Preface
Organization
Contents – Part I
Contents – Part II
Aggregation Theory Beyond the Unit Interval
Aggregation on a Cartesian Product of Bounded Partially Ordered Sets
1 Introduction
2 Aggregation on Besets
3 Aggregation on a Cartesian Product of Bounded Posets
3.1 The Beset Structure of a Cartesian Product of Bounded Posets
3.2 Classical Aggregation Functions on a Cartesian Product of Bounded Posets
3.3 Componentwise Aggregation Functions on a Cartesian Product of Bounded Posets
4 Conclusion
References
Flexible-Dimensional EVR-OWA as Mean Estimator for Symmetric Distributions
1 Introduction
2 Preliminaries
2.1 Mean Estimation
2.2 The EVR-OWA Operator
3 OWA Operator for Mean Estimation
4 Convergence of Cumulative Weights
5 EVR-OWA Operator as Mean Estimator for Symmetric Distributions
6 Conclusions and Future Work
References
Sugeno Integral Extended to Undefined Inputs
1 Introduction
2 Classical Sugeno Integral
3 Undefined Values as Inputs or Outputs
4 Sugeno Integral for Undefined Inputs
4.1 Representation Using Alpha-Level Sets
4.2 Algorithm of Computation
5 Conclusion
References
Sugeno Integral Based Pandemic Risk Assessment
1 Introduction
2 Preliminaries
3 Sugeno Integral Based Risk Assessment Model
4 Decision Rules and Sugeno Integrals
5 The Italian System
6 Conclusions
References
On the Aggregation of n-distances
1 Introduction
2 Aggregation of n-distances
3 On S-generalized n-distances
4 On n-distances, S-generalized n-distances and n-T-indistinguishabilities
5 Conclusions
References
Formal Concept Analysis and Uncertainty
Fuzzy Rough Set Decision Algorithms
1 Introduction
2 Basic Notions in RST
2.1 Decision Rules
2.2 Decision Algorithm
3 Decision Rules in Fuzzy Rough Set Theory
4 Decision Algorithms in Fuzzy Rough Set Theory
5 Conclusions and Further Work
References
Relational Extension of Closure Structures
1 Introduction
2 Preliminary Notions
3 On Closure Relations
4 Conclusions and Further Work
References
Computing the Mixed Concept Lattice
1 Introduction
2 Preliminary Notions
3 Main Results
3.1 Embedding of B(K) and B(K) into B#(K)
3.2 Decomposition of Concepts in B#(K)
3.3 An Algorithm for Computing the Mixed Lattice
4 Conclusions and Future Work
References
On the Definition of Fuzzy Relational Galois Connections Between Fuzzy Transitive Digraphs
1 Introduction
2 Preliminary Notions
3 Fuzzy Powerings: Extending Relations to Fuzzy Powersets
4 Fuzzy Relational Galois Connections Between Fuzzy T-Digraphs
5 Conclusions and Future Works
References
Study on the Necessity Operator to Factorize Formal Contexts in a Multi-adjoint Framework
1 Introduction
2 Preliminaries
2.1 Formal Concept Analysis
2.2 Multi-adjoint Framework
3 Properties of the Factorization in Classic FCA
4 Properties of the Factorization in the Multi-adjoint Framework
5 Conclusions and Future Work
References
Encoding Non-global Time Representations into the Lattice of Divisibility
1 Motivation: Modelling Imprecise, Local Time
2 Theory: The Lattice of Divisibility
3 Results
3.1 The Log-Prime and Exponential-Prime Functions
3.2 Embedding Finite Lattices Within the Lattice of Divisibility
3.3 Affordances of the Embedding
4 Discussion and Conclusions
References
On the Effects of Conjunctions in the Solution Set of Multi-adjoint Fuzzy Relation Equations
1 Introduction
2 Multi-adjoint Fuzzy Relation Equations
3 Effects of Conjunctions in the Solution Set of a Multi-adjoint FRE
