengths based on the Poisson regression for modelling match outcomes is proposed. Various performance metrics are estimated reflecting the agreement between latent teams' strength parameters and their final rank in the league table. The tournament designs studied here are used in the majority of European top-tier association football competitions. Based on numerical experiments, it turns out that a two-stage league format comprising of the three round-robin tournament together with an extra single round-robin is the most efficacious setting. In particular, it is the most accurate in selecting the best team as the winner of the league. Its efficacy can be enhanced by setting the number of points allocated for a win to two (instead of three that is currently in effect in association football).