Ebook: Soft Methods for Integrated Uncertainty Modelling

This edited volume is the proceedings of the 2006 International Conference on Soft Methods in Probability and Statistics (SMPS 2006) hosted by the Artificial Intelligence Group at the University of Bristol, between 5-7 September 2006. This is the third of a series of biennial conferences organized in 2002 by the Systems Research Institute from the Polish Academy of Sciences in Warsaw, and in 2004 by the Department of Statistics and Operational Research at the University of Oviedo in Spain. These conferences provide a forum for discussion and research into the fusion of soft methods with probability and statistics, with the ultimate goal of integrated uncertainty modelling in complex systems involving human factors. In addition to probabilistic factors such as measurement error and other random effects, the modelling process often requires us to make qualitative and subject judgments that cannot easily be translated into precise probability values. Such judgments give rise to a number of different types of uncertainty including; fuzziness if they are based on linguistic information; epistemic uncertainty when their reliability is in question; ignorance when they are insufficient to identify or restrict key modelling parameters; imprecision when parameters and probability distributions can only be estimated within certain bounds. Statistical theory has not traditionally been concerned with modelling uncertainty arising in this manner but soft methods, a range of powerful techniques developed within AI, attempt to address those problems where the encoding of subjective information is unavoidable. These are mathematically sound uncertainty modelling methodologies which are complementary to conventional statistics and probability theory. Therefore, a more realistic modelling process providing decision makers with an accurate reflection of the true current state of our knowledge (and ignorance) requires an integrated framework incorporating both probability theory, statistics and soft methods. This fusion motivates innovative research at the interface between computer science (AI), mathematics and systems engineering.

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This edited volume is the proceedings of the 2006 International Conference on Soft Methods in Probability and Statistics (SMPS 2006) hosted by the Artificial Intelligence Group at the University of Bristol, between 5-7 September 2006. This is the third of a series of biennial conferences organized in 2002 by the Systems Research Institute from the Polish Academy of Sciences in Warsaw, and in 2004 by the Department of Statistics and Operational Research at the University of Oviedo in Spain. These conferences provide a forum for discussion and research into the fusion of soft methods with probability and statistics, with the ultimate goal of integrated uncertainty modelling in complex systems involving human factors. In addition to probabilistic factors such as measurement error and other random effects, the modelling process often requires us to make qualitative and subject judgments that cannot easily be translated into precise probability values. Such judgments give rise to a number of different types of uncertainty including; fuzziness if they are based on linguistic information; epistemic uncertainty when their reliability is in question; ignorance when they are insufficient to identify or restrict key modelling parameters; imprecision when parameters and probability distributions can only be estimated within certain bounds. Statistical theory has not traditionally been concerned with modelling uncertainty arising in this manner but soft methods, a range of powerful techniques developed within AI, attempt to address those problems where the encoding of subjective information is unavoidable. These are mathematically sound uncertainty modelling methodologies which are complementary to conventional statistics and probability theory. Therefore, a more realistic modelling process providing decision makers with an accurate reflection of the true current state of our knowledge (and ignorance) requires an integrated framework incorporating both probability theory, statistics and soft methods. This fusion motivates innovative research at the interface between computer science (AI), mathematics and systems engineering.

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This edited volume is the proceedings of the 2006 International Conference on Soft Methods in Probability and Statistics (SMPS 2006) hosted by the Artificial Intelligence Group at the University of Bristol, between 5-7 September 2006. This is the third of a series of biennial conferences organized in 2002 by the Systems Research Institute from the Polish Academy of Sciences in Warsaw, and in 2004 by the Department of Statistics and Operational Research at the University of Oviedo in Spain. These conferences provide a forum for discussion and research into the fusion of soft methods with probability and statistics, with the ultimate goal of integrated uncertainty modelling in complex systems involving human factors. In addition to probabilistic factors such as measurement error and other random effects, the modelling process often requires us to make qualitative and subject judgments that cannot easily be translated into precise probability values. Such judgments give rise to a number of different types of uncertainty including; fuzziness if they are based on linguistic information; epistemic uncertainty when their reliability is in question; ignorance when they are insufficient to identify or restrict key modelling parameters; imprecision when parameters and probability distributions can only be estimated within certain bounds. Statistical theory has not traditionally been concerned with modelling uncertainty arising in this manner but soft methods, a range of powerful techniques developed within AI, attempt to address those problems where the encoding of subjective information is unavoidable. These are mathematically sound uncertainty modelling methodologies which are complementary to conventional statistics and probability theory. Therefore, a more realistic modelling process providing decision makers with an accurate reflection of the true current state of our knowledge (and ignorance) requires an integrated framework incorporating both probability theory, statistics and soft methods. This fusion motivates innovative research at the interface between computer science (AI), mathematics and systems engineering.

