Information Processing and Management of Uncertainty in Knowledge-Based Systems: 19th International Conference, IPMU 2022, Milan, Italy, July 11–15, ... in Computer and Information Science)

This two-volume set (CCIS 1601-1602) constitutes the proceedings of the 19th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2021, held in Milan, Italy, in July 2022. The 124 papers were carefully reviewed and selected from 188 submissions. The papers are organized in topical sections as follows: aggregation theory beyond the unit interval; formal concept analysis and uncertainty; fuzzy implication functions; fuzzy mathematical analysis and its applications; generalized sets and operators; information fusion techniques based on aggregation functions, pre-aggregation functions, and their generalizations; interval uncertainty; knowledge acquisition, representation and reasoning; logical structures of opposition and logical syllogisms; mathematical fuzzy logics; theoretical and applied aspects of imprecise probabilities; data science and machine learning; decision making modeling and applications; e-health; fuzzy methods in data mining and knowledge discovery; soft computing and artificia intelligence techniques in image processing; soft methods in statistics and data analysis; uncertainty, heterogeneity, reliability and explainability in AI; weak and cautious supervised learning. Preface Organization Contents – Part II Contents – Part I Data Science and Machine Learning Nonlinear Weighted Independent Component Analysis 1 Introduction 2 Related Work 3 Weighted Independence Index 3.1 Introducing wii Index 4 WICA Algorithm 5 Nonlinear Mixing 6 Measuring the Quality of Obtained Results 6.1 Optimal Transport Spearman Measure 6.2 Discussion on OTS Properties 7 Experiments 7.1 Qualitative Results 7.2 Quantitative Results 8 Conclusions References Statistical Models for Partial Orders Based on Data Depth and Formal Concept Analysis 1 Introduction 2 Motivation and Related Work 3 Formal Concept Analysis, Data Depth and Unimodality 4 Formal Context Defined by All Partial Orders 5 Specifying Unimodal Distributions of Partial Orders 6 Simulation 7 Conclusion References BEUD: Bifold-Encoder Uni-Decoder Based Network for Anomaly Detection 1 Introduction 2 Related Work and Background 3 Dataset 4 BEUD: Bifold-Encoder Uni-Decoder Network 4.1 Reconstruction Error as the Anomaly Score 4.2 Training Classifier for the Output Encoding Returned by the Encoder of BEUD 5 Experimental Results 5.1 Using Reconstruction Error as Anomaly Score 5.2 Training Classifier for the Output Encoding Returned by the Encoder of BEUD 6 Discussions and Conclusion References Prescriptive Analytics for Optimization of FMCG Delivery Plans*-6pt 1 Introduction 2 Related Works 3 Solution Overview 4 Experiments 4.1 Experimental Setup 4.2 Data 4.3 Experimental Results of Profitability Optimization 5 Summary References A Multilevel Clustering Method for Risky Areas in the Context of Avalanche Danger Management 1 Introduction 2 Multilevel Clustering Method 2.1 First Level (PCA HC K-means) 2.2 Second Level (AP) 3 Results and Validation 3.1 Multilevel Clustering Applied to Our Data: Results 3.2 Two Validation Cases 4 Discussion 5 Conclusion References Fast Text Based Classification of News Snippets for Telecom Assurance 1 Introduction 2 Related Work 2.1 SVM 2.2 kNN 2.3 Fuzzy Fingerprints 3 Experimental Setup 3.1 Corpus 3.2 Preprocessing 3.3 Methods 3.4 Evaluation Metrics 4 Results 4.1 SVM 4.2 K-Nearest Neighbors 4.3 Fuzzy Fingerprints 5 Conclusion and Future Work References Decision Making Modeling and Applications Reciprocal Preference-Aversion Structures 1 Introduction 2 Preliminaries 2.1 Standard Fuzzy Preference Structures 2.2 The Preference-Aversion Model 2.3 Compatible Reciprocal Preference Structures 3 Reciprocal P-A Structures 3.1 Reciprocal Basic Preference and Aversion Structures 3.2 The Complete Reciprocal P-A Structure 