4 Conclusions and Future Work
References
Comparing Attribute Reduction in Multi-adjoint Concept Lattices and the CR-method
1 Introduction
2 Preliminaries
2.1 Multi-adjoint Formal Concept Analysis
2.2 Attribute Classification in Multi-adjoint Concept Lattices
2.3 Clarification and Reduction Method
3 Comparison Between Both Methods
4 Worked Example
5 Conclusion and Future Work
References
Determining Cause-Effect Relations from Fuzzy Relation Equations
1 Introduction
2 Preliminaries
2.1 Fuzzy Relation Equations
2.2 Enterprise Architecture to Strategic Management
3 Analysing Theoretical Cause-Effect Relationships
4 FRE to Detect Cause-Effect Relationships
5 Conclusions and Further Work
References
Fuzzy Implication Functions
Monodistances from Fuzzy Implications
1 Introduction
1.1 Motivation for This Work
1.2 Contributions of This Work
2 Distance Functions from Fuzzy Implications
3 SLK-Transitive Fuzzy Implications
3.1 SLK-Transitivity of I FI Obtained from Other FLCs
3.2 SLK-Transitivity of Transformations of Fuzzy Implications
3.3 SLK-Transitivity of I FI Obtained from Unary Generators
4 Monodistances from Fuzzy Implications
4.1 Monodistances on the B-Sets Obtained from a Poset
4.2 B-Sets Obtainable from a Poset: A Characaterisation
5 Concluding Remarks
References
On the Additional Properties of Fuzzy Polynomial Implications of Degree 4
1 Introduction
2 Preliminaries
3 Fuzzy Polynomial Implications
4 Study of Additional Properties
5 Conclusions and Future Work
References
Preservation of the Ordering Property Under the Quadratic Polynomial Construction of Fuzzy Implication Functions
1 Introduction
2 Preliminaries
3 Construction of Fuzzy Implication from Other Implications
3.1 Construction of Fuzzy Implications Using Quadratic Polynomials
4 Preserving Properties Under Quadratic Construction
4.1 Preservation of Ordering Property Under Quadratic Construction
5 Polynomial Construction of Arbitrary Degree
6 Conclusions
References
On a New Contrapositivisation Technique for Fuzzy Implications Constructed from Triangular Conorms
1 Introduction
2 Preliminaries
3 Contrapositivisation Techniques
4 (S,N)-Contrapositivisation
5 Final Remarks
References
Construction of Fuzzy Implications from the Bandler-Kohout Subproduct
1 Introduction
2 Preliminaries
3 BKS Composition
4 Conclusions
References
Fuzzy Mathematical Analysis and its Applications
On Conflicts of Linguistic Fuzzy Rules
1 Introduction and Motivation
2 Preliminaries
2.1 Linguistic Fuzzy IF-THEN Rules
2.2 Perception-Based Logical Deduction Inference Method
3 Conflicting Linguistic Fuzzy Rules
3.1 1-Coherence of PbLD Interpretation and Conflicting Rules
3.2 How to Determine Conflicting Rules
3.3 Algorithmic Implementation
4 Conclusions and Remark
References
A Review on Differentiability and Optimality Conditions in Fuzzy Environments
1 Introduction
2 Preliminaries
3 Differentiability for Interval-Valued and Fuzzy Functions: New Necessary and Sufficient Conditions
4 Notion of gH-Differentiability for Fuzzy Functions with Several Real Variables
5 Optimality Conditions in Fuzzy Multiobjective Optimization
6 Conclusions
References
Selected Dynamical Properties of Fuzzy Dynamical Systems
1 Introduction
2 Definitions and Notation
2.1 Spaces of Fuzzy Sets
2.2 Induced Discrete Dynamical Systems
2.3 Elementary Notions from Topological Dynamics
2.4 Transitivity-Like Properties
