Partially Ordered Preferences in Decision Trees: Computing Strategies with Imprecision in Probabilities

Partially ordered preferences generally lead to choices that do not abide by standard expected utility guidelines; often such preferences are revealed by imprecision in probability values. We investigate five criteria for strategy selection in decision trees with imprecision in probabilities: “extensive” Γ-maximin and Γ-maximax, interval dominance, maximality and E-admissibility. We present algorithms that generate strategies for all these criteria; our main contribution is an algorithm for Eadmissibility that runs over admissible strategies rather than over sets of probability distributions.

Location-routing problems of semi-obnoxious facilities: approaches and decision support

A presente tese resulta de um trabalho de investigação cujo objectivo se centrou no problema de localização-distribuição (PLD) que pretende abordar, de forma integrada, duas actividades logísticas intimamente relacionadas: a localização de equipamentos e a distribuição de produtos. O PLD, nomeadamente a sua modelação matemática, tem sido estudado na literatura, dando origem a diversas aproximações que resultam de diferentes cenários reais. Importa portanto agrupar as diferentes variantes por forma a facilitar e potenciar a sua investigação. Após fazer uma revisão e propor uma taxonomia dos modelos de localização-distribuição, este trabalho foca-se na resolução de alguns modelos considerados como mais representativos. É feita assim a análise de dois dos PLDs mais básicos (os problema capacitados com procura nos nós e nos arcos), sendo apresentadas, para ambos, propostas de resolução. Posteriormente, é abordada a localização-distribuição de serviços semiobnóxios. Este tipo de serviços, ainda que seja necessário e indispensável para o público em geral, dada a sua natureza, exerce um efeito desagradável sobre as comunidades contíguas. Assim, aos critérios tipicamente utilizados na tomada de decisão sobre a localização destes serviços (habitualmente a minimização de custo) é necessário adicionar preocupações que reflectem a manutenção da qualidade de vida das regiões que sofrem o impacto do resultado da referida decisão. A abordagem da localização-distribuição de serviços semiobnóxios requer portanto uma análise multi-objectivo. Esta análise pode ser feita com recurso a dois métodos distintos: não interactivos e interactivos. Ambos são abordados nesta tese, com novas propostas, sendo o método interactivo proposto aplicável a outros problemas de programação inteira mista multi-objectivo. Por último, é desenvolvida uma ferramenta de apoio à decisão para os problemas abordados nesta tese, sendo apresentada a metodologia adoptada e as suas principais funcionalidades. A ferramenta desenvolvida tem grandes preocupações com a interface de utilizador, visto ser direccionada para decisores que tipicamente não têm conhecimentos sobre os modelos matemáticos subjacentes a este tipo de problemas.

Energy of line graphs

The energy of a graph is equal to the sum of the absolute values of its eigenvalues. The energy of a matrix is equal to the sum of its singular values. We establish relations between the energy of the line graph of a graph G and the energies associated with the Laplacian and signless Laplacian matrices of G. © 2010 Elsevier B.V. All rights reserved.

Efficient edge domination in regular graphs

An induced matching of a graph G is a matching having no two edges joined by an edge. An efficient edge dominating set of G is an induced matching M such that every other edge of G is adjacent to some edge in M. We relate maximum induced matchings and efficient edge dominating sets, showing that efficient edge dominating sets are maximum induced matchings, and that maximum induced matchings on regular graphs with efficient edge dominating sets are efficient edge dominating sets. A necessary condition for the existence of efficient edge dominating sets in terms of spectra of graphs is established. We also prove that, for arbitrary fixed p ≥ 3, deciding on the existence of efficient edge dominating sets on p-regular graphs is NP-complete. © 2008 Elsevier B.V. All rights reserved.

Spectral characterization of families of split graphs

An upper bound for the sum of the squares of the entries of the principal eigenvector corresponding to a vertex subset inducing a k-regular subgraph is introduced and applied to the determination of an upper bound on the order of such induced subgraphs. Furthermore, for some connected graphs we establish a lower bound for the sum of squares of the entries of the principal eigenvector corresponding to the vertices of an independent set. Moreover, a spectral characterization of families of split graphs, involving its index and the entries of the principal eigenvector corresponding to the vertices of the maximum independent set is given. In particular, the complete split graph case is highlighted.

The Jordan canonical form for a class of weighted directed graphs

Recently, Cardon and Tuckfield (2011) [1] have described the Jordan canonical form for a class of zero-one matrices, in terms of its associated directed graph. In this paper, we generalize this result to describe the Jordan canonical form of a weighted adjacency matrix A in terms of its weighted directed graph.

Spectra of graphs obtained by a generalization of the join graph operation

Taking a Fiedler’s result on the spectrum of a matrix formed from two symmetric matrices as a motivation, a more general result is deduced and applied to the determination of adjacency and Laplacian spectra of graphs obtained by a generalized join graph operation on families of graphs (regular in the case of adjacency spectra and arbitrary in the case of Laplacian spectra). Some additional consequences are explored, namely regarding the largest eigenvalue and algebraic connectivity.