4 Conclusions References Calibration of Radiation-Induced Cancer Risk Models According to Random Data 1 Introduction 2 Problem Statement 3 Forward Calibration Approach 4 Inverse Calibration Approach 4.1 Data Mapping 4.2 Optimal Calibrated Model 5 Performance Analysis 5.1 Risk Analysis 5.2 Comparative Analysis of Competing Models 6 Example: Calibration of a Radiation Dose-Effect Model 6.1 Maximal Expected Log-Likelihood 6.2 Maximal -quantile of the Log-Likelihood 6.3 Generalization Properties 7 Concluding Remarks References A Novel Variable Selection Approach Based on Multi-criteria Decision Analysis 1 Introduction 2 Methods 2.1 Variable Importance Ranking by TOPSIS 2.2 Determine Weight Values for Criteria in TOPSIS 3 Results 4 Conclusions References Fintech Lending Decisions: An Interpretable Knowledge-Base System for Retail and Commercial Loans 1 Introduction 2 Methodology: Interpretable Belief-Rule-Based System 3 Integration of Credit Data and Lending Institution Data 4 Knowledge Acquisition and Rule-Base Development 5 Results 6 Conclusion References Intuitionistic Fuzzy Selected Element Reduction Approach (IF-SERA) on Service Quality Evaluation of Digital Suppliers 1 Introduction 2 Intuitionistic Fuzzy Sets 3 Methodology 4 Application 5 Conclusion References A New Approach to Polarization Modeling Using Markov Chains 1 Introduction 2 Preliminaries 2.1 Polarization Measures 2.2 Markov Chains 3 A New Problem: Modeling Polarization with Markov Chains 3.1 Hypotheses 3.2 A New Probabilistic Model: PMMC 3.3 Illustrative Example 4 Conclusion References Intervals and Possibility Degree Formulae for Usage Prioritization of Cartagena Coastal Military Batteries 1 Introduction 2 Intervals and Possibility Functions to Rank Solutions According to the User's Preferences 3 Data Description 4 Experiments and Results 4.1 Analysis of Scores 4.2 Analysis of Rankings 5 Conclusions References Stability of Preferences over Time: Preferences on COVID-19 Vaccine from Spanish and French People 1 Introduction 2 Background 2.1 Notation and Starting Hypothesis 2.2 Codification Procedure of Preferences 2.3 Methodological Framework and Basic Definitions 3 Cases of Study 3.1 Spanish Case: Stability of Spaniards' Preferences on Getting COVID-19 Vaccine 3.2 French Case: Stability of the French's Preferences on Getting COVID-19 Vaccine 4 Conclusions References On the Notion of Influence in Sensory Analysis 1 Introduction 2 Decision-Making Power of an Agent 3 Decision Model in Sensory Analysis 4 Model of Influence in Sensory Evaluation 5 Illustrative Example 6 Conclusion References Study of the Instability of the Sign of the Nonadditivity Index in a Choquet Integral Model 1 Introduction 2 Notations and Definitions 2.1 Framework 2.2 Choquet Integral 2.3 Nonadditivity Index 3 Necessary and Possible Nonadditivity Index on X 3.1 Some Definitions and Notations 3.2 Results on X 4 Necessary and Possible Nonadditivity Index with Generalized Binary Alternatives 4.1 Framework of Binary Alternatives 4.2 Results on Binary Alternatives 5 Conclusion References The d-Interaction Index in MCDA 1 Introduction 2 Settings 2.1 The Independence Axiom in MCDA 2.2 The Choquet Integral Model 2.3 A Link Between the Independence Axiom and the Null Choquet-interaction Index 3 A New Definition of the Interaction Index 4 Computation of the d-Interaction Index 4.1 Coming Back to the Classic Example 4.2 Another Example in Which the Violation of the Independence Axiom Is Not Obvious 5 Conclusion References E-Health Analysis of Graphical Causal Models with Discretized Data 1 Introduction 2 Graphical Causal Models 3 Illustration of Discretization Effects 4 Effects of Discretization in Graphical Causal Models 4.1 Simulation Study Setup 4.2 Effects of Discretization on Estimated Adjacency Matrices 4.3 Effects of Discretization on Estimated Causal Effects 5 Conclusion and Future Work References Population and Individual Level Meal