Ebook: Soft Methodology and Random Information Systems

The analysis of experimental data resulting from some underlying random process is a fundamental part of most scientific research. Probability Theory and Statistics have been developed as flexible tools for this analyis, and have been applied successfully in various fields such as Biology, Economics, Engineering, Medicine or Psychology. However, traditional techniques in Probability and Statistics were devised to model only a singe source of uncertainty, namely randomness. In many real-life problems randomness arises in conjunction with other sources, making the development of additional "softening" approaches essential. This book is a collection of papers presented at the 2nd International Conference on Soft Methods in Probability and Statistics (SMPS’2004) held in Oviedo, providing a comprehensive overview of the innovative new research taking place within this emerging field.

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The analysis of experimental data resulting from some underlying random process is a fundamental part of most scientific research. Probability Theory and Statistics have been developed as flexible tools for this analyis, and have been applied successfully in various fields such as Biology, Economics, Engineering, Medicine or Psychology. However, traditional techniques in Probability and Statistics were devised to model only a singe source of uncertainty, namely randomness. In many real-life problems randomness arises in conjunction with other sources, making the development of additional "softening" approaches essential. This book is a collection of papers presented at the 2nd International Conference on Soft Methods in Probability and Statistics (SMPS’2004) held in Oviedo, providing a comprehensive overview of the innovative new research taking place within this emerging field.

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The analysis of experimental data resulting from some underlying random process is a fundamental part of most scientific research. Probability Theory and Statistics have been developed as flexible tools for this analyis, and have been applied successfully in various fields such as Biology, Economics, Engineering, Medicine or Psychology. However, traditional techniques in Probability and Statistics were devised to model only a singe source of uncertainty, namely randomness. In many real-life problems randomness arises in conjunction with other sources, making the development of additional "softening" approaches essential. This book is a collection of papers presented at the 2nd International Conference on Soft Methods in Probability and Statistics (SMPS’2004) held in Oviedo, providing a comprehensive overview of the innovative new research taking place within this emerging field.