Content:
Front Matter....Pages I-X
Front Matter....Pages I-X
Generalized Theory of Uncertainty (GTU) – Principal Concepts and Ideas....Pages 3-4
Reasoning with Vague Probability Assessments....Pages 5-6
Soft Methods in Earth Systems Engineering....Pages 7-10
Statistical Data Processing under Interval Uncertainty: Algorithms and Computational Complexity....Pages 11-26
Front Matter....Pages I-X
On Testing Fuzzy Independence....Pages 29-36
Variance Decomposition of Fuzzy Random Variables....Pages 37-44
Fuzzy Histograms and Density Estimation....Pages 45-52
Graded Stochastic Dominance as a Tool for Ranking the Elements of a Poset....Pages 53-60
On Neyman-Pearson Lemma for Crisp, Random and Fuzzy Hypotheses....Pages 61-69
Fuzzy Probability Distributions Induced by Fuzzy Random Vectors....Pages 71-78
On the Identifiability of TSK Additive Fuzzy Rule-Based Models....Pages 79-86
An Asymptotic Test for Symmetry of Random Variables Based on Fuzzy Tools....Pages 87-94
Exploratory Analysis of Random Variables Based on Fuzzifications....Pages 95-102
A Method to Simulate Fuzzy Random Variables....Pages 103-110
Friedman’s Test for Ambiguous and Missing Data....Pages 111-118
Front Matter....Pages I-X
Measure-Free Martingales with Application to Classical Martingales....Pages 121-128
A Note on Random Upper Semicontinuous Functions....Pages 129-135
Optional Sampling Theorem and Representation of Set-Valued Amart....Pages 137-143
On a Choquet Theorem for Random Upper Semicontinuous Functions....Pages 145-151
A General Law of Large Numbers, with Applications....Pages 153-160
Front Matter....Pages I-X
Fuzzy Production Planning Model for Automobile Seat Assembling....Pages 163-171
Optimal Selection of Proportional Bounding Quantifiers in Linguistic Data Summarization....Pages 173-181
A Linguistic Quantifier Based Aggregation for a Human Consistent Summarization of Time Series....Pages 183-190
Efficient Evaluation of Similarity Quantified Expressions in the Temporal Domain....Pages 191-198
Front Matter....Pages I-X
Conditional Lower Previsions for Unbounded Random Quantities....Pages 201-209
Extreme Lower Probabilities....Pages 211-221
Equivalence Between Bayesian and Credal Nets on an Updating Problem....Pages 223-230
Varying Parameter in Classification Based on Imprecise Probabilities....Pages 231-239
Comparing Proportions Data with Few Successes....Pages 241-248
A Unified View of Some Representations of Imprecise Probabilities....Pages 249-257
Front Matter....Pages I-X
Estimating an Uncertain Probability Density....Pages 261-265
Theory of Evidence with Imperfect Information....Pages 267-274
Conditional IF-probability....Pages 275-283
On Two Ways for the Probability Theory on IF-sets....Pages 285-290
A Stratification of Possibilistic Partial Explanations....Pages 291-298
Finite Discrete Time Markov Chains with Interval Probabilities....Pages 299-306
Evidence and Compositionality....Pages 307-315
High Level Fuzzy Labels for Vague Concepts....Pages 317-324
Front Matter....Pages I-X
Possibilistic Channels for DNA Word Design....Pages 327-335
Transformation of Possibility Functions in a Climate Model of Intermediate Complexity....Pages 337-345
Front Matter....Pages I-X
Fuzzy Logic for Stochastic Modeling....Pages 347-355
A CUSUM Control Chart for Fuzzy Quality Data....Pages 357-364
A Fuzzy Synset-Based Hidden Markov Model for Automatic Text Segmentation....Pages 365-372
Applying Fuzzy Measures for Considering Interaction Effects in Fine Root Dispersal Models....Pages 373-381
Scoring Feature Subsets for Separation Power in Supervised Bayes Classification....Pages 383-391
Interval Random Variables and Their Application in Queueing Systems with Long–Tailed Service Times....Pages 393-403
Online Learning for Fuzzy Bayesian Prediction....Pages 405-412
Back Matter....Pages 413-413

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This edited volume is the proceedings of the 2006 International Conference on Soft Methods in Probability and Statistics (SMPS 2006) hosted by the Artificial Intelligence Group at the University of Bristol, between 5-7 September 2006. This is the third of a series of biennial conferences organized in 2002 by the Systems Research Institute from the Polish Academy of Sciences in Warsaw, and in 2004 by the Department of Statistics and Operational Research at the University of Oviedo in Spain. These conferences provide a forum for discussion and research into the fusion of soft methods with probability and statistics, with the ultimate goal of integrated uncertainty modelling in complex systems involving human factors. In addition to probabilistic factors such as measurement error and other random effects, the modelling process often requires us to make qualitative and subject judgments that cannot easily be translated into precise probability values. Such judgments give rise to a number of different types of uncertainty including; fuzziness if they are based on linguistic information; epistemic uncertainty when their reliability is in question; ignorance when they are insufficient to identify or restrict key modelling parameters; imprecision when parameters and probability distributions can only be estimated within certain bounds. Statistical theory has not traditionally been concerned with modelling uncertainty arising in this manner but soft methods, a range of powerful techniques developed within AI, attempt to address those problems where the encoding of subjective information is unavoidable. These are mathematically sound uncertainty modelling methodologies which are complementary to conventional statistics and probability theory. Therefore, a more realistic modelling process providing decision makers with an accurate reflection of the true current state of our knowledge (and ignorance) requires an integrated framework incorporating both probability theory, statistics and soft methods. This fusion motivates innovative research at the interface between computer science (AI), mathematics and systems engineering.

