Soft Methods in Probability, Statistics and Data AnalysisPrzemyslaw Grzegorzewski, Olgierd Hryniewicz, Maria A. Gil Classical 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. |
Contents
| 3 | |
Toward a PerceptionBased Theory of Probabilistic | 27 |
Independence and Conditioning in a Connectivistic Fuzzy | 65 |
About Ideals on the Set of Fuzzy Measures | 76 |
Operators for Convolution of Fuzzy Measures | 84 |
Probabilities of Fuzzy Events Based on Scalar Cardinalities | 92 |
On the Variation of the fInequality of a Random Variable | 98 |
Probability of Intuitionistic Fuzzy Events | 105 |
Imprecise Calculation with the Qualitative Information | 164 |
Variants of Defining the Cardinalities of Fuzzy Sets | 178 |
Acceptance Sampling Plans by Variables for Vague Data | 197 |
Fuzzy Comparison of Frequency Distributions | 219 |
Blackwell Sufficiency and Fuzzy Eaſperiments | 236 |
Fuzzy Conjoint Analysis | 255 |
A Contribution to Stochastic Modeling of Volcanic | 274 |
Towards Fuzzy cmeans Based Microaggregation | 289 |
A New Calculus for Linguistic Prototypes in Data Analysis | 116 |
Upper Probabilities and Selectors of Random Sets | 126 |
On Multivalued Logic and Probability Theory | 134 |
Reversing the Order of Integration in Iterated Eaſpectations | 140 |
Lower Previsions for Unbounded Random Variables | 146 |
An Algorithm for Identifying Fuzzy Measures with Ordinal | 321 |
Classifiers for | 338 |
Aggregation Methods to Evaluate Multiple Protected | 355 |
On Multivariate Fuzzy Time Series Analysis and | 363 |
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Common terms and phrases
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 Dempster–Shafer 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 method MV-algebras natural language o-cut obtain operations optimal stopping paper parameters perception-based perceptions possibilistic possibility distribution possibility theory Prade Prade H preference 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