Over the last forty years there has been a growing interest to extend probability theory and statistics and to allow for more flexible modelling of imprecision, uncertainty, vagueness and ignorance. The fact that in many real-life situations data uncertainty is not only present in the form of randomness (stochastic uncertainty) but also in the form of imprecision/fuzziness is but one point underlining the need for a widening of statistical tools. Most such extensions originate in a "softening" of classical methods, allowing, in particular, to work with imprecise or vague data, considering imprecise or generalized probabilities and fuzzy events, etc. About ten years ago the idea of establishing a recurrent forum for discussing new trends in the before-mentioned context was born and resulted in the first International Conference on Soft Methods in Probability and Statistics (SMPS) that was held in Warsaw in 2002. In the following years the conference took place in Oviedo (2004), in Bristol (2006) and in Toulouse (2008). In the current edition the conference returns to Oviedo. This edited volume is a collection of papers presented at the SMPS 2010 conference held in Mieres and Oviedo. It gives a comprehensive overview of current research into the fusion of soft methods with probability and statistics.

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Prior Knowledge in the Classification of Biomedical Data.-Estimation of a Simple Genetic Algorithm Applied to a Laboratory Experiment .- A Comparison of Robust Methods for Pareto Tail Modeling in the Case of Laeken Indicators.- R Code for Hausdorff and Simplex Dispersion Orderings in the 2D Case On Some Confidence Regions to Estimate a Linear Regression.- Model for Interval Data Possibilistic Coding: Error Detection vs. Error Correction . Coherent Correction for Conditional Probability Assessments.- with RInferential Rules for Weak Graphoid.-Fast Factorization of Probability Trees and its Application to Recursive Trees Learning.- Option Pricing in Incomplete Markets Based on Partial Information.- Lorenz Curves of extrema.- Likelihood in a Possibilistic and Probabilistic Context: A Comparison.- Nonparametric Predictive Inference for Order Statistics of Future Observations.- Expected Pair-Wise Comparison of the Outcomes of a Fuzzy Random Variable.- The Behavioral Meaning of the Median Functional Classification and the Random Tukey Depth. Practical Issues.- . On Concordance Measures and Copulas with Fractal Support.- Factorisation Properties of the Strong Product etc. ...