A multivalued network on a complement-closed set (MCN) is a dynamical network model whose entities can take multiple state values in a totally ordered set equipped with a complement operator. Multivalued networks extend the framework of standard (binary) Boolean networks and several types of multivalued network models. In this work, we study steady states in MCN where an undirected graph, in which the entities may or may not have self-loops, encodes the dependencies in the network, and all the local functions are maximum (respectively minimum)- type. Specifically, we give a necessary and sufficient condition for the existence of steady states and provide a complete structural description of them. Additionally, we completely characterize when the steady states of MCN cannot be directly obtained from those of its binary counterpart. In doing so, we show that a Fixed Point Theorem does not hold for these systems, when they are non-binary. Moreover, this result extends to broader classes of MCN in which more general independent local functions are considered.

In this work, we provide a procedure that allows us to transform certain kinds of deterministic Boolean networks on minterm or maxterm functions into symmetric ones, so inferring that such symmetrizable networks can present only periodic points of periods 1 or 2. In particular, we deal with generalized parallel (or synchronous) dynamical systems (GPDS) over undirected graphs, i.e., discrete parallel dynamical systems over undirected graphs where some of the self-loops may not appear. We also study the class of anti-symmetric GPDS (which are non-symmetrizable), proving that their periodic orbits have period 4. In addition, we introduce a class of non-symmetrizable systems which admit periodic orbits with arbitrary large periods.

The Label Ranking (LR) problem is a well-known nonstandard supervised classification problem, the goal of which is to learn preference classifiers from data, mapping instances to rankings of the labels of the class variable. In the literature, the particular setting where the output of the LR problem is a complete ranking without ties (a.k.a. permutation) has been profusely studied, and many algorithms have been designed to solve these particular instances based on the use of specific probability distributions and aggregation methods for permutations. However, also partial orders (a.k.a. bucket orders) can be considered as output in LR problems (i.e., some labels of the class variable may be tied), but the algorithms available do not tackle this kind of ranking. We refer to this particular case of LR as the Partial Label Ranking (PLR) problem. Thus, motivated by the lack of current methods to deal with the PLR problem, we design machine learning algorithms based on instance-based and decision tree approaches to tackle the PLR problem. We evaluate our proposals on a benchmark of 15 data sets obtained by transforming multiclass instances, and analyze their performance by carrying out a standard machine learning statistical analysis procedure.

The Optimal Bucket Order Problem (OBOP) is a rank aggregation problem which consists in finding a consensus ranking (with ties) that generalizes a set of input rankings. In this paper, with the aim of solving the OBOP in an efficient and scalable way, we propose several greedy algorithms based on different sort-first and cluster-second strategies. More specifically, the sorting step is based on the Borda method, whereas in the cluster step, pairs of adjacent buckets are suitably joined. The proposed methods are experimentally compared with the state-of-the-art greedy algorithms for solving the OBOP by using a large benchmark of real-world databases. Furthermore, we provide a complete statistical analysis of the experimental study, which shows that several of the proposed algorithms outperform the current state-of-the-art greedy algorithms. We also analyze the trade-off between accuracy and execution time of the algorithms to guide the users regarding the selection of the best option for each particular case. The study carried out shows that our proposal is not only competitive in terms of accuracy with the state-of-the-art evolutionary strategy for dealing with the OBOP, but is also fast and scalable.

Annual journal rankings are usually considered a tool for the evaluation of research and researchers. Although they are an objective resource for such evaluation, they also present drawbacks: (a) the uncertainty about the definite position of a target journal in the corresponding annual ranking when selecting a journal, and (b) in spite of the nonsignificant difference in score (for instance, impact factor) between consecutive journals in the ranking, the journals are strictly ranked and eventually placed in different terciles/quartiles, which may have a significant influence in the subsequent evaluation. In this article we present several proposals to obtain an aggregated consensus ranking as an alternative/complementary tool to standardize annual rankings. To illustrate the proposed methodology we use as a case study the Journal Citation Reports, and in particular the category of Computer Science: Artificial Intelligence (CS:AI). In the context of the consensus rankings obtained by the different methods, we discuss the convenience of using one or the other procedure according to the corresponding framework. In particular, our proposals allow us to obtain consensus rankings that avoid crisp frontiers between similarly ranked journals and consider the longitudinal/temporal evolution of the journals.