Response Patterns in Continuous Glucose Data 1 Introduction 2 Preliminaries 3 Identifying Patterns in CGM Time Series 3.1 Clustering Responses to Establish Patterns 3.2 Looking for Matches 4 Experimental Setup 5 Results 5.1 Response Patterns 5.2 Matches 6 Conclusion References Analyzing Patient Feedback Data with Topic Modeling 1 Introduction 2 Topic Modeling 3 Analyzing Patient Feedback 3.1 Data Collection 3.2 Data Preprocessing 3.3 Topic Modeling 3.4 Evaluation 4 Results 4.1 Intrinsic Evaluation 4.2 Extrinsic Evaluation 5 Discussion 6 Conclusion References A Framework for Active Contour Initialization with Application to Liver Segmentation in MRI 1 Introduction 2 A Framework for Active Contour Model Initialization 3 Active Contour Model Initialization for Liver Segmentation in MRI Imagery 3.1 Spatial Fuzzy c-means for Object Detection 3.2 Object Selection 3.3 Object Isolation 3.4 Center Detection 4 Case of Study 5 Conclusions References Fuzzy Methods in Data Mining and Knowledge Discovery Improving Text Clustering Using a New Technique for Selecting Trustworthy Content in Social Networks 1 Introduction 2 Related Works 3 Trustworthy Content Selection Pipeline 3.1 System Architecture 3.2 Text Pre-processing 3.3 Content Filter 3.4 Clustering 4 Experimentation 4.1 Dataset 4.2 Evaluation Metrics 4.3 Clustering Results 5 Conclusions and Future Work References Fuzzy System-Based Solutions for Traffic Control in Freeway Networks Toward Sustainable Improvement 1 Introduction 2 Traffic Flow Models with Sustainable Objectives 3 Fuzzy System-Based Controllers in Transportation 3.1 The Case Study 3.2 The Fuzzy Inference System 3.3 The Fuzzy Cognitive Map 4 Results and Discussion 4.1 FIS in Congestion Level Prediction 4.2 FCM in Traffic Flow Simulation 5 Conclusion References Contextual Sentence Embeddings for Obtaining Food Recipe Versions 1 Introduction 2 Related Work 3 Data 4 Method 5 Experiments 6 Discussion 7 Conclusions and Future Work References A Fuzzy-Based Approach for Cyberbullying Analysis 1 Introduction 2 Related Works 3 Fuzzy Analysis of Cyberbullying 3.1 Text Preprocessing 3.2 Sentence Embeddings 3.3 Fuzzy Analysis 4 Experimentation 4.1 Dataset 4.2 Experiment Setup 4.3 Analysis of Our Fuzzy Approach 4.4 Expert Evaluation 5 Conclusions and Future Work References Flexible Division Queries Based on RL-Instances 1 Introduction 2 Preliminaries 2.1 Relational Databases and Division Queries 2.2 Fuzzy Instances and Flexible Division Queries 3 RL-Instances and RL-Relational Algebra 4 Gradual Division on RL-Instances 4.1 RL-Systems with SQL 4.2 SQL Division Patterns Based on NOT EXISTS 4.3 SQL Division Patterns for Flexible Querying with RL-Instances 5 Conclusions References Soft Computing and Artificial Intelligence Techniques in Image Processing Image Segmentation Losses with Modules Expressing a Relationship Between Predictions 1 Introduction 2 Related Work and Preliminaries 3 The Modules 3.1 Module 1 3.2 Module 2 4 Benchmark 5 Discussion 6 Summary References Fuzzy Clustering to Encode Contextual Information in Artistic Image Classification 1 Introduction 2 Background 2.1 Knowledge Graphs 2.2 Fuzzy C-Means 2.3 Multi-task Learning 2.4 Representation Learning 3 Fuzzy Representations for Contextual Information Using Fuzzy C-Means 3.1 Encoding Context Using Bag of Words 3.2 Extracting Relevant Context Information Using Fuzzy C-Means 4 Artistic Image Classification Framework 5 Experimentation 6 Conclusions and Future Lines References New Aggregation Strategies in Color Edge Detection with HSV Images 1 Introduction 2 Preliminaries 2.1 Digital Image Processing 2.2 Color Edge Detection 2.3 HSV and Other Color Models 2.4 Aggregation Operators 3 Aggregating Channels in Color Edge Detection 4 Comparisons and Results 5 Conclusions References Representing Vietnamese Traditional Dances and Handling Inconsistent Information 1 Introduction 2 An Ontology-based Modelling for Ethnic Vietnamese