New Results on the Aggregation of Norms

It is a natural question if a Cartesian product of objects produces an object of the same type. For example, it is well known that a countable Cartesian product of metrizable topological spaces is metrizable. Related to this question, Borsík and Doboš characterized those functions that allow obtaining a metric in the Cartesian product of metric spaces by means of the aggregation of the metrics of each factor space. This question was also studied for norms by Herburt and Moszyńska. This aggregation procedure can be modified in order to construct a metric or a norm on a certain set by means of a family of metrics or norms, respectively. In this paper, we characterize the functions that allow merging an arbitrary collection of (asymmetric) norms defined over a vector space into a single norm (aggregation on sets). We see that these functions are different from those that allow the construction of a norm in a Cartesian product (aggregation on products). Moreover, we study a related topological problem that was considered in the context of metric spaces by Borsík and Doboš. Concretely, we analyze under which conditions the aggregated norm is compatible with the product topology or the supremum topology in each case.

MRP-PCI: A Multiple Reference Point Based Partially Compensatory Composite Indicator for Sustainability Assessment

Assessing different types of sustainability is a complex procedure, which implies considering aspects of very different nature. One way to do this is using a system of single indicators measuring all these different aspects and aggregating them in an overall composite indicator. In line with the concepts of weak and strong sustainability, the compensability degree among the indicators allowed by the aggregation procedure is a crucial issue. There exist methods that allow for full compensability, zero compensability, or partial compensability. In most of them, the compensation degree is established in a global way, that is, it is the same for all the indicators. In this paper, we develop the Multiple Reference Point Partially Compensatory Indicator (MRP-PCI), where a different compensation index can be established for each indicator. The resulting method can be applied to any system of indicators, and successfully considers the compensation indices given. Some examples and comparisons are used to illustrate its behavior.

Investigation of the motion of magnetic nanoparticles in microfluidics with a micro domain model

In this paper the magnetic nanoparticle (MNP) dynamics in a microfluidic device is investigated in the presence of an external magnetic field. The nanoparticles are used for enzyme-substrate reaction measurements, where the enzyme is immobilized to the surface of the nanoparticles. During the measurements the microreactors, called microchambers are filled up with the MNPs where the distribution of the nanoparticles significantly influences the results of the further reaction measurements. In this paper the procedure of the nanoparticle aggregation is investigated numerically in the microchamber in a micro domain simulation space. First the acting forces on the MNPs are examined from the different phenomena. An in-house numerical model is presented where the dynamics of several MNPs are simulated in the micro-size domain. This model is also embedded in the open source CFD software OpenFOAM. The theoretical calculations and the simulations show that the particle-particle interaction due to magnetization plays an important role during the aggregation procedure. The particles in the magnetic field cluster over the time into chains, which phenomenon is in good agreement with the literature. A theoretical model of the chain dynamics is also established, which is compared to the simulation results. The presented micro domain model was later used to improve an Eulerian-Eulerian based two-phase CFD model and solver, which is able to model the complete MNP aggregation procedure in the magnetic field in macroscopic domains.

Aggregation of L-Probabilistic Quasi-Uniformities

The problem of aggregating fuzzy structures, mainly fuzzy binary relations, has deserved a lot of attention in the last years due to its application in several fields. Here, we face the problem of studying which properties must satisfy a function in order to merge an arbitrary family of (bases of) L-probabilistic quasi-uniformities into a single one. These fuzzy structures are special filters of fuzzy binary relations. Hence we first make a complete study of functions between partially-ordered sets that preserve some special sets, such as filters. Afterwards, a complete characterization of those functions aggregating bases of L-probabilistic quasi-uniformities is obtained. In particular, attention is paid to the case L={0,1}, which allows one to obtain results for functions which aggregate crisp quasi-uniformities. Moreover, we provide some examples of our results including one showing that Lowen’s functor ι which transforms a probabilistic quasi-uniformity into a crisp quasi-uniformity can be constructed using this aggregation procedure.

Enhancing the Wisdom of the Crowd With Cognitive-Process Diversity: The Benefits of Aggregating Intuitive and Analytical Judgments

Drawing on dual-process theory, we suggest that the benefits that arise from combining several quantitative individual judgments will be heightened when these judgments are based on different cognitive processes. We tested this hypothesis in three experimental studies in which participants provided estimates for the dates of different historical events (Study 1, N = 152), made probabilistic forecasts for the outcomes of soccer games (Study 2, N = 98), and estimated the weight of individuals on the basis of a photograph (Study 3, N = 3,695). For each of these tasks, participants were prompted to make judgments relying on an analytical process, on their intuition, or (in a control condition) on no specific instructions. Across all three studies, our results show that an aggregation of intuitive and analytical judgments provides more accurate estimates than any other aggregation procedure and that this advantage increases with the number of aggregated judgments.

The Influence of the Zonation Effect on a System of Hierarchical Functional Regions

Background: Hierarchical functional regions (FRs) can be calculated using data on interactions between basic spatial units (BSUs) and a hierarchical aggregation procedure. However, the results depend on the selected system of initial BSUs. In spatial sciences, this is known as the zonation effect, which is one of the effects of the Modifiable Areal Unit Problem (MAUP). Objectives: In this paper, we analyse the influence of the zonation effect on a system of hierarchical functional regions. Methods/Approach: We compared two systems of hierarchical functional regions of Slovenia modelled by the Intramax aggregation procedure using the inter-municipal labour commuting flows for the same year, but for two different initial sets of municipalities. Besides, we have introduced a new measure to compare systems of hierarchical FRs. Results: The results show that the zonation effect has an influence on hierarchical functional regions. The clustering comparison measure suggested here is a metric measure, which is appropriate for comparing hierarchical FRs. Conclusions: The zonation effect has influence on hierarchical FRs. The clustering comparison measure suggested in this paper is easy to interpret, but it should be adjusted for the number of clusterings

Use of Constraints in the Hierarchical Aggregation Procedure Intramax

Background:Intramax is a hierarchical aggregation procedure for dealing with the multi-level specification problem and with the association issue of data set reduction, but it was used as a functional regionalization procedure many times in the past.Objectives:In this paper, we analyse the simultaneous use of three different constraints in the original Intramax procedure, i.e. the contiguity constraint, the higher-inner-flows constraint, and the lower-variation-of-inner-flows constraint.Methods/Approach:The inclusion of constraints in the Intramax procedure was analysed by a programme code developed in Mathematica 10.3 by the processing time, by intra-regional shares of total flows, by self-containment indexes, by numbers of singleton and isolated regions, by the number of aggregation steps where a combination of constraints was applied, by the number of searching steps until the combination of constraints was satisfied, and by surveying the results geographically.Results:The use of the contiguity constraint is important only at the beginning of the aggregation procedure; the higher-inner-flows constraint gives singleton regions, and the lower-variation constraint forces the biggest employment centre as an isolated region up to a relatively high level of aggregation.Conclusions:The original Intramax procedure (without the inclusion of any constraint) gives the most balanced and operative hierarchical sets of functional regions without any singletons or isolated regions.

Avoiding predicate whiplash: social choice theory and linguistic vagueness

Vagueness effects predictably occur in predicates that aggregate judgments along a number of different criteria. With these types of aggregations, small changes along one of the criteria can lead to big changes in the outcome of the aggregation procedure. Vagueness results from avoiding this ‘whiplash’ effect.