This work extends our research on fuzzy relational Galois connections, previously established in the context of complete Heyting algebras, to the broader framework of arbitrary residuated lattices. In this context, we study the properties of fuzzy closure relations and fuzzy closure systems, and the relationship with fuzzy relational Galois connections. The main result of the paper is the generalization of the necessary and sufficient conditions for the existence of a right adjoint for a fuzzy relation linking a fuzzy transitive directed graph to an unstructured set.

A stagewise graph has distinct edge types that represent the different stages. Two nodes can be connected by an edge of the current stage only if an edge of the preceding one is already connecting them. Stagewise graphs can represent many kinds of interactions. For example, a jobseeker-vacancy interaction can be labeled by the subsequent edge typesclick,apply,job interview, and, finally,hired. Also, biological and medical interactions, such as infection processes or administration of drugs, often occur in stages. In this work, we formalize link prediction problems on such graphs as ‘stagewise link prediction’. Though relevant and rapidly gaining attention, these types of problems are to date highly underexplored. We identify and address arising difficulties, such as competition in stagewise networks. We explore an activation function for stagewise modelling and an evaluation strategy that satisfies the stagewise constraints. We confirm our insights through a set of experiments on both well-chosen simulated data sets and real data related to job recommendation and synthetic biology.

In this paper, we study non-uniform elementary cellular automata on the infinite grid in the context of number conservation. These automata operate in a one-dimensional setting, where individual cells can employ distinct Wolfram rules for updating their states. The result is an exhaustive characterization of such number-conserving cellular automata. Until now, such a characterization was known only for finite grids, for which research hypotheses could be derived on the basis of computer experiments. It turns out that when considering number conservation for non-uniform cellular automata, the infinite grid cannot be treated as a limiting case of finite grids, i.e., there are number-conserving non-uniform cellular automata on the infinite grid that have no analogous counterpart on finite grids.

In this paper, we represent (moving) point configurations along a curved directed line qualitatively by means of a system of relational symbols based on two distance descriptors: one representing distance along the curved directed line and the other representing signed orthogonal distance to the curved directed line. The curved directed line represents the direction of the movement of interest. For instance, it could be straight as in the case of driving along a highway or could be curved as in the case of an intersection or a roundabout. Inspired by the Point Calculus, the order between the points on the curved directed line is described by means of a small set of binary relations (<,=,>) acting upon the distance descriptors. We call this representation the Point-Descriptor-Precedence-Static (PDPS) representation at a time point and Point-Descriptor-Precedence-Dynamic (PDPD) representation during a time interval. To illustrate how the proposed approach can be used to represent and analyse curved movements, some basic micro-analysis traffic examples are studied. Finally, we discuss some extensions of our work to highlight the practical benefits of PDP in identifying motion patterns that could be useful in GIS, autonomous vehicles, sports analytics, and gait analysis.

Comparison and similarity measurement have been a key topic in computer vision for a long time. There is, indeed, an extensive list of algorithms and measures for image or subimage comparison. The superiority or inferiority of different measures is hard to scrutinize, especially considering the dimensionality of their parameter space and their many different configurations. In this work, we focus on the comparison of binary images, and study different variations of Baddeley’s Delta Metric, a popular metric for such images. We study the possible parameterizations of the metric, stressing the numerical and behavioural impact of different settings. Specifically, we consider the parameter settings proposed by the original author, as well as the substitution of distance transformations by regularized distance transformations, as recently presented by Brunet and Sills. We take a qualitative perspective on the effects of the settings, and also perform quantitative experiments on separability of datasets for boundary evaluation.

There is an increased interest in the application of information technology to advance nutritional research. In nutrition science, a graph database enables the creation of multilateral logic relationships throughout the database, which can be used to electronically store, visualize, and scale the outputs of nutritional research. It provides a knowledge structure to standardize nutritional research outputs, which is both human- and machine-readable in a Resource Description Framework format. However, the development of various specific graph databases may cause difficulties for data integration and decrease human-readability. In this article, we propose an approach to develop a graph database according to the Data, Information, Knowledge, and Wisdom or “DIKW” pyramid for nutritional epidemiologic data. Then, authoritative ontologies are suggested to construct the nodes and edges of the graph database to facilitate data integration. Finally, the findability and re-usability of the knowledge in the graph database are showcased using the SPARQL and SQWRL query languages.

The study of conditions, under which the existence of an “absolute” best winner can be assured, is a hot topic in the field of social choice. Unanimity is an evident example of a condition under which the winner is obvious. However, many more properties weaker than unanimity have been analysed in literature: the presence of a Condorcet winner, strong stochastic transitivity, the presence of a candidate that Borda dominates all other candidates, etc. Unfortunately, one could easily find a prominent ranking rule, for which the outcome does not agree with these relaxed conditions. In this study, we aim to identify a condition weaker than unanimity, but under which the social outcome is still obvious. This condition, defined as the conjunction of three properties already studied by the present authors and hereinafter referred to as acclamation, will be proven to be a meeting point for the most prominent ranking rules in social choice theory, and will be used for introducing an intuitively appealing ranking rule.

