
Advances in Computational Intelligence, Part III
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Content
- Title
- Preface
- Organization
- Table of Contents - Part III
- Fuzzy Numbers and Their Applications
- Fuzzy Arithmetics for Fuzzy n-Poles: When Is Interactivity Irrelevant?
- Introduction
- Preliminaries: -Slices and -Chunks
- Results and Examples
- References
- Possibility and Gradual Number Approaches to Ranking Methods for Random Fuzzy Intervals
- Introduction
- Preliminaries
- Ranking Intervals
- Comparison of Random Variables
- Comparison of Gradual Numbers
- Ranking Fuzzy Intervals
- Ranking Ordinal Possibility Distributions
- Ranking Fuzzy Intervals as Intervals of Gradual Numbers
- Stochastic Dominance of Fuzzy Random Variables
- Stochastic Dominance of Fuzzy Random Variables Using Possibilty and Necessity
- Stochastic Dominance of Fuzzy Random Variables Using Gradual Random Variables
- Statistical Preference between Fuzzy Random Variables
- Conclusion
- References
- On Mean Value and Variance of Interval-Valued Fuzzy Numbers
- Introduction
- Interval-Valued Fuzzy Numbers
- Mean Value for Interval-Valued Fuzzy Numbers
- Variance for Interval-Valued Fuzzy Numbers
- New Ranking Method for Interval-Valued Fuzzy Numbers
- Project Selection with Interval-Valued Fuzzy Numbers
- Conclusions
- References
- Metric Properties of the Extended Weighted Semi-trapezoidal Approximations of Fuzzy Numbers and Their Applications
- Introduction
- Preliminaries
- Extended Weighted Semi-trapezoidal Approximation of a Fuzzy Number
- Metric Properties of the Extended Weighted Semi-trapezoidal Approximation
- Applications
- Weighted Semi-trapezoidal and Semi-triangular Approximations Preserving Parameters
- Weighted Semi-trapezoidal, Weighted Semi-triangular Approximations and Aggregation
- References
- Uncertain Evidence in Bayesian Networks: Presentation and Comparison on a Simple Example
- Introduction
- Different Types of Evidence in Bayesian Networks
- Definitions and Vocabulary
- Algorithms Dealing with Uncertain Evidence
- Comparison of Different Types of Evidence with a Simple Example
- Presentation of the "Snow Example
- Junction Tree Algorithm
- Hard Evidence
- Virtual Evidence
- Soft Evidence
- Fuzzy Evidence
- Fuzzy Reasoning in Bayesian Networks
- Conclusion
- References
- Weighted Semi-trapezoidal Approximation of a Fuzzy Number Preserving the Weighted Ambiguity
- Introduction
- Preliminaries
- Extended Weighted Semi-trapezoidal Approximation and Metric Properties
- Weighted Semi-trapezoidal Approximation Preserving the Weighted Ambiguity
- Trapezoidal Approximation Preserving Ambiguity
- Conclusion
- References
- On the Interval Approximation of Fuzzy Numbers
- Introduction
- Fuzzy Numbers
- Interval Approximation of a Fuzzy Number
- Interval Approximation with Respect to , Distance
- Properties
- Conclusions
- References
- Approximation of Fuzzy Numbers by F-Transform
- Introduction
- F-Transform and Its Basic Properties
- F-Transform Approximation of Fuzzy Numbers
- Spaces of Functions Generated by F-Transform
- Fuzzy Numbers Generated by F-Transform
- Fuzzy Arithmetic with F-Transform
- F-Transform and Type-2 Fuzzy Numbers
- Concluding Remarks
- References
- Numerical Solution of Linear Fuzzy Fredholm Integral Equations of the Second Kind Using Fuzzy Haar Wavelet
- Introduction
- Preliminaries
- Proposed Method for Solving Linear FFIE-2
- Error Estimation
- Numerical Examples
- Conclusions
- References
- On a View of Zadeh's Z-Numbers
- Introduction
- Modeling Z-Valuations
- Operations on Z-Valuations
- Reasoning with Z-Valuations
- Linguistic Summaries and Z-Valuations
- References
- Solving Real-World Fuzzy Quadratic Programming Problems by a Parametric Method
- Introduction
- Using a Parametric Approach to Solve Quadratic Programming Problems with Fuzzy Constraints
- Numerical Experiments
- Portfolio Selection Problem
- Economic Dispatch Problem
- Conclusions
- References
- Information Processing and Management of Uncertainty in Knowledge-Based Systems
- Naive Bayesian Classifier Based on Neighborhood Probability
- Introduction
- The Related Works