Thai Dances 3 Automated Detection of EVTD ``CaUoc" Movements 4 Practical Inconsistency-Tolerant Strategies 5 Conclusion References Laplace Operator in Connection to Underlying Space Structure 1 Introduction 2 Various Versions of Definition 2.1 Sum of Partial Derivatives 2.2 Divergence of the Gradient 2.3 Nonlocal Approach 2.4 Discrete Laplacian 3 Structure of the Underlying Space, Proximity 3.1 Fuzzy Partition 3.2 Fuzzy Transform 3.3 Discrete F-transform 4 Discrete FT-Based Laplacian 4.1 Properties 5 Conclusion References Noise Reduction as an Inverse Problem in F-Transform Modelling 1 Preliminaries 2 Assumptions on the Data 3 Singular Value Decomposition of the Closeness Matrix 4 Orthogonal Characterization 5 Inverse Denoising Problem 5.1 Special Case h=1 5.2 Special Case h=2 6 Inverse Signal and Noise Separation Problem 7 Application to Image Processing References Selection of Keypoints in 2D Images Using F-Transform 1 Introduction 2 Space with a Fuzzy Partition 2.1 Fuzzy Partition 2.2 Discrete Universe and Its Fuzzy Partition 3 Discrete (Non-local) Laplace Operator 4 Keypoints Localization 4.1 Keypoint Compression 4.2 Keypoint Filtering 4.3 Reconstruction 5 Experiments with Images 6 Conclusion References 3D Shapes Classification Using Intermediate Parts Representation 1 Introduction 2 Related Work 3 Description of the Approach 4 Graph Neural Networks 5 Discovery of Parts of the Object 6 Supervised Segmentation 7 Classification of the Graph of Object Parts 7.1 Constructing the Graph of Object Parts 7.2 Tensor Field Networks 8 Data Augmentations and Noise Injection 9 Experiments 10 Discussion 11 Conclusion References Content-Aware Image Smoothing Based on Fuzzy Clustering 1 Introduction 2 Clustering-Based Content-Aware Smoothing 3 Content-Aware Smoothing Based on Spatial Fuzzy c-Means 4 Experimental Results 4.1 Progressive Supranuclear Palsy 4.2 Experimental Configuration 4.3 Result Evaluation 5 Conclusions References Soft Methods in Statistics and Data Analysis A Probabilistic Tree Model to Analyze Fuzzy Rating Data 1 Introduction 2 Model 2.1 About the Probabilistic Term (1) 2.2 About the Probabilistic Term (2) 2.3 Sampling Schema 2.4 Parameter Estimation 3 Application 4 Conclusions References Distance Metrics for Evaluating the Use of Exogenous Data in Load Forecasting 1 Introduction 2 Exogenous Data Evaluation Metrics 3 Evaluation of Elastic Metrics 4 Time Series Alignment Methods Evaluation 5 Towards a Significance Analysis Methodology 6 Conclusions References On the Role of the Considered Measure in a Quantile-Based Graded Version of Stochastic Dominance 1 Introduction 2 Stochastic Dominance 3 Graded Stochastic Dominance for a Location-Scale Distribution Family 4 ROC Curves for Different Measures 5 Conclusions and Open Problems References Bootstrapped Kolmogorov-Smirnov Test for Epistemic Fuzzy Data 1 Introduction 2 The Kolmogorov-Smirnov Test 3 Epistemic Fuzzy Data 4 Epistemic Bootstrap 5 Bootstrapped Kolmogorov-Smirnov Test 6 Simulation Study 7 Conclusions References Connections Between Granular Counts and Twofold Fuzzy Sets 1 Introduction 2 Twofold Fuzzy Sets 3 Granular Count 4 Twofold Fuzzy Sets from Possibilistic Assignment Tables 5 Interactivity-Aware Operations on Twofold Fuzzy Sets 6 Conclusion References Testing Independence with Fuzzy Data 1 Introduction 2 Fuzzy Data 3 Fuzzy Random Variables 4 Distance Covariance and Distance Correlation 5 Testing Independence with Fuzzy Data 6 Empirical Study 7 Conclusions References Uncertainty, Heterogeneity, Reliability and Explainability in AI Learning from Categorical Data Subject to Non-random Misclassification and Non-response Under Prior Quasi-Near-Ignorance Using an Imprecise Dirichlet Model 1 Introduction 2 Bayesian Learning from Potentially Misclassified Categorical Data Under Prior Near-Ignorance 2.1 Learning from Correctly Classified Categorical Data 2.2 The Imprecise Dirichlet Model (IDM) as a Means to Express Prior Near-Ignorance 2.3 Learning from Potentially Misclassified Categorical Data Under Prior Near-Ignorance Using the IDM 3 Prior Quasi-Near-Ignorance 4 Learning from Potentially Misclassified and Incomplete Categorical Data Under Prior Quasi-Near-Ignorance 4.1 Misclassified and Incomplete Categorical Data 4.2 Learning from Potentially Misclassified and Incomplete Categorical Data Under Prior Quasi-Near-Ignorance Using the IDM 5 Examples 6 Discussion References Uncertainty in Predictive Process Monitoring 1 Introduction 2 Related Works 3 Problem Statement and Framework 4 Methods 4.1 Uncertainty Estimation 4.2 Model and Training 5 Data 6 Results 6.1 Calibration 6.2 Total Uncertainty 6.3 Overconfidence 7 Conclusions and Future Works References Set-Based Counterfactuals in Partial Classification 1 Introduction 1.1 Explainable Artificial Intelligence 1.2 Uncertain Labels and Partial (Set-Based) Classification 1.3 Set-Based Counterfactuals 2 Singleton-class Counterfactual Explanations 2.1 Counterfactual Generation Task as an Optimization Problem 2.2 Constrained Form 2.3 Unconstrained Form 3 Towards Set-Based Counterfactuals 4 Conclusions and Future Works References Logic Operators and Sibling Aggregators for Z-grades 1 Introduction 2 Z-grades 3 Logic Operators 3.1 Negation Operator 3.2 Conjunction Operators 3.3 Disjunction Operators 3.4 De Morgan's Laws 4 Sibling Aggregators 4.1 Weighted Mean 4.2 Ordered Weighted Average 4.3 Generalized Conjunction Disjunction Aggregators 5 Conclusions and Future Work References Canonical Extensions of Conditional Probabilities and Compound Conditionals 1 Introduction 2 Preliminaries 3 Canonical Extension of a Conditional Probability 4 The Canonical Extension for Subalgebras 5 Probability of the Conjunction and the Disjunction 6 Conclusions References Classifier Probability Calibration Through Uncertain Information Revision 1 Introduction 2 Basic Background Notions 2.1 Classification 2.2 Classifier Probability Calibration 2.3 Updating Uncertain Information with New Uncertain Inputs: Jeffrey's Rule 3 Motivating Example 4 Probability Calibration Based on Jeffrey's Rule 4.1 Jeffrey's Rule-Based Probability Calibration 4.2 Jeffrey's Rule-Based Probability Calibration in Practice 5 Experimental Study 6 Concluding Remarks References Evidential Hybrid Re-sampling for Multi-class Imbalanced Data 1 Introduction 2 Evidence Theory 3 Evidential Hybrid Re-sampling for Multi-class Imbalanced Data 3.1 Computation of Evidential Labels 3.2 Evidential Adaptive Undersampling 3.3 Evidential Adaptive Oversampling 4 Experimental Study 4.1 Set-up 4.2 Results and Discussion 5 Conclusion References A Parallel Declarative Framework for Mining High Utility Itemsets*-6pt 1 Introduction 2 Background 2.1 High Utility Itemset Mining Problem 2.2 Propositional Logic and SAT Problem 3 SAT Encoding of (Closed) High Utility Itemset Mining 4 Parallel High Utility Itemsets Mining Using Propositional Satisfiability 5 Experimental Results 5.1 Parallel Evaluation 5.2 Load Balancing 6 Conclusion References Towards an FCA-Based Approach for Explaining Multi-label Classification 1 Introduction 2 Preliminaries 2.1 Multi-label Classification 2.2 Explainable AI 2.3 Formal Concept Analysis 3 From Multi-label Predictions to FCA Representation 3.1 Building a Formal Context for the Classifier Predictions 3.2 Computing Explanations as Formal Concepts 4 Multi-label Prediction Explanations 4.1 Sufficient Reason Explanations 4.2 Significant Attributes Set 4.3 Beyond Das and Ssa Explanations 5 Case Study 6 Concluding Remarks References Characterizing the Possibilistic Repair for Inconsistent Partially Ordered Assertions 1 Introduction 2 Preliminaries 2.1 Overview of DL-LiteR 2.2 The IAR Semantics 3 Partially Preordered Possibilistic Repair 4 Revisiting -acceptance 4.1 A New Characterization of -acceptance 4.2 The Case of Non-binary Conflicts 5 Conclusion References Coherent Upper