The accuracy of old maps can hold interesting historical information, and is therefore studied using distortion analysis methods. These methods start from a set of ground control points that are identified both on the old map and on a modern reference map or globe, and conclude with techniques that compute and visualise distortion. Such techniques have advanced over the years, but leave room for improvement, as the current ones result in approximate values and a coarse spatial resolution. We propose a more elegant and more accurate way to compute distortion of old maps by translating the technique of differential distortion analysis, used in map projection theory, to the setting where an old map and a reference map are directly compared. This enables the application of various useful distortion metrics to the study of old maps, such as the area scale factor, the maximum angular distortion and the Tissot indicatrices. As such a technique is always embedded in a full distortion analysis method we start by putting forward an optimal analysis method for a general-purpose study, which then serves as the foundation for the development of our technique. Thereto, we discuss the structure of distortion analysis methods and the various options available for every step of the process, including the different settings in which the old map can be compared to its modern counterpart, the techniques that can be used to interpolate between both, and the techniques available to compute and visualise the distortion. We conclude by applying our general-purpose method, including the differential distortion analysis technique, to an example map also used in other literature.

The notion of extensionality, introduced by Höhle and Blanchard, and the notion of compatibility, as coined by Bělohlávek, of a fuzzy relation with respect to a fuzzy equality are trivially equivalent. Here, this compatibility property is dissected into left and right compatibility, mimicking the original twofold definition of extensionality, and studied in detail in the context of arbitrary fuzzy relations. Relying on the notions of left and right traces of a fuzzy relation, it is shown that compatibility can be characterized in terms of inclusions, shedding another light on the matter.

The spatio-temporal dynamics of cellular automata (CAs) has attracted the attention of researchers from different fields, mainly mathematics, computer science and engineering, as a consequence of both the intriguing spatio-temporal patterns that these dynamical systems evolve and the fact that they enable the modelling of complex natural phenomena. Yet, to this day, there are only a few studies that focus on the automated classification of cellular automata on the basis of the space-time diagrams they evolve. Here, we present an innovative approach to classify CAs according to Wolfram's classification scheme in an automated way by relying on texture descriptors that capture the nature of the evolved space-time diagrams. More specifically, we propose the use of one of two well-known texture descriptors, namely Local Binary Pattern Variance and Fourier descriptors, to generate features grasping the diagrams' nature, followed by nearest neighbor classification. The performance of this approach is assessed through a cross-validation and by analysing the percentage of pre-classified rules that is required to arrive at an acceptable success rate. The experiments involve the family of elementary CAs and four families of totalistic CAs with neighborhood radii ranging from one to three, and a state space consisting of up to three states. The results show the potential of our proposal with success rates varying between 65% and 98% depending on the size of the training set, which ranges from 10% to 90% of the rules in the CA family at stake. For totalistic CAs, this training set should be classified manually to start the process of automated classification.

Abstract A large‐scale study was set up aiming at the clarification of the influence of demographic and musical background on the semantic description of music. Our model for rating high‐level music qualities distinguishes between affective/emotive, structural and kinaesthetic descriptors. The focus was on the understanding of the most important attributes of music in view of the development of efficient search and retrieval systems. We emphasized who the users of such systems are and how they describe their favorite music. Particular interest went to inter‐subjective similarities among listeners. The results from our study suggest that gender, age, musical expertise, active musicianship, broadness of taste and familiarity with the music have an influence on the semantic description of music.

Forest‐management decision‐support systems are largely monolithic structures. Spatial details are left out during the optimization process and are elaborated during the operational planning. This might produce misleading results and plans that are impossible to implement. In this paper, a forest‐management spatial decision‐support systems is presented, in which spatial formulation needed for wildlife models is included during the optimization process. To this end, a multiple‐objective genetic algorithm is combined with a geographical information system. An online spatial evaluation of the objective functions is made possible. This is illustrated by a pilot study in Kirkhill forest, Aberdeen.

This special issue encompasses eight papers devoted to recent developments in the field of preference modeling.The issue originates from presentations at the EUROFUSE Workshop on Preference Modeling and Applications (EUROFUSE 2001) that was held in Granada, Spain, April 25-27, 2001.These eight original contributions have been revised thoroughly and expanded to become the articles currently presented in this issue.Preference modeling is a fundamental step in solving problems in various fields such as economics, medical diagnosis, information retrieval, decision theory, etc.Most of these problems take place in a complex environment where uncertain and imprecise knowledge and possibly vague preferences have to be considered.To face such complexity, preference modeling requires the use of specific techniques and concepts that allow the available information to be represented appropriately.As is well known, the fuzzy approach has led to considerable advances in preference modeling, mainly because the use of fuzzy techniques increases the reliability and flexibility of decision models.The present issue includes different proposals of fuzzy preference modeling in several application fields.The first group of articles is focused on the study of different aspects of preference modeling in Multicriteria Decision Making

Although ranking (ordinal classification/regression) based on criteria is related closely to classification based on attributes, the development of methods for learning a ranking on the basis of data is lagging far behind that for learning a classification. Most of the work being done focuses on maintaining monotonicity (sometimes even only on the training set). We argue that in doing so, an essential aspect is mostly disregarded, namely, the importance of the role of the decision maker who decides about the acceptability of the generated rule base. Certainly, in ranking problems, there are more factors besides accuracy that play an important role. In this article, we turn to the field of multicriteria decision aid (MCDA) in order to cope with the aforementioned problems. We show that by a proper definition of the notion of partial dominance, it is possible to avoid the counter-intuitive outcomes of classification algorithms when applied to ranking problems. We focus on tree-based approaches and explain how the tree expansion can be guided by the principle of partial dominance preservation, and how the resulting rule base can be graphically represented and further refined. © 2003 Wiley Periodicals, Inc.