Defining Bonferroni means over lattices

In the face of mass amounts of information and the need for transparent and fair decision processes, aggregation functions are essential for summarizing data and providing overall evaluations. Although families such as weighted means and medians have been well studied, there are still applications for which no existing aggregation functions can capture the decision makers\u27 preferences. Furthermore, extensions of aggregation functions to lattices are often needed to model operations on L-fuzzy sets, interval-valued and intuitionistic fuzzy sets. In such cases, the aggregation properties need to be considered in light of the lattice structure, as otherwise counterintuitive or unreliable behavior may result. The Bonferroni mean has recently received attention in the fuzzy sets and decision making community as it is able to model useful notions such as mandatory requirements. Here, we consider its associated penalty function to extend the generalized Bonferroni mean to lattices. We show that different notions of dissimilarity on lattices can lead to alternative expressions.<br /

A penalty-based aggregation operator for non-convex intervals

In the case of real-valued inputs, averaging aggregation functions have been studied extensively with results arising in fields including probability and statistics, fuzzy decision-making, and various sciences. Although much of the behavior of aggregation functions when combining standard fuzzy membership values is well established, extensions to interval-valued fuzzy sets, hesitant fuzzy sets, and other new domains pose a number of difficulties. The aggregation of non-convex or discontinuous intervals is usually approached in line with the extension principle, i.e. by aggregating all real-valued input vectors lying within the interval boundaries and taking the union as the final output. Although this is consistent with the aggregation of convex interval inputs, in the non-convex case such operators are not idempotent and may result in outputs which do not faithfully summarize or represent the set of inputs. After giving an overview of the treatment of non-convex intervals and their associated interpretations, we propose a novel extension of the arithmetic mean based on penalty functions that provides a representative output and satisfies idempotency

Scalable Learning In Distributed Robot Teams

Mobile robots are already in use for mapping, agriculture, entertainment, and the delivery of goods and people. As robotic systems continue to become more affordable, large numbers of mobile robots may be deployed concurrently to accomplish tasks faster and more efficiently. Practical deployments of very large teams will require scalable algorithms to enable the distributed cooperation of autonomous agents. This thesis focuses on the three main algorithmic obstacles to the scalability of robot teams: coordination, control, and communication. To address these challenges, we design graph-based abstractions that allow us to apply Graph Neural Networks (GNNs).First, a team of robots must continually coordinate to divide up mission requirements among all agents. We focus on the case studies of exploration and coverage to develop a spatial GNN controller that can coordinate a team of dozens of agents as they visit thousands of landmarks. A routing problem of this size is intractable for existing optimization-based approaches. Second, a robot in a team must be able to execute the trajectory that will accomplish its given sub-task. In large teams with high densities of robots, planning and execution of safe, collision-free trajectories requires the joint optimization over all agent trajectories, which may be impractical in large teams. We present two approaches to scalable control: a) a controller for flocking that uses delayed communication formalized via a GNN; and b) an inverse optimal planning method that learns from real air traffic data. Third, robot teams may need to operate in harsh environments without existing communication infrastructure, requiring the formation of ad-hoc networks to exchange information. Many algorithms for control of multi-robot teams operate under the assumption that low-latency, global state information necessary to coordinate agent actions can readily be disseminated among the team. Our approach leverages GNNs to control the connectivity within the ad-hoc network and to provide the data distribution infrastructure necessary for countless multi-robot algorithms. Finally, this thesis develops a framework for distributed learning to be used when centralized information is unavailable during training. Our approach allows robots to train controllers independently and then share their experiences by composing multiple models represented in a Reproducing Kernel Hilbert Space

Fuzzy Sets, Fuzzy Logic and Their Applications 2020

The present book contains the 24 total articles accepted and published in the Special Issue “Fuzzy Sets, Fuzzy Logic and Their Applications, 2020” of the MDPI Mathematics journal, which covers a wide range of topics connected to the theory and applications of fuzzy sets and systems of fuzzy logic and their extensions/generalizations. These topics include, among others, elements from fuzzy graphs; fuzzy numbers; fuzzy equations; fuzzy linear spaces; intuitionistic fuzzy sets; soft sets; type-2 fuzzy sets, bipolar fuzzy sets, plithogenic sets, fuzzy decision making, fuzzy governance, fuzzy models in mathematics of finance, a philosophical treatise on the connection of the scientific reasoning with fuzzy logic, etc. It is hoped that the book will be interesting and useful for those working in the area of fuzzy sets, fuzzy systems and fuzzy logic, as well as for those with the proper mathematical background and willing to become familiar with recent advances in fuzzy mathematics, which has become prevalent in almost all sectors of the human life and activity

