Abstract. The constrained ordered weighted averaging (OWA) aggregation problem arises when we aim to maximize or minimize a convex combination of order statistics under linear inequality constraints that act on the variables with respect to their original sources. The standalone approach to optimizing the OWA under constraints is to consider all permutations of the inputs, which becomes quickly infeasible when there are more than a few variables, however in certain cases we can take advantage of the relationships amongst the constraints and the corresponding solution structures. For example, we can consider a land-use allocation satisfaction problem with an auxiliary aim of balancing land-types, whereby the response curves for each species are non-decreasing with respect to the land-types. This results in comonotone constraints, which allow us to drastically reduce the complexity of the problem.
In this paper, we show that if we have an arbitrary number of constraints that are comonotone (i.e., they share the same ordering permutation of the coefficients), then the optimal solution occurs for decreasing components of the solution. After investigating the form of the solution in some special cases and providing theoretical results that shed light on the form of the solution, we detail practical approaches to solving and give real-world examples.
Abstract. The Sugeno integral is a function particularly suited to the aggregation of ordinal inputs. Defined with respect to a fuzzy measure, its ability to account for complementary and redundant relationships between variables brings much potential to the field of biomedicine, where it is common for measurements and patient information to be expressed qualitatively. However, practical applications require well-developed methods for identifying the Sugeno integral's parameters, and this task is not easily expressed using the standard optimisation approaches. Here we formulate the objective function as the difference of two convex functions, which enables the use of specialised numerical methods. Such techniques are compared with other global optimisation frameworks through a number of numerical experiments.
Abstract. The property of monotonicity, which requires a function to preserve a given order, has been considered the standard in the aggregation of real numbers for decades. In this paper, we argue that, for the case of multidimensional data, an order-based definition of monotonicity is far too restrictive. We propose several meaningful alternatives to this property not involving the preservation of a given order by returning to its early origins stemming from the field of calculus. Numerous aggregation methods for multidimensional data commonly used by practitioners are studied within our new framework.
Abstract. In the field of information fusion, the problem of data aggregation has been formalized as an order-preserving process that builds upon the property of monotonicity. However, fields such as computational statistics, data analysis and geometry, usually emphasize the role of equivariances to various geometrical transformations in aggregation processes. Admittedly, if we consider a unidimensional data fusion task, both requirements are often compatible with each other. Nevertheless, in this paper we show that, in the multidimensional setting, the only idempotent functions that are monotone and orthogonal equivariant are the over-simplistic weighted centroids. Even more, this result still holds after replacing monotonicity and orthogonal equivariance by the weaker property of orthomonotonicity. This implies that the aforementioned approaches to the aggregation of multidimensional data are irreconcilable, and that, if a weighted centroid is to be avoided, we must choose between monotonicity and a desirable behaviour with regard to orthogonal transformations.
Abstract. On the grounds of the revealed, mutual resemblance between the behaviour of users of Stack Exchange and the dynamics of the citations accumulation process in the scientific community, we tackled an outwardly intractable problem of assessing the impact of introducing "negative" citations.
Although the most frequent reason to cite a paper is to highlight the connection between the two publications, researchers sometimes mention an earlier work to cast a negative light. While computing citation-based scores, for instance the h-index, information about the reason why a paper was mentioned is neglected. Therefore it can be questioned whether these indices describe scientific achievements accurately.
In this contribution we shed insight into the problem of "negative" citations, analysing data from Stack Exchange and, to draw more universal conclusions, we derive an approximation of citations scores. Here we show that the quantified influence of introducing negative citations is of lesser importance and that they could be used as an indicator of where attention of scientific community is allocated.
stringibrings significant improvements in the way substring extraction tasks are performed.
Change-log since v1.3.1:
* [NEW FEATURE] #30: New function `stri_sub_all()` - a version of `stri_sub()` accepting list `from`/`to`/`length` arguments for extracting multiple substrings from each string in a character vector. * [NEW FEATURE] #30: New function `stri_sub_all<-()` (and its `%<%`-friendly version, `stri_sub_replace_all()`) - for replacing multiple substrings with corresponding replacement strings. * [NEW FEATURE] In `stri_sub_replace()`, `value` parameter has a new alias, `replacement`. * [NEW FEATURE] New convenience functions based on `stri_remove_empty()`: `stri_omit_empty_na()`, `stri_remove_empty_na()`, `stri_omit_empty()`, and also `stri_remove_na()`, `stri_omit_na()`. * [BUGFIX] #343: `stri_trans_char()` did not yield correct results for overlapping pattern and replacement strings. * [WARNFIX] #205: `configure.ac` is now included in the source bundle.
agopis now available on CRAN. See below for more details.
0.2-2 /2019-03-05/ * [IMPORTANT CHANGE] All functions dealing with binary relations now are named like `rel_*`. Moreover, `de_transitive()` has been renamed `rel_reduction_hasse()`. * [IMPORTANT CHANGE] The definition of `owa()`, `owmax()`, and `owmin()` is now consistent with that of (Grabisch et al., 2009), i.e., uses nondecreasing vectors, and not nonincreasing ones. * [NEW FUNCTIONS] `rel_closure_reflexive()`, `rel_reduction_reflexive()`, `rel_is_symmetric()`, `rel_closure_symmetric()`, `rel_is_irreflexive()`, `rel_is_asymmetric()`, `rel_is_antisymmetric()`, `rel_is_cyclic()`, etc., modify given adjacency matrices representing binary relations over finite sets. * [NEW FUNCTIONS] some predefined fuzzy logic connectives have been added, e.g. ,`tnorm_minimum()`, `tnorm_drastic()`, `tnorm_product()`, `tnorm_lukasiewicz()`, `tnorm_fodor()`, `tconorm_minimum()`, `tconorm_drastic()`, `tconorm_product()`, `tconorm_lukasiewicz()`, `tconorm_fodor()`, `fnegation_classic()`, `fnegation_minimal()`, `fnegation_maximal()`, `fnegation_yager()`, `fimplication_minimal()`, `fimplication_maximal()`, `fimplication_kleene()`, `fimplication_lukasiewicz()`, `fimplication_reichenbach()`, `fimplication_fodor()`, `fimplication_goguen()`, `fimplication_goedel()`, `fimplication_rescher()`, `fimplication_weber()`, `fimplication_yager()`. * [NEW FUNCTION] `check_comonotonicity()` determines if two vectors are comonotonic. * [NEW FUNCTIONS] `pord_spread()`, `pord_spreadsym()`, `pord_nd()` - example preorders on sets of vectors. * [NEW FEATURE] `plot_producer()` gained a new argument: `a`. * [BUGFIX] `rel_closure_transitive()` - a resulting matrix was not necessarily transitive. * [BUGFIX] `prepare_arg_numeric_sorted` (internal, C++) did not sort some vectors. * [BUGFIX] All built-in aggregation functions now throw an error on empty vectors. * [INFO] The package no longer depends on the `Matrix` package. The `igraph` package is only suggested. * [INFO] Most of the functions are now implemented in C++.