- The Normal Method
- The Kernel Method
- NBC Based on Neighborhood Probability-NPNBC
- The Basic Idea of NPNBC
- The Principle of NPNBC
- The Feasibility of NPNBC
- Experiments and Results
- Conclusion
- References
- FiveWeaknesses of ASPIC+
- Introduction
- APIC+ Argumentation Framework
- Tarski's Monotonic Logics
- Rules as Object Level Language
- Rules as Reasoning Patterns
- Conclusion
- References
- A Feature Reduction Strategy for the Analysis of Voluminous Biomedical Patterns
- Introduction
- Dimensionality Reduction Using Feature Sampling
- Feature Performance Histogram
- Aggregating Feature Regions
- Experiment Design
- Validation Protocol
- Experiment Parameters
- Results and Discussion
- Conclusion
- References
- Discovering the Preferences of Physicians with Regards to Rank-Ordered Medical Documents
- Introduction
- Background Research
- Experimental Design
- Results
- Discussion
- References
- Experiences with Eliciting Probabilities from Multiple Experts
- Introduction
- The Context
- Set-Up of the Project Meetings
- Taking a Quantitative Perspective: Summary Statistics
- The Data Obtained, the Analyses and the Results
- Discussion
- Taking a Qualitative Perspective: Stochastic Dominance
- The Data Obtained, the Analyses and the Results
- Discussion
- Conclusions
- References
- Discretisation Effects in Naive Bayesian Networks
- Introduction
- Preliminaries
- Naive Bayesian Networks
- Sensitivity Analysis
- Studying the Effects of Discretisation
- Binary Discretisation in Two-Class Naive Bayesian Networks
- Discretisation in Naive Bayesian Networks in General
- Conclusions and Further Research
- References
- Fuzzy Concept Lattices with Incomplete Knowledge
- Introduction
- Preliminaries
- Residuated Lattices and Fuzzy Sets
- Formal Concept Analysis in Fuzzy Setting
- Residuated Lattices with Variables
- Incomplete Contexts and Their Concept Lattices
- Illustrative Example
- Conclusion
- References
- Imperfect Information Fusion Using Rules with Bilattice Based Fixpoint Semantics
- Introduction
- Extended Logic Programs on Bilattices
- Bilattice Based Fixpoint Semantics
- Computational Results
- Further Results and Ongoing Work
- References
- Assimilation of Information in RDF-Based Knowledge Base
- Introduction
- Repository of User's Experience and Knowledge
- Personal Linked Data and Special Properties
- Personal Linked Data as User's Knowledge Base
- Information Assimilation Mechanism
- Relevance Determination
- Knowledge Integration
- Case Study
- Experimental Setup
- Integration Process
- Conclusion
- References
- Quantitative Semantics for Uncertain Knowledge Bases
- Introduction
- The Logic Lm
- Logic Programs and Their Quantitative Semantics
- Programs
- Valuations and Models
- Quantitative Semantics of Positive Programs
- Quantitative Semantics of Programs with Negation
- Knowledge Bases with Uncertain Information
- Quantitative Semantics for Knowledge Bases
- Knowledge Base Updating
- Properties of Updates
- Conclusion
- References
- Weighted Attribute Combinations Based Similarity Measures
- Introduction
- Preliminaries
- Weighted Attribute Combinations Based Similarities
- Learning the Significance Assessment
- Experimental Results
- Conclusions and Future Works
- References
- Algorithms for Computation of Concept Trilattice of Triadic Fuzzy Context
- Introduction
- Preliminaries
- Fuzzy Logic and Fuzzy Sets
- Formal Concept Analysis, Triadic Concept Analysis
- Reduction to the Ordinary Case
- Trias in Fuzzy Setting
- Conclusions
- References
- Classification of Uncertain Data: An Application in Nondestructive Testing
- Motivation and Background
- State of the Art
- Classification of MFL Data
- Classification under Uncertainty
- Modeling Uncertainties with Trust Management
- Concept and Realization
- Investigation and Results
- Investigation Set-Up
- Pure Classification Performance
- Assessment of the Results with Trust Management
- Discussion
- Conclusion and Outlook
- References
- Ant Based Clustering of Two-Class Sets with Well Categorized Objects
- Preliminaries
- Algorithm
- Experiments
- Conclusions
- References