Conditional Previsions with Respect to Outer Hausdorff Measures and the Mathematical Representation of the Selective Attention 1 Introduction 2 Coherent Upper and Lower Conditional Previsions Defined by Hausdorff Outer and Inner Measures 2.1 Preference Ordering and Indifference Between Random Variables Represented by Coherent Lower and Upper Conditional Previsions 2.2 Hausdorff Outer Measures 3 Absolute Continuity of Coherent Conditional Probability Measures Defined by Hausdorff Measures 4 The Invisible Gorilla Experiment: A Mathematically Explanation of the Selective Attention 4.1 A Mathematically Explanation of the Confirmation Bias 5 A Comparison Between the Model and Other Conditioning Rules 6 Conclusions References Handling Disagreement in Hate Speech Modelling 1 Introduction 2 Data Selection and Annotation 2.1 Annotation Schema 2.2 Data Selection and Annotation Setup 3 Model Training and Evaluation 3.1 Evaluation Measures 3.2 Annotator Agreement and Model Performance 4 Discussion 4.1 Methodological Implications 4.2 Ethical Implications 5 Conclusions and Future Work References What Is the Cost of Privacy? 1 Introduction 2 Related Work 3 Anonymization Methods 3.1 Methods that Remove the Privacy Data 3.2 Methods that Replace Privacy Data 4 Experiments 4.1 Dataset 4.2 Models 4.3 Training Specification 4.4 Results 4.5 Discussion and Future Work 5 Summary References Integrating Prior Knowledge in Post-hoc Explanations 1 Introduction 2 Background 2.1 Post-hoc Explanations 2.2 Representation of Knowledge 2.3 Integration of Knowledge 3 Proposed General Framework 3.1 Proposed Optimization Problem 3.2 An Example of Existing Method Under This Formalism 4 Knowledge Integration in Counterfactual Explanation (KICE) 4.1 Proposed Cost Function: Instantiation of the Framework 4.2 Algorithm Description 5 Experiments 5.1 Experimental Protocol 5.2 Illustrative Examples 5.3 Evaluation of the KICE Method 6 Conclusion and Perspectives References Weak and Cautious Supervised Learning PANDA: Human-in-the-Loop Anomaly Detection and Explanation 1 Introduction 2 Related Works 2.1 Anomaly Detection 2.2 Anomaly Explanation 3 Proposed PANDA Approach 3.1 Notations and Illustrative Data Set 3.2 Data Processing 3.3 Anomaly Analysis: Cross Comparison of Detected Anomalies 4 Use Case: Secondhand Car Ads 4.1 Experimental Protocol 4.2 Result Analysis 5 Conclusion and Perspectives References SSFuzzyART: A Semi-Supervised Fuzzy ART Through Seeding Initialization 1 Introduction 2 Related Works 3 Semi-supervised Fuzzy ART (SSFuzzyART) 3.1 Fuzzy ART Algorithm 3.2 SSFuzzyART Algorithm 4 Experiments 4.1 Evaluation Measures 4.2 Results & Discussion 5 Conclusion References Informed Weak Supervision for Battery Deterioration Level Labeling 1 Introduction 2 Battery Deterioration Types 2.1 Energy and Power Losses 2.2 Latent Variables of the Deterioration Model 3 Learning the Deterioration Model 3.1 Uncertainty and Inconsistency in the Data 3.2 Numerically Efficient Solution Through Informed Learning 4 Numerical Results 4.1 Simulated Batteries 4.2 Actual Batteries 5 Concluding Remarks and Future Work References Rough-set Based Genetic Algorithms for Weakly Supervised Feature Selection 1 Introduction 2 Background 2.1 Possibility Theory 2.2 Rough Set Theory 3 Rough Set-Based Weakly Supervised Feature Selection 3.1 Possibilistic Decision Tables and Reducts 3.2 Genetic Rough Set Selection 4 Experiments and Results 4.1 Experimental Design 4.2 Results and Discussion 5 Conclusion References Choosing the Decision Hyper-parameter for Some Cautious Classifiers 1 Introduction 2 Reminders and Notations 2.1 F Measure 2.2 The Decision Step in ndc 2.3 The Decision Step in eclair 2.4 Evaluation Measures for the Imprecise Classifiers 3 The Expected Gains Related to 3.1 The Case of Ndc 3.2 The Case of Eclair 4 Illustration 4.1 Illustration Using Simulated Data 4.2 Illustration Using UCI Data 5 Conclusion References Author Index