Content:
Front Matter....Pages I-X
Front Matter....Pages I-X
Generalized Theory of Uncertainty (GTU) – Principal Concepts and Ideas....Pages 3-4
Reasoning with Vague Probability Assessments....Pages 5-6
Soft Methods in Earth Systems Engineering....Pages 7-10
Statistical Data Processing under Interval Uncertainty: Algorithms and Computational Complexity....Pages 11-26
Front Matter....Pages I-X
On Testing Fuzzy Independence....Pages 29-36
Variance Decomposition of Fuzzy Random Variables....Pages 37-44
Fuzzy Histograms and Density Estimation....Pages 45-52
Graded Stochastic Dominance as a Tool for Ranking the Elements of a Poset....Pages 53-60
On Neyman-Pearson Lemma for Crisp, Random and Fuzzy Hypotheses....Pages 61-69
Fuzzy Probability Distributions Induced by Fuzzy Random Vectors....Pages 71-78
On the Identifiability of TSK Additive Fuzzy Rule-Based Models....Pages 79-86
An Asymptotic Test for Symmetry of Random Variables Based on Fuzzy Tools....Pages 87-94
Exploratory Analysis of Random Variables Based on Fuzzifications....Pages 95-102
A Method to Simulate Fuzzy Random Variables....Pages 103-110
Friedman’s Test for Ambiguous and Missing Data....Pages 111-118
Front Matter....Pages I-X
Measure-Free Martingales with Application to Classical Martingales....Pages 121-128
A Note on Random Upper Semicontinuous Functions....Pages 129-135
Optional Sampling Theorem and Representation of Set-Valued Amart....Pages 137-143
On a Choquet Theorem for Random Upper Semicontinuous Functions....Pages 145-151
A General Law of Large Numbers, with Applications....Pages 153-160
Front Matter....Pages I-X
Fuzzy Production Planning Model for Automobile Seat Assembling....Pages 163-171
Optimal Selection of Proportional Bounding Quantifiers in Linguistic Data Summarization....Pages 173-181
A Linguistic Quantifier Based Aggregation for a Human Consistent Summarization of Time Series....Pages 183-190
Efficient Evaluation of Similarity Quantified Expressions in the Temporal Domain....Pages 191-198
Front Matter....Pages I-X
Conditional Lower Previsions for Unbounded Random Quantities....Pages 201-209
Extreme Lower Probabilities....Pages 211-221
Equivalence Between Bayesian and Credal Nets on an Updating Problem....Pages 223-230
Varying Parameter in Classification Based on Imprecise Probabilities....Pages 231-239
Comparing Proportions Data with Few Successes....Pages 241-248
A Unified View of Some Representations of Imprecise Probabilities....Pages 249-257
Front Matter....Pages I-X
Estimating an Uncertain Probability Density....Pages 261-265
Theory of Evidence with Imperfect Information....Pages 267-274
Conditional IF-probability....Pages 275-283
On Two Ways for the Probability Theory on IF-sets....Pages 285-290
A Stratification of Possibilistic Partial Explanations....Pages 291-298
Finite Discrete Time Markov Chains with Interval Probabilities....Pages 299-306
Evidence and Compositionality....Pages 307-315
High Level Fuzzy Labels for Vague Concepts....Pages 317-324
Front Matter....Pages I-X
Possibilistic Channels for DNA Word Design....Pages 327-335
Transformation of Possibility Functions in a Climate Model of Intermediate Complexity....Pages 337-345
Front Matter....Pages I-X
Fuzzy Logic for Stochastic Modeling....Pages 347-355
A CUSUM Control Chart for Fuzzy Quality Data....Pages 357-364
A Fuzzy Synset-Based Hidden Markov Model for Automatic Text Segmentation....Pages 365-372
Applying Fuzzy Measures for Considering Interaction Effects in Fine Root Dispersal Models....Pages 373-381
Scoring Feature Subsets for Separation Power in Supervised Bayes Classification....Pages 383-391
Interval Random Variables and Their Application in Queueing Systems with Long–Tailed Service Times....Pages 393-403
Online Learning for Fuzzy Bayesian Prediction....Pages 405-412
Back Matter....Pages 413-413
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