Soft Methods for Handling Variability and Imprecision by Jean-Marc Bernard (auth.), Didier Dubois, M. Asunción
By Jean-Marc Bernard (auth.), Didier Dubois, M. Asunción Lubiano, Henri Prade, María Ángeles Gil, Przemysław Grzegorzewski, Olgierd Hryniewicz (eds.)
Probability concept has been the single well-founded idea of uncertainty for a very long time. It used to be considered both as a robust device for modelling random phenomena, or as a rational method of the proposal of measure of trust. over the last thirty years, in components founded round determination idea, synthetic intelligence and knowledge processing, various ways extending or orthogonal to the prevailing idea of chance and mathematical data have come to front. the typical function of these makes an attempt is to permit for softer or wider frameworks for bearing in mind the incompleteness or imprecision of knowledge. lots of those ways come right down to mixing period or fuzzy period research with probabilistic tools.
This e-book gathers contributions to the 4th overseas convention on gentle equipment in chance and records. Its objective is to provide contemporary effects illustrating such new developments that amplify the statistical and uncertainty modeling traditions, in the direction of the dealing with of incomplete or subjective info. It covers a vast scope starting from philosophical and mathematical underpinnings of latest uncertainty theories, with a tension on their effect within the region of statistics and knowledge research, to numerical equipment and purposes to environmental threat research and mechanical engineering. a distinct characteristic of this assortment is to set up a discussion among fuzzy random variables and vague chance theories.
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Additional info for Soft Methods for Handling Variability and Imprecision
Example text
But in many cases (Figure 2c), the range of possible outcomes is so wide that the threshold lies within this range, in which case it is necessary to be able to discriminate between the relative likelihoods of possible outcomes. In order to discriminate between levels of likelihood, researchers and decisionmakers in the field of environmental risks often rely on the use of unique probability distributions (PDFs). The problem of course is that, in this field, we are typically confronted with information that is incomplete/imprecise and therefore the choice of unique PDFs is arbitrary.
Fuzzy Sets and Systems, Possibility Theory and Special Topics in Systems Research, vol. VI, pp. 2831–2836. : On the notions of distance and deviation in a fuzzy structure. , Pichler, F. ) Proceedings of the 5th European Meeting on Cybernetics and Systems Research (Vienna, 1980) Progress in Cybernetics and Systems Research, vol. 8, pp. 443–447. Hemisphere Pub. : Structure pr´e-uniforme classique et structure pr´e-uniforme floue. Note de travail, ERA 639. : Fuzzy specifications and random fuzzy events considered as basic tools for statistical prediction.
Imprecision of data can be modelled by special fuzzy subsets of the set of real numbers, and statistical methods have to be generalized to fuzzy data. Another kind of fuzziness is the fuzziness of a-priori information in Bayesian inference. It is possible to apply so-called fuzzy probability distributions as a-priori distributions. The corresponding generalization of Bayes’ theorem is basic for what is called fuzzy Bayesian inference. Keywords: Bayesian inference, Bayes’ theorem, Decision analysis, Fuzzy Bayesian inference, Fuzzy data, Fuzzy information, Fuzzy intervals, Fuzzy probability distributions, Fuzzy utility, Non-precise numbers.