Content:
Front Matter....Pages I-XIV
Front Matter....Pages 1-1
Probability Theory Should be Based on Fuzzy Logic — A Contentious View....Pages 3-7
Applications of Random Sets in Image Analysis. How to Average a Cat and a Dog?....Pages 8-18
Choquet Weak Convergence of Capacity Functionals of Random Sets....Pages 19-31
On Limit Theorems for Random Fuzzy Sets Including Large Deviation Principles....Pages 32-44
Fuzzy Probability and Some Applications....Pages 45-49
Development and Maintenance of Fuzzy Models in Financial Applications....Pages 50-66
Information Mining with Semi-Supervised Learning....Pages 67-74
Front Matter....Pages 75-75
On Statistical Inference with Random Sets....Pages 77-84
Interval-Valued and Fuzzy-Valued Random Variables: From Computing Sample Variances to Computing Sample Covariances....Pages 85-92
Estimability and Admissibility in Sample Survey Models....Pages 93-100
Riesz Space and Fuzzy Upcrossing Theorems....Pages 101-108
On Laws of Large Numbers for Exchangeable Random Sets....Pages 109-116
Strong and Weak Laws of Large Numbers for Weighted Sums of Fuzzy Set-Valued Random Variables....Pages 117-124
Assessing Debris Flow Hazard by Credal Nets....Pages 125-132
A Possibilistic Interpretation of the Expectation of a Fuzzy Random Variable....Pages 133-140
Learning and Optimal Control of Imprecise Markov Decision Processes by Dynamic Programming Using the Imprecise Dirichlet Model....Pages 141-148
Representation of Incomplete Probabilistic Information....Pages 149-156
Range of Entropy for Credal Sets....Pages 157-164
From the Comparison of Ordered Lists to the Construction of Copulas....Pages 165-172
Compatibility of Three Bivariate Quasi-Copulas: Applications to Copulas....Pages 173-180
Front Matter....Pages 75-75
Transformations of Copulas and Quasi-Copulas....Pages 181-188
Compositions of Copulas and Quasi-Copulas....Pages 189-196
Countably Generated Idempotent Copulas....Pages 197-204
1-Lipschitz Aggregation Operators, Quasi-Copulas and Copulas with Given Diagonals....Pages 205-211
Fuzzy Integrals on Partially-Known Measures....Pages 212-218
Characterization of the Scalar (s,t)-Additive Measures: Probabilities and Cardinalities....Pages 219-226
On Pareto Process....Pages 227-234
Representation of Probabilities on IFS Events....Pages 235-242
Possibilistic Time Processes and Soft Decoding....Pages 243-248
Some Aspects of Conditioning in a Coherent Setting....Pages 249-256
The Role of Zero Probabilities in Dealing with Zero Frequency Problems....Pages 257-264
Generalized Stochastic Transitivity for Probabilistic Relations....Pages 265-272
The Concept of Non-Symmetric Independence on MV-Algebras....Pages 273-280
On Limit Theorems for t-Normed Sums of Fuzzy Random Variables....Pages 281-288
Front Matter....Pages 289-296
Phi-Residual Based on Minimum Phi-Divergence Estimator in the Loglinear Model of Symmetry....Pages 297-297
Bahadur Efficiency of the Phi-Divergence Test Statistic....Pages 299-306
On the Selection of the Best Rukhin’s Statistic for the Uniform Exact Distribution Function....Pages 307-314
Front Matter....Pages 315-322
On Testing Hypotheses with Divergence Statistics....Pages 323-330
Testing a Hierarchical Sequence of Linear Logistic Models....Pages 331-338
Inference for Three-Dimensional Contingency Tables Based on ?1—Divergences....Pages 297-297
Information Theory and Complexity in Probability and Statistics....Pages 339-346
Measures of Multivariate Association and Dependence....Pages 347-354
Phi-Divergence Test Statistics for Trends in Binary Responses....Pages 355-362
A Random Set View on Fuzzy Random Variables....Pages 363-370
Fuzzy Information and Bayesian Statistics....Pages 371-378
Fuzzy Probability Distributions....Pages 379-386
Least Squares Estimation in Linear Regression Models with Vague Concepts....Pages 387-391
Testing One-Sided Hypotheses for the Expectation of Fuzzy Random Variables....Pages 392-398
The Zonoid Hull of a Multivariate Probability Distribution and its Trimmed Regions....Pages 399-406
Bootstrap Approach to Test the Linear Independence between Interval-valued Random Sets....Pages 407-414
Detection of Influential Case in Fuzzy Regression....Pages 415-422
A Proposal of Fuzzy Correspondence Analysis Based on Flexible Data Mining Techniques....Pages 423-430
Uncertainty Measures and Hierarchical Classification....Pages 431-438
Informational Paradigm and Entropy-Based Dynamic Clustering in a Complete Fuzzy Framework....Pages 439-446
Induction of Fuzzy Prototypes with Feature Selection....Pages 447-454
A Comparison of Variable Selection Methods with the Main Focus on Orthogonalization....Pages 455-462
Introduction to ANOVA with Fuzzy Random Variables....Pages 463-470
Front Matter....Pages 471-478
Distribution-Free Tests for Vague Data....Pages 479-486
Measures of Association for Fuzzy Ordered Categorical Data....Pages 487-494
Designing Confidence Intervals under Vague Information....Pages 297-297
Decision Rules for Bayesian Hierarchical Classifier with Fuzzy Factor....Pages 495-502
On the Notion of Statistical Fuzzy Entropy....Pages 503-510
Fuzzy Extended Lexicographic Goal Programming....Pages 511-518
Fuzzy Dynamic Programming with Stochastic Systems under Various Aggregation Operators: Solvability and Perceived Meaning....Pages 519-526
Interval Fuzzy Bayesian Inference....Pages 527-534
Inconsistency Analysis for Statistical Tests of Hypotheses....Pages 535-542
An Alternative Criterion to Likelihood for Parameter Estimation Accounting for a Prior Information on a Nuisance Parameter....Pages 543-550
Application of Regime-Switching Models of Time Series with Cubic Spline Transition Function....Pages 551-558
Identification of the Structure of Linear and Non-Linear Time Series Models, Using Nonparametric Local Linear Kernel Estimation....Pages 559-566
Neural Networks and Statistics: A Review of the Literature....Pages 567-574
Multivariate Imputation of Qualitative Missing Data Using Bayesian Networks....Pages 575-580
Towards the Optimal Feature Selection in High-Dimensional....Pages 581-588
Addition Nodes in Influence Diagrams with Fuzzy-Valued Utilities and Variables....Pages 589-596
Front Matter....Pages 597-604
About Weakly Locally Compact Spaces....Pages 605-612
Hadamard and Jensen Inequalities for s-Convex Fuzzy Processes....Pages 613-620
Front Matter....Pages 621-627
Continuity for s-Convex Fuzzy Processes....Pages 629-629
Fuzzy Solution for Approximating Constrained Optimal PWM Using Quantum Evolutionary Algorithm....Pages 631-637
A Note on Chaos in Fuzzy Systems....Pages 638-644
Front Matter....Pages 645-652
The Double Quadratic Uncertainty Measures and Their Economic Applications....Pages 629-629
Medium-Term Electricity Generation with Fuzzy Availability....Pages 653-660
Enhanced QTL Linkage Analysis with DNA Pooling by Means of Monte Carlo EM....Pages 661-668
Characterization of Human Electrocardiogram by Analyses of Phase Attributes....Pages 669-674
A Posteriori Inference of Model Parameters in a Geophysical Inverse Problem Using GA....Pages 675-675
Bayesian Networks to Improve the Balanced Scorecard....Pages 677-684
Classification Techniques, Sample Size and Predictive Performance: A Comparative Analysis Based on a Spanish Case....Pages 685-692
Metapopulations Study with Subjective Biotic and Abiotic Processes....Pages 693-700
Fuzzy Rule Generation in Hydrological Modelling....Pages 701-708
Robust Change Detection Method Using Akaike Information Criterion for Signal Segmentation....Pages 709-716
Erratum to: The Role of Zero Probabilities in Dealing with Zero Frequency Problems....Pages 717-724
Erratum to: On Limit Theorems for t-Normed Sums of Fuzzy Random Variables....Pages 725-732
Erratum to: Distribution-Free Tests for Vague Data....Pages 733-740
Erratum to: Fuzzy Solution for Approximating Constrained Optimal PWM Using Quantum Evolutionary Algorithm....Pages 741-748
Back Matter....Pages 749-756
....Pages 761-761