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This research monograph presents basic foundational aspects for a theory of statistics with fuzzy data, together with a set of practical applications. Fuzzy data are modeled as observations from random fuzzy sets. Theories of fuzzy logic and of random closed sets are used as basic ingredients in building statistical concepts and procedures in the context of imprecise data, including coarse data analysis. The monograph also aims at motivating statisticians to look at fuzzy statistics to enlarge the domain of applicability of statistics in general. HUNG T. NGUYEN is a professor of Mathematical Sciences at New Mexico State University, USA. BERLIN WU is a professor of Mathematical Sciences at National Chengchi University, Taipei, Taiwan.
Mathematics --- Statistical physics --- Engineering sciences. Technology --- Artificial intelligence. Robotics. Simulation. Graphics --- statistische kwaliteitscontrole --- analyse (wiskunde) --- industriële statistieken --- toegepaste wiskunde --- KI (kunstmatige intelligentie) --- ingenieurswetenschappen --- robots
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Healthcare is an information problem needing an information solution using modern information technology. The traditional medical record does not suffice, but the new technologies of internet services do. Existing technologies can be combined for new methods of gathering and analyzing health information, via monitors using sensors and clusters using supercomputers. There is a way of utilizing both the electronic medical record of the past and the personalized genomic medicine of the future. It gathers information from all the sources affecting personal health: from the bodies of individuals to the societies of populations. Healthcare Infrastructure: Health Systems for Individuals and Populations describes the new healthcare infrastructure that will gather these personal health records from every individual and correlate each longitudinal record across whole populations. This book explains the problems of personal medicine and public health, then the solutions possible with information technology. Health determinants for individuals and populations are examined at length, along with present and future technologies to measure these. Computer analysis will produce clusters of persons with similar measurements of health status. The analysis discovers which persons have which outcomes and the management uses this knowledge to provide efficient healthcare. The new healthcare infrastructure will provide information for decision makers to effectively manage provider care and manage patient expectations. Thus, this book will be a key reference for all professionals working within the management of health, from informatician to healthcare executive, health information technologist to computer scientist, and physician to patient.
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In many practical situations, we are interested in statistics characterizing a population of objects: e.g. in the mean height of people from a certain area. Most algorithms for estimating such statistics assume that the sample values are exact. In practice, sample values come from measurements, and measurements are never absolutely accurate. Sometimes, we know the exact probability distribution of the measurement inaccuracy, but often, we only know the upper bound on this inaccuracy. In this case, we have interval uncertainty: e.g. if the measured value is 1.0, and inaccuracy is bounded by 0.1, then the actual (unknown) value of the quantity can be anywhere between 1.0 - 0.1 = 0.9 and 1.0 + 0.1 = 1.1. In other cases, the values are expert estimates, and we only have fuzzy information about the estimation inaccuracy. This book shows how to compute statistics under such interval and fuzzy uncertainty. The resulting methods are applied to computer science (optimal scheduling of different processors), to information technology (maintaining privacy), to computer engineering (design of computer chips), and to data processing in geosciences, radar imaging, and structural mechanics.
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