- Aggregation Functions
- Construction Methods for Uninorms via Rotation, Rotation-Annihilation, and Twin Rotation
- Introduction and Preliminaries
- Preliminaries
- Rotation of Uninorms
- Rotation-Annihilation with Uninorms
- Twin Rotation of Semigroups
- References
- Natural Means of Indistinguishability Operators
- Introduction
- Preliminaries
- The Lattices of Indistinguishability Operators, Sets of Extensional Fuzzy Subsets, Upper and Lower Approximations
- Natural Means Operating on Indistinguishability Operators, Sets of Extensional Fuzzy Subsets, Upper and Lower Approximations
- Concluding Remarks
- References
- Aggregation Operators for Awareness of General Information
- Introduction
- Preliminaries
- Statment of the Problem: Awareness AWJ
- Some Aggregation Operators for AWJ
- Solution of the Problem
- Conclusion
- References
- On the Relation between Effort-Dominating and Symmetric Minitive Aggregation Operators
- Preliminaries
- Notational Convention
- Aggregation Operators
- Effort-Dominating Impact Functions
- Symmetric Minitive Aggregation Operators
- The Relationship between the Two Classes
- Conclusions
- References
- On Migrative t-Conorms and Uninorms
- Introduction
- Preliminaries
- Uninorms
- (,S0)-Migrative t-Conorms
- (,U0)-Migrative Uninorms
- When U0 is in Umin
- When U0 is in Umax
- Conclusions and Future Work
- References
- Fuzzy Relations between Two Universes: Soft Assessments of R-neighborhoods
- Introduction
- Assessments by Pairs of Fuzzy Sets
- Interval-Valued Assessments
- Assessments by Pairs of Fuzzy Relations
- Conclusion
- References
- Qualitative Integrals and Desintegrals: How to Handle Positive and Negative Scales in Evaluation
- Introduction
- General Setting and Motivation
- Algebraic Framework
- Aggregation and Scale Polarity
- Three Qualitative Weighted Aggregations for Positive Scales
- Three Qualitative Weighting Methods for Negative Scales
- Properties of the Drastic Desintegrals
- Concluding Remarks
- References
- Stability in Aggregation Operators
- Introduction
- Stability of a Family of Aggregation Operators
- Weak Stability of a Family of Aggregation Operators
- Stability Levels of Some Well-Known Families of Aggregation Operators
- Conclusions and Final Remarks
- References
- Negations Generated by Bounded Lattices t-Norms
- Introduction
- Bounded Lattices
- Negations on L
- T-norms on L
- Negation on L Obtained from t-norms on L
- Final Remarks
- References
- The Problem of Missing Data in LSP Aggregation
- Introduction
- The Structure of LSP Criterion Functions
- Penalty-Controlled Numerical Coding of Missing Data
- Missingness-Tolerant Aggregation
- Conclusions
- References
- General Interpolation by Polynomial Functions of Distributive Lattices
- Introduction and Motivation
- Preliminaries
- Main Results
- Further Work
- Applications and Concluding Remarks
- References
- Aggregation of Weakly Quasi-convex Fuzzy Sets
- Introduction
- Case of Quasi-convex Fuzzy Sets
- Main Results
- Conclusion
- References
- The Bipolar Universal Integral
- Introduction
- Basic Concepts
- The Universal Integral and the Bipolar Universal Integral
- An Illustrative Example
- The Bipolar Universal Integral with Respect to a Level Dependent Bi-capacity
- Conclusions
- References
- Web-Geometric View on Uninorms and Structure of Some Special Classes
- Introduction
- Preliminaries
- Web-Geometric View on Uninorms
- Structure of Uninorms Given by Idempotent and Involutive t-Norms and t-Conorms
- Concluding Remarks
- References
- Multi-polar Aggregation
- Introduction
- m-Polar Aggregation Operators
- Properties of Multi-polar Aggregation Operators
- Metric on K[0,1]
- Properties of m-Polar Aggregation Operators
- Conclusions
- References
- Imprecise Probabilities
- An Imprecise Probability Approach to Joint Extensions of Stochastic and Interval Orderings
- Introduction and Motivation
- Comparing Random Variables v.s. Ill-Known Quantities
- Stochastic Orderings
- A Common Formulation
- Comparing Ill-Known Quantities Modeled by Real Intervals
- Preference Relations within Imprecise Probability Theory
- Generalizations of First Stochastic Dominance