A recursive construction of the regular exceptional graphs with least eigenvalue -2

In spectral graph theory a graph with least eigenvalue 2 is exceptional if it is connected, has least eigenvalue greater than or equal to 2, and it is not a generalized line graph. A ðk; tÞ-regular set S of a graph is a vertex subset, inducing a k-regular subgraph such that every vertex not in S has t neighbors in S. We present a recursive construction of all regular exceptional graphs as successive extensions by regular sets.

Determination of (0,2)-regular sets in graphs and applications

In this paper, relevant results about the determination of (k,t)-regular sets, using the main eigenvalues of a graph, are reviewed and some results about the determination of (0,2)-regular sets are introduced. An algorithm for that purpose is also described. As an illustration, this algorithm is applied to the determination of maximum matchings in arbitrary graphs.

A critical narrative analysis of shared decision-making in acute, inpatient mental health care

Shared decision-making (SDM) is a high priority in healthcare policy and is complementary to the recovery philosophy in mental health care. This agenda has been operationalised within the Values-Based Practice (VBP) framework, which offers a theoretical and practical model to promote democratic interprofessional approaches to decision-making. However, these are limited by a lack of recognition of the implications of power implicit within the mental health system. This study considers issues of power within the context of decision-making and examines to what extent decisions about patients? care on acute in-patient wards are perceived to be shared. Focus groups were conducted with 46 mental health professionals, service users, and carers. The data were analysed using the framework of critical narrative analysis (CNA). The findings of the study suggested each group constructed different identity positions, which placed them as inside or outside of the decision-making process. This reflected their view of themselves as best placed to influence a decision on behalf of the service user. In conclusion, the discourse of VBP and SDM needs to take account of how differentials of power and the positioning of speakers affect the context in which decisions take place.

Hydroinformatics based decision.making integrating modelling, sampling and profiling: the Ria Formosa case

A Waste Water monitoring program aiming to help decision making is presented. The program includes traditional and inboard sensor sampling, hydrodynamic and water quality modeling and a GIS based database to help the decision making of manager authorities. The focus is in the quality of waters receiving discharges from Waste Water Treatment Plants. Data was used to feed model simulations and produce hydrodynamic, effluent dispersion and ecological results. The system was then used to run different scenarios of discharge flow, concentration and location. The results enable to access the current water quality state of the lagoon and are being used as a decision making tool by the waste water managers in the evaluation phase of the treatment plant project to decide the location and the level of treatment of the discharge.

Biopolymers - facts and statistics

The IfBB – Institute for Bioplastics and Biocomposites is a research institute within the Hochschule Hannover, University of Applied Sciences and Arts, which was established in 2011 to respond to the growing need for expert knowledge in the area of bioplastics. With its practice-oriented research and its collaboration with industrial partners, the IfBB is able to shore up the market for bioplastics and, in addition, foster unbiased public awareness and understanding of the topic. As an independent research-led expert institution for bioplastics, the IfBB is willing to share its expertise, research findings and data with any interested party via the Internet, online and offline publications or at fairs and conferences. In carrying on these efforts, substantial information regarding market trends, processes and resource needs for bioplastics is being presented here in a concise format, in addition to the more detailed and comprehensive publication and “Engineering Biopolymers”1. One of our main concerns is to furnish a more rational basis for discussing bioplastics and use fact-based arguments in the public discourse. Furthermore, “Biopolymers – facts and statistics” aims to provide specific, qualified answers easily and quickly for decision-makers in particular from public administration and the industrial sector. Therefore, this publication is made up like a set of rules and standards and largely foregoes textual detail. It offers extensive market-relevant and technical facts presented in graphs and charts, which means that the information is much easier to grasp. The reader can expect comparative market figures for various materials, regions, applications, process routes, agricultural land use or resource consumption, production capacities, geographic distribution, etc.

Application of Decision-Making Theory to the Regulation of Muscular Work Rate During Self-Paced Competitive Endurance Activity.

Successful participation in competitive endurance activities requires continual regulation of muscular work rate in order to maximise physiological performance capacities, meaning that individuals must make numerous decisions with regards to the muscular work rate selected at any point in time. Decisions relating to the setting of appropriate goals and the overall strategic approach to be utilised are made prior to the commencement of an event, whereas tactical decisions are made during the event itself. This review examines current theories of decision-making in an attempt to explain the manner in which regulation of muscular work is achieved during athletic activity. We describe rational and heuristic theories, and relate these to current models of regulatory processes during self-paced exercise in an attempt to explain observations made in both laboratory and competitive environments. Additionally, we use rational and heuristic theories in an attempt to explain the influence of the presence of direct competitors on the quality of the decisions made during these activities. We hypothesise that although both rational and heuristic models can plausibly explain many observed behaviours in competitive endurance activities, the complexity of the environment in which such activities occur would imply that effective rational decision-making is unlikely. However, at present, many proposed models of the regulatory process share similarities with rational models. We suggest enhanced understanding of the decision-making process during self-paced activities is crucial in order to improve the ability to understand regulation of performance and performance outcomes during athletic activity.