On the intelligent management of sepsis in the intensive care unit

The management of the Intensive Care Unit (ICU) in a hospital has its own, very specific requirements that involve, amongst others, issues of risk-adjusted mortality and average length of stay; nurse turnover and communication with physicians; technical quality of care; the ability to meet patient's family needs; and avoid medical error due rapidly changing circumstances and work overload. In the end, good ICU management should lead to an improvement in patient outcomes. Decision making at the ICU environment is a real-time challenge that works according to very tight guidelines, which relate to often complex and sensitive research ethics issues. Clinicians in this context must act upon as much available information as possible, and could therefore, in general, benefit from at least partially automated computer-based decision support based on qualitative and quantitative information. Those taking executive decisions at ICUs will require methods that are not only reliable, but also, and this is a key issue, readily interpretable. Otherwise, any decision tool, regardless its sophistication and accuracy, risks being rendered useless. This thesis addresses this through the design and development of computer based decision making tools to assist clinicians at the ICU. It focuses on one of the main problems that they must face: the management of the Sepsis pathology. Sepsis is one of the main causes of death for non-coronary ICU patients. Its mortality rate can reach almost up to one out of two patients for septic shock, its most acute manifestation. It is a transversal condition affecting people of all ages. Surprisingly, its definition has only been standardized two decades ago as a systemic inflammatory response syndrome with confirmed infection. The research reported in this document deals with the problem of Sepsis data analysis in general and, more specifically, with the problem of survival prediction for patients affected with Severe Sepsis. The tools at the core of the investigated data analysis procedures stem from the fields of multivariate and algebraic statistics, algebraic geometry, machine learning and computational intelligence. Beyond data analysis itself, the current thesis makes contributions from a clinical point of view, as it provides substantial evidence to the debate about the impact of the preadmission use of statin drugs in the ICU outcome. It also sheds light into the dependence between Septic Shock and Multi Organic Dysfunction Syndrome. Moreover, it defines a latent set of Sepsis descriptors to be used as prognostic factors for the prediction of mortality and achieves an improvement on predictive capability over indicators currently in use.La gestió d'una Unitat de Cures Intensives (UCI) hospitalària presenta uns requisits força específics incloent, entre altres, la disminució de la taxa de mortalitat, la durada de l'ingrès, la rotació d'infermeres i la comunicació entre metges amb al finalitad de donar una atenció de qualitat atenent als requisits tant dels malalts com dels familiars. També és força important controlar i minimitzar els error mèdics deguts a canvis sobtats i a la presa ràpida de deicisions assistencials. Al cap i a la fi, la bona gestió de la UCI hauria de resultar en una reducció de la mortalitat i durada d'estada. La presa de decisions en un entorn de crítics suposa un repte de presa de decisions en temps real d'acord a unes guies clíniques molt restrictives i que, pel que fa a la recerca, poden resultar en problemes ètics força sensibles i complexos. Per tant, el personal sanitari que ha de prendre decisions sobre la gestió de malalts crítics no només requereix eines de suport a la decisió que siguin fiables sinó que, a més a més, han de ser interpretables. Altrament qualsevol eina de decisió que no presenti aquests trets no és considerarà d'utilitat clínica. Aquesta tesi doctoral adreça aquests requisits mitjançant el desenvolupament d'eines de suport a la decisió per als intensivistes i es focalitza en un dels principals problemes als que s'han denfrontar: el maneig del malalt sèptic. La Sèpsia és una de les principals causes de mortalitats a les UCIS no-coronàries i la seva taxa de mortalitat pot arribar fins a la meitat dels malalts amb xoc sèptic, la seva manifestació més severa. La Sèpsia és un síndrome transversal, que afecta a persones de totes les edats. Sorprenentment, la seva definició ha estat estandaritzada, fa només vint anys, com a la resposta inflamatòria sistèmica a una infecció corfimada. La recerca presentada en aquest document fa referència a l'anàlisi de dades de la Sèpsia en general i, de forma més específica, al problema de la predicció de la supervivència de malalts afectats amb Sèpsia Greu. Les eines i mètodes que formen la clau de bòveda d'aquest treball provenen de diversos camps com l'estadística multivariant i algebràica, geometria algebraica, aprenentatge automàtic i inteligència computacional. Més enllà de l'anàlisi per-se, aquesta tesi també presenta una contribució des de el punt de vista clínic atès que presenta evidència substancial en el debat sobre l'impacte de l'administració d'estatines previ a l'ingrès a la UCI en els malalts sèptics. També s'aclareix la forta dependència entre el xoc sèptic i el Síndrome de Disfunció Multiorgànica. Finalment, també es defineix un conjunt de descriptors latents de la Sèpsia com a factors de pronòstic per a la predicció de la mortalitat, que millora sobre els mètodes actualment més utilitzats en la UCI