- Generalizations of Expectation Dominance
- Generalizations of Statistical Preference
- A General Common Expression of Preference between Gambles
- General Formulation
- The Special Case of Fuzzy Intervals
- References
- Imprecise Bernoulli Processes
- Introduction
- Desirability and Coherence
- Imprecise Bernoulli Experiments
- Exchangeability
- Imprecise Bernoulli Processes
- Justifying a Sensitivity Analysis Approach
- Conclusions
- References
- Possibilistic KNN Regression Using Tolerance Intervals
- Introduction
- Possibility Theory
- Inferring Possibility Distribution from Data
- Interval Prediction with K-Nearest Neighbors
- K-Nearest Neighbors (KNN)
- Possibilistic KNN with Fixed K
- KNN Interval Regression with Variable K Using 0.95 CTP Distribution
- Application to Aircraft Trajectory Prediction
- Conclusion
- References
- Classification Based on Possibilistic Likelihood
- Introduction
- Background
- Possibility Distribution
- A Possibility Distribution as a Family of Probability Distributions
- Possibilistic Likelihood
- A Possibilistic Likelihood-Based Classifier
- Principle
- Construction and Learning of a Possibilistic Classifier
- Experimentations
- Conclusions and Further Works
- References
- Maximin and Maximal Solutions for Linear Programming Problems with Possibilistic Uncertainty
- Introduction
- Reformulation as a Decision Problem
- Probability Mass Functions
- Generalizing the Probabilistic Case
- Intervals
- Possibility Distributions
- Conclusions
- References
- Lower Previsions Induced by Filter Maps
- Introduction and Motivation
- Basic Notions
- Motivation
- Induced Lower Previsions
- Properties of Induced Lower Previsions
- Conclusion
- References
- Probabilistic Graphical Models with Imprecision: Theory and Applications
- Conditioning in Evidence Theory from the Perspective of Multidimensional Models
- Introduction
- Basic Concepts
- Set Projections and Extensions
- Set Functions
- Conditioning
- Conditioning of Events
- Conditional Variables
- Conditional Independence and Irrelevance
- Independence
- Irrelevance
- Relationship between Independence and Irrelevance
- Conclusions
- References
- A New Method for Learning Imprecise Hidden Markov Models
- Introduction
- Hidden Markov Models and Basic Notions
- Precise Hidden Markov Models
- Imprecise Hidden Markov Models
- Learning Imprecise Local Uncertainty Models
- Imprecise Dirichlet Model
- Known State Sequence
- Unknown State Sequence
- Imprecision of the Imprecise Local Uncertainty Models
- The Baum-Welch Algorithm
- Likelihood in Hidden Markov Models
- Expectation Step
- Maximisation Step
- Predicting the Earth's Earthquake Rate
- Introduction
- Results
- 6 Conclusion
- References
- Inference Using Compiled Product-Based Possibilistic Networks
- Introduction
- Basic Backgrounds
- Possibility Theory
- Possibilistic Networks
- Compilation Concepts
- Compilation-Based Inference of G*
- Encoding and Compilation Phase
- Inference Phase
- Prod-DNNF vs Min-DNNF
- Conclusion
- References
- Dynamic Directed Evidential Networks with Conditional Belief Functions: Application to System Reliability
- Introduction
- Static and Dynamic Directed Graphical Models
- Static Directed Graphical Models
- Dynamic Directed Graphical Models
- Static and Dynamic Directed Evidential Networks with Conditional Belief Functions
- Directed Evidential Networks with Conditional Belief Functions
- Dynamic Directed Evidential Networks with Conditional Belief Functions (DDEVN)
- Propagation in DDEVN
- Illustrative Case Study
- Application of the DDEVN to the Valve System Reliability
- DEN and DDEVN for the System Reliability Assessment
- Conclusion
- References
- Likelihood-Based Robust Classification with Bayesian Networks
- Introduction
- Background
- Classification with Bayesian Networks
- Likelihood-Based Learning of Imprecise-Probabilistic Models
- Robust Likelihood-Based Classifiers
- A Demonstrative Example
- Coping with Zero Counts
- Analytic Formulae for the Upper Envelope of the Likelihood
- Preliminary Results
- Conclusions and Outlooks
- References
- Belief Function Theory: Basics and/or Applications
- Collecting Information Reported by Imperfect Information Sources
- Introduction
- A Logical Model
- The Logical Framework
- Agent i Is in Direct Contact with the Source
- There Is a Third Agent between Agent i and the Source
- Taking Uncertainty into Account
- The Numerical Model
- Agent i Is in Direct Contact with the Source
- There Is a Third Agent between i and the Source
- Concluding Remarks
- References
- Ranking Aggregation Based on Belief Function
- Introduction
- Ranking Aggregation Methods
- Belief Functions Theory
- Method
- Notation and Definition of the Problem
- Belief Ranking Estimator
- Experimental Results on Synthetic Data
- Conclusion
- Evaluating the Uncertainty of a Boolean Formula with Belief Functions
- Introduction
- Evaluation of the Probability of a Boolean Expression
- Without Any Independence Hypothesis
- When Variables xi Are Stochastically Independent
- The Case of Independent Sources of Information
- The Belief and Plausibility of a Boolean Formula
- Conjunctions and Disjunctions of Literals
- Application to Fault-Trees
- General Case
- Comparison between Interval Analysis and Dempster-Shafer Theory
- Conclusion
- References
- Introduction to an Algebra of Belief Functions on Three-Element Frame of Discernment - A Quasi Bayesian Case
- Introduction
- Preliminaries
- General Primer on Belief Functions
- Belief Functions on 2-Element Frame of Discernment
- Dempster's Semigroup
- BFs on n-Element Frames of Discernment
- Dempster's Semigroup of Belief Functions on 3-Element Frame of Discernment 3
- Basics
- The Extended Dempster's Semigroup
- Subalgebras of Dempster's Semigroup
- Subalgebras of D0 and Ideas of Subalgebras of D3
- The Subgroups/Subalgebras of Bayesian Belief Functions
- The Subsemigroup of Quasi-bayesian Belief Functions
- Ideas for Future Research and Open Problems
- Conclusion
- References
- Application of Evidence Theory and Discounting Techniques to Aerospace Design
- Introduction
- Theory of Belief Functions
- Evidential Operations
- Case Study
- Implementation of Scenario
- Conclusion
- References
- Constructing Rule-Based Models Using the Belief Functions Framework
- Introduction
- Belief Functions
- Basic Concepts
- Evidential c-Means Algorithm
- Rule-Based Model
- Regression Problem
- Model Structure
- Model Parameters
- Examples
- Conclusions and Future Work
- References
- An Evidential Framework for Associating Sensors to Activities for Activity Recognition in Smart Homes
- Introduction
- Activities and Uncertainty in Smart Homes
- Basics of the Dempster-Shafer (DS) Theory of Evidence
- Formulation of Association between Sensors and Activities
- Uncertainty with Sensor Sources
- A Preliminary Evaluation
- Summary and Future Work
- References
- Positive and Negative Dependence for Evidential Database Enrichment
- Introduction
- Theory of Belief Functions
- Conditioning
- Generalized Bayesian Theorem and Disjunctive Rule of Combination
- Evidential Database
- Independence
- Clustering
- Independence Measure
- Negative and Positive Dependence
- Example
- Conclusion
- References
- Handling Interventions with Uncertain Consequences in Belief Causal Networks
- Introduction
- Belief Function Theory and Causal Networks
- Basics of Belief Function Theory
- Belief Function Causal Networks
- Jeffrey Rule of Conditioning
- Jeffrey's Rule in a Probabilistic Framework
- Extension of Jeffrey's Rule to the Belief Function Framework
- Observations vs Interventions
- Observations
- Interventions
- Graphical Representation of Interventions
- Belief Graph Mutilation for Interventions Controlling the State of the Variable
- Belief Graph Augmentation for Interventions Interacting with Initial Causes
- Conclusion
- References
- K-Modes Clustering Using Possibilistic Membership
- Introduction
- The K-Modes Method
- Possibility Theory
- Possibility Distribution
- Possibilistic Clustering
- The K-Modes Method with Possibilistic Membership
- Experiments
- The Framework
- Evaluation Criteria
- Experimental Results
- Conclusion
- References
- Author Index
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