## Soft Methods in Probability, Statistics and Data AnalysisClassical probability theory and mathematical statistics appear sometimes too rigid for real life problems, especially while dealing with vague data or imprecise requirements. These problems have motivated many researchers to "soften" the classical theory. Some "softening" approaches utilize concepts and techniques developed in theories such as fuzzy sets theory, rough sets, possibility theory, theory of belief functions and imprecise probabilities, etc. Since interesting mathematical models and methods have been proposed in the frameworks of various theories, this text brings together experts representing different approaches used in soft probability, statistics and data analysis. |

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### Contents

Quantitative Possibility Theory and its Probabilistic | 3 |

Toward a PerceptionBased Theory of Probabilistic | 27 |

Independence and Conditioning in a Connectivistic Fuzzy | 65 |

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algebra algorithm analysis applications approach assume attributes belief functions classical clusters concept condition conjoint analysis conjoint model consider constraint convex corresponding crisp decision decision problem defined Definition denote described Dubois and Prade example expected expected value extended lower prevision Fuzzy Logic fuzzy measures fuzzy numbers fuzzy random variable fuzzy sets fuzzy time series given imprecise probabilities inequalities information granules integral label Lemma linear mapping mathematical means membership function methods MV-algebras natural language o-cut obtain operations optimal optimal stopping paper parameters perception-based perceptions possibilistic possibility distribution possibility theory Prade Prade H probability distribution probability measure probability space probability theory problem properties proposition random set relation representation represented rough set rules sampling plan semantics Sets and Systems simulation ſº statistical stochastic subsets t-norm Theorem tuple uncertainty values vector Zadeh