Axiomatizations of quasi-polynomial functions on bounded chains

Two emergent properties in aggregation theory are investigated, namely horizontal maxitivity and comonotonic maxitivity (as well as their dual counterparts) which are commonly defined by means of certain functional equations. We completely describe the function classes axiomatized by each of these properties, up to weak versions of monotonicity in the cases of horizontal maxitivity and minitivity. While studying the classes axiomatized by combinations of these properties, we introduce the concept of quasi-polynomial function which appears as a natural extension of the well-established notion of polynomial function. We give further axiomatizations for this class both in terms of functional equations and natural relaxations of homogeneity and median decomposability. As noteworthy particular cases, we investigate those subclasses of quasi-term functions and quasi-weighted maximum and minimum functions, and provide characterizations accordingly

Characterizations of discrete Sugeno integrals as polynomial functions over distributive lattices

We give several characterizations of discrete Sugeno integrals over bounded distributive lattices, as particular cases of lattice polynomial functions, that is, functions which can be represented in the language of bounded lattices using variables and constants. We also consider the subclass of term functions as well as the classes of symmetric polynomial functions and weighted minimum and maximum functions, and present their characterizations, accordingly. Moreover, we discuss normal form representations of these functions

Mathematically aggregating experts' predictions of possible futures

Structured protocols offer a transparent and systematic way to elicit and combine/aggregate, probabilistic predictions from multiple experts. These judgements can be aggregated behaviourally or mathematically to derive a final group prediction. Mathematical rules (e.g., weighted linear combinations of judgments) provide an objective approach to aggregation. The quality of this aggregation can be defined in terms of accuracy, calibration and informativeness. These measures can be used to compare different aggregation approaches and help decide on which aggregation produces the “best” final prediction. When experts’ performance can be scored on similar questions ahead of time, these scores can be translated into performance-based weights, and a performance-based weighted aggregation can then be used. When this is not possible though, several other aggregation methods, informed by measurable proxies for good performance, can be formulated and compared. Here, we develop a suite of aggregation methods, informed by previous experience and the available literature. We differentially weight our experts’ estimates by measures of reasoning, engagement, openness to changing their mind, informativeness, prior knowledge, and extremity, asymmetry or granularity of estimates. Next, we investigate the relative performance of these aggregation methods using three datasets. The main goal of this research is to explore how measures of knowledge and behaviour of individuals can be leveraged to produce a better performing combined group judgment. Although the accuracy, calibration, and informativeness of the majority of methods are very similar, a couple of the aggregation methods consistently distinguish themselves as among the best or worst. Moreover, the majority of methods outperform the usual benchmarks provided by the simple average or the median of estimates

Using fuzzy numbers and OWA operators in the weighted average and its application in decision making

Se presenta un nuevo método para tratar situaciones de incertidumbre en los que se utiliza el operador OWAWA (media ponderada – media ponderada ordenada). A este operador se le denomina operador OWAWA borroso (FOWAWA). Su principal ventaja se encuentra en la posibilidad de representar la información incierta del problema mediante el uso de números borrosos los cuales permiten una mejor representación de la información ya que consideran el mínimo y el máximo resultado posible y la posibilidad de ocurrencia de los valores internos. Se estudian diferentes propiedades y casos particulares de este nuevo modelo. También se analiza la aplicabilidad de este operador y se desarrolla un ejemplo numérico sobre toma de decisiones en la selección de políticas fiscalesWe present a new approach for dealing with an uncertain environment when using the ordered weighted averaging – weighted averaging (OWAWA) operator. We call it the fuzzy OWAWA (FOWAWA) operator. The main advantage of this new aggregation operator is that it is able to represent the uncertain information with fuzzy numbers. Thus, we are able to give more complete information because we can consider the maximum and the minimum of the problem and the internal information between these two results. We study different properties and different particular cases of this approach. We also analyze the applicability of the new model and we develop a numerical example in a decision making problem about selection of fiscal policies

Systematic approach to nonlinear filtering associated with aggregation operators. Part 1. SISO-filters

There are various methods to help restore an image from noisy distortions. Each technique has its advantages and disadvantages. Selecting the appropriate method plays a major role in getting the desired image. Noise removal or noise reduction can be done on an image by linear or nonlinear filtering. The more popular linear technique is based on average (on mean) linear operators. Denoising via linear filters normally does not perform satisfactorily since both noise and edges contain high frequencies. Therefore, any practical denoising model has to be nonlinear. In this work, we introduce and analyze a new class of nonlinear SISO-filters that have their roots in aggregation operator theory. We show that a large body of non-linear filters proposed to date constitute a proper subset of aggregation filters. (C) 2017 The Authors. Published by Elsevier Ltd.This work was supported by grants the RFBR No. 17-07-00886 and by Ural State Forest Engineering's Center of Excellence in "Quantum and Classical Information Technologies for Remote Sensing Systems"

Measuring voting power in convex policy spaces

Classical power index analysis considers the individual's ability to influence the aggregated group decision by changing its own vote, where all decisions and votes are assumed to be binary. In many practical applications we have more options than either "yes" or "no". Here we generalize three important power indices to continuous convex policy spaces. This allows the analysis of a collection of economic problems like e.g. tax rates or spending that otherwise would not be covered in binary models.Comment: 31 pages, 9 table

Systematic approach to nonlinear filtering associated with aggregation operators. Part 2. Frechet MIMO-filters

Median filtering has been widely used in scalar-valued image processing as an edge preserving operation. The basic idea is that the pixel value is replaced by the median of the pixels contained in a window around it. In this work, this idea is extended onto vector-valued images. It is based on the fact that the median is also the value that minimizes the sum of distances between all grey-level pixels in the window. The Frechet median of a discrete set of vector-valued pixels in a metric space with a metric is the point minimizing the sum of metric distances to the all sample pixels. In this paper, we extend the notion of the Frechet median to the general Frechet median, which minimizes the Frechet cost function (FCF) in the form of aggregation function of metric distances, instead of the ordinary sum. Moreover, we propose use an aggregation distance instead of classical metric distance. We use generalized Frechet median for constructing new nonlinear Frechet MIMO-filters for multispectral image processing. (C) 2017 The Authors. Published by Elsevier Ltd.This work was supported by grants the RFBR No 17-07-00886, No 17-29-03369 and by Ural State Forest University Engineering's Center of Excellence in "Quantum and Classical Information Technologies for Remote Sensing Systems"

CENTURION: Incentivizing Multi-Requester Mobile Crowd Sensing

The recent proliferation of increasingly capable mobile devices has given rise to mobile crowd sensing (MCS) systems that outsource the collection of sensory data to a crowd of participating workers that carry various mobile devices. Aware of the paramount importance of effectively incentivizing participation in such systems, the research community has proposed a wide variety of incentive mechanisms. However, different from most of these existing mechanisms which assume the existence of only one data requester, we consider MCS systems with multiple data requesters, which are actually more common in practice. Specifically, our incentive mechanism is based on double auction, and is able to stimulate the participation of both data requesters and workers. In real practice, the incentive mechanism is typically not an isolated module, but interacts with the data aggregation mechanism that aggregates workers' data. For this reason, we propose CENTURION, a novel integrated framework for multi-requester MCS systems, consisting of the aforementioned incentive and data aggregation mechanism. CENTURION's incentive mechanism satisfies truthfulness, individual rationality, computational efficiency, as well as guaranteeing non-negative social welfare, and its data aggregation mechanism generates highly accurate aggregated results. The desirable properties of CENTURION are validated through both theoretical analysis and extensive simulations