2.5 Chaotic Properties
2.6 Topological Entropy
3 Topological Entropy of g-fuzzifications
4 Transitivity
5 Density of Periodic Points
6 Devaney-Like Chaos
References
Parameterized Metrics and Their Applications in Word Combinatorics
1 Introduction and Preliminaries
1.1 t-conorms
1.2 Parameterized Pseudometrics
2 Parameterized Metric on the Universe of Infinite Words
2.1 Parameter Regulating Function
2.2 Construction of a Parameterized Metric on the Set of All Infinite Words Based on a t-conorm
2.3 Analysis of Acceptable t-conorms
3 Examples of Application of the Constructed Parameterized Metrics in Word Combinatorics
3.1 Analysis of the Impact of the Choice of a Parameter
3.2 Analysis of the Impact of a t-conorm
4 Conclusions
References
CI Approach to Numerical Methods for Solving Fuzzy Integral Equations
1 Introduction
1.1 The Fuzzy Fredholm Integral Equations
1.2 F1-transform of Functions of Two Variables
2 Function Approximation
2.1 Properties of and
3 General Scheme of the Proposed Method
4 Examples
5 Conclusion
References
A Characterization for Generalized Hukuhara Differentiable Interval-Valued Functions and Some Rules of Calculus
1 Introduction
2 Preliminaries
3 Characterization of gH-differentiable Interval-Valued Functions via Its Length Function
4 Sum of gH-differentiable Interval-Valued Functions
5 Conclusion
References
Generalized Sets and Operators
Selection of Relevant Features Based on Optimistic and Pessimistic Similarities Measures of Interval-Valued Fuzzy Sets
1 Introduction
2 Interval-Valued Fuzzy Setting
2.1 Orders in the Interval Setting
2.2 Interval-Valued (I-V) Aggregation Functions
2.3 Inclusion and Similarity Degree Measures for IVFSs
3 Possibility and Necessity Issue
3.1 Aggregation Functions. Possible and Necessary
3.2 Negation Functions. Possible and Necessary
3.3 Precedence Indicator. Possible and Necessary
3.4 Similarity Measure. Possible and Necessary
4 Application. Attribute Selection Algorithm
4.1 Algorithm IVRelief - Interval-Valued Fuzzy Relief
4.2 Application of K-NN Classifiers
References
Applications of Monads in Semiring-Valued Fuzzy Sets
1 Introduction
2 Semiring-Valued Fuzzy Sets
3 Monads in (R,R)-Fuzzy Set Theory
3.1 Zadeh's Extension Principle for (R,R)-Fuzzy Sets
3.2 Approximations of (R,R)-Fuzzy Sets
4 Conclusions
References
Similarity for Multisets and Heterogeneous Sets
1 Introduction
2 Similarity over Measure Space
3 Multisets
4 Types, Heterogeneous Sets, Typed and Mixed Similarities
5 Similarity Axioms
6 Consistency of Similarity Indexes
7 Final Comment
References
Attribute Ranking with Bipolar Information
1 Introduction
2 Background
2.1 Models for Bipolar Information
2.2 Training Set in Machine Learning
2.3 Approaches to Construct Ant IFS from a Probability Distribution
2.4 Construction of an IFS/IVFS from a Training Set
3 Attributes Ranking with Bipolar Information
3.1 Entropies of IFS
3.2 Ranking with Entropies
4 Experimental Study
4.1 Comparing the Approaches to Build IFS/IVFS
4.2 Experiment with a Machine Learning Dataset
5 Conclusion
References
Information Fusion Techniques based on Aggregation Functions, Pre-aggregation Functions, and Their Generalizations
On Construction Methods of (Interval-Valued) General Grouping Functions
1 Introduction
2 Preliminaries
2.1 Aggregation Functions and Related Concepts
2.2 Interval Mathematics and Interval-Valued Functions
3 About Construction Methods of General Grouping Functions
4 On Construction Methods of iv-General Grouping Functions
5 Conclusions
References
Aggregation Functions in Flexible Classification by Ordinal Sums
1 Introduction
2 Classification into Three Classes by Ordinal Sums of Conjunctive and Disjunctive Functions
2.1 Classification into Three Classes
2.2 Preliminaries of Ordinal Sums
3 Averaging Functions in Ordinal Sums for Classification
4 Conjunctive and Disjunctive Functions in Ordinal Sums for Classification
5 Illustrative Example and Discussion
5.1 Illustrative Examples
5.2 Discussion and Future Work
6 Conclusion
References
Honeycomb-Based Polygonal Chains Aggregation Functions
1 Introduction
2 Preliminary
2.1 Geometry
2.2 Binary Sequence
3 Honeycomb-Based Polygonal Chains Foundations
3.1 Representation of a Structure with a Binary Sequence
3.2 Rotation of a Structure
3.3 Reflection of a Structure
4 Aggregation Functions
4.1 The Basic Aggregation Function Notion
4.2 Rotations Invariantness Case
4.3 Rotations and Reflections Invariantness Case
5 Summary and Future Work
References
Polarization Measures in Bi-partition Networks Based on Fuzzy Graphs
1 Introduction
2 Preliminaries
2.1 Aggregation Operators: Overlapping and Grouping Functions
2.2 Polarization Measures
2.3 Graphs, Community Detection. Crisp and Fuzzy Cases
3 Polarization Indices in Networks
4 Some Computational Results and Conclusions
References
On Rational Bivariate Aggregation Funcions
1 Introduction
2 Preliminaries
3 Rational Binary Aggregation Functions: Definition and Basic Properties
4 Rational Binary Aggregation Functions of Degree (1,1)
5 Conclusions and Future Work
References
Parameterized Pre-aggregation Function with Interval Values in Medical Decisions Making
1 Introduction
2 Preliminaries
2.1 Interval-Valued Fuzzy Set Theory. Orders in the Interval-Valued Fuzzy Sets
2.2 Interval-Valued Aggregation Functions
2.3 Directional Monotonicity of IV Functions
3 Parameterized Operators in Interval-Valued Fuzzy Setting
3.1 Preservation of Basic Properties by Operator Wt
3.2 Composition of Interval-Valued Fuzzy Relations
3.3 Basic Properties of A-Wt Composition
4 Algorithm of General Approximate Reasoning
5 Application
5.1 Analyzing the Behaviour of the Different Aggregation Functions and Weak Operator when Accomplishing the Inference Process
6 Conclusions
References
Int-FLBCC: Exploring Fuzzy Consensus Measures via Penalty Functions
1 Introduction
2 Preliminary Concepts on Fuzzy Logic
2.1 Fuzzy Consensus Measures
2.2 Fuzzy Penalty Functions
3 Cloud Computing
4 Int-FLBCC: Type-2 Fuzzy System Modelling
4.1 Modelling the Membership Functions in the Fuzzyfication Step
4.2 Rule Base Acting on Inference System and the Defuzzification Step
4.3 Consensus Measures Applied on the Int-FLBCC Approach
5 Conclusions
References
Aggregated Fuzzy Equivalence Relations in Clustering Process
1 Introduction
2 Preliminaries
2.1 Fuzzy Clustering Approach
2.2 T-norm as a Generalized Conjuction
2.3 Fuzzy Equivalence Relation
3 Fuzzy Clustering Approach
4 Numerical Example
5 Conclusion
References
Fuzzy-Valued Distance Between Fuzzy Numbers Based on a Generalized Extension Principle
1 Introduction
2 Preliminaries
3 Generalizing the Extension Principle Using Binary Aggregation Functions
4 Concluding Remarks
References
On an Application of Integral Transforms for Lattice-Valued Functions in Image Processing
1 Introduction
2 Preliminary
2.1 Algebra of Truth Values
2.2 Fuzzy Sets
2.3 Fuzzy Measure Spaces
2.4 Multiplication Based Sugeno-Like Fuzzy Integral
3 Integral Transforms
4 Application of Integral Transforms to Image Processing
4.1 Method Description
4.2 Illustration of Filtering and Compression/Decompression
5 Conclusion
References
Interval Uncertainty
Why People Tend to Overestimate Joint Probabilities
1 Formulation of the Problem
1.1 Description of the Situation
1.2 A Natural Solution to Such Situations
1.3 What if We Apply This Approach to Our Situation
1.4 How Do People Actually Estimate the Joint Probability
1.5 Formulation of the Problem
1.6 Important Comment
2 Our Explanation
2.1 Main Idea Behind This Explanation
2.2 This Idea Explains the Observed Overestimation: Case When 0<a<0.5 and 0<b<0.5
2.3 This Idea Explains the Observed Overestimation: Case When 0.5<a<1 and 0.5<b<1
2.4 What About the General Case?
3 Discussion
3.1 Is There an Inconsistency Here?
3.2 What if We Have Three of More Events?
3.3 Computational Conclusion
3.4 Physical Conclusions
References
Necessary and Possibly Optimal Items in Selecting Problems
1 Introduction
2 The Interval Case
2.1 Setting
2.2 Possibly and Necessarily Optimal Items
3 Compact Representation of Possible Optimal Solution
4 Extension to the Credal Set Case
4.1 Precise Probabilities
4.2 Generic Credal Sets
5 Conclusion
References
Anomaly Detection in Crowdsourced Work with Interval-Valued Labels
1 Introduction
1.1 The Problem We Study
1.2 IVLs and Notations
1.3 The Motivation of This Study
2 Indicators of Worker's Reliability
2.1 Worker's Correctness
2.2 Worker's Confidence
2.3 Worker's Stability and Predictability
3 Detecting Anomaly and Adversarial Attackers
3.1 Anomaly Detection
3.2 Identifying Possible Adversarial Attackers
3.3 Monitor Worker's Behavior Dynamically
4 Computational Experiments
4.1 The Design of Our Experiments
4.2 The Effectiveness of Anomaly Detection and Attackers Identification
4.3 Impacts of Attackers on the Quality of a Crowdsourced Work
5 Summary
References
Atanassov's Intuitionistic Fuzzy Sets Demystified
1 Introduction
2 A Brief Introduction to the IFSs
3 Expressing the IFSs by Intervals
4 Other Differences Between the IFSs and Interval-Valued Fuzzy Sets
4.1 Different Measures for the IFSs and Interval-Valued Fuzzy Sets
4.2 Different Operators for IFSs and Interval-Valued Fuzzy Sets. Problem of Interpretability
5 Conclusions
References
Towards Explainable Summary of Crowdsourced Reviews Through Text Mining
1 Introduction
1.1 About This Study
1.2 The Sample Dataset
2 Overall Sentiment Ranking of the Reviews
3 Corpus Summarization
3.1 Summarizing the Corpus Directly
3.2 Summarizing the Corpus After Clustering Its Documents
3.3 Investigating Information in Each Cluster Further
3.4 Beyond Extractive Summarization
4 Generating an Explainable Summary from the Reviews
5 Summary
References
A New Similarity Measure for Real Intervals to Solve the Aliasing Problem
1 Introduction
2 Similarity Measures
3 A New Similarity Measure
4 Analysis of the Properties of the Similarity Measures
4.1 Property 1
4.2 Property 2
4.3 Property 3
4.4 Property 4
4.5 Property 5
4.6 Property 6
5 Application
6 Conclusion
References
Knowledge Acquisition, Representation and Reasoning
Similarity Fuzzy Semantic Network for Social Media Analysis
1 Introduction and Motivation
2 Fuzzy Semantic Networks
2.1 Semantic Networks
2.2 Fuzzy Semantic Networks
2.3 Combining Inferences
3 Similarity Fuzzy Semantic Networks
3.1 Similarity Semantic Relations
3.2 Meta-relations
3.3 Similarity Inference
3.4 Inference Strategy
4 Similarity Fuzzy Semantic Network for Social Media
4.1 Basic Concepts and Semantic Relations in Social Media
4.2 Fuzzy Semantic Relations for Social Media
4.3 Similarity Fuzzy Relations in Social Media
5 Application to Radical Discourse in Twitter
5.1 Determining Degrees for the Fuzzy Relations
5.2 Real-World Experiments
6 Conclusions
References
Management of Uncertain Data in Event Graphs
1 Introduction
2 Uncertainty Management in Event Graphs
2.1 Rules and Rule Mining
2.2 Logic on Graphs
3 Methodology Proposal and Real Case Study Application
3.1 The Data Set
3.2 Assigning Weights and Creating Edges
3.3 Rule Mining
3.4 Answer Sets
3.5 Argument Graphs
3.6 Possibility Networks
3.7 Revisions
4 Conclusion
References
Possibilistic Preference Networks and Lexicographic Preference Trees – A Comparison
1 Introduction
2 Possibilistic Preferences
3 Lexicographic Preferences
4 Comparison -pref-net/LP-tree
5 Concluding Remarks
References
Generating Contextual Weighted Commonsense Knowledge Graphs
1 Introduction
1.1 Defining Commonsense
1.2 Related Work
1.3 Contributions
2 Methodology
2.1 Processing of Images
2.2 Formalizing Commonsense Knowledge Graph Generation
3 Generation of Commonsense Knowledge Graphs
3.1 Context-Free Commonsense Knowledge Graph
3.2 Contextual Commonsense Knowledge Graph
4 Reasoning with Contextual Commonsense Knowledge Graph
4.1 Extraction of Relevant Nodes and Occurrences
4.2 Reasoning: Inference with Uncertain Premises
5 Conclusion
References
Logical Structures of Opposition and Logical Syllogisms
Modelling of Fuzzy Peterson's Syllogisms Related to Graded Peterson's Cube of Opposition
1 Introduction
2 Preliminaries
2.1 Fuzzy Type Theory
2.2 Theory of Evaluative Linguistic Expressions
3 Fuzzy Intermediate Quantifiers
3.1 Cube of Opposition
4 New Forms of Syllogisms
4.1 Syllogisms by Weakening of the Conclusion
4.2 Syllogisms by Strengthening of the First Premise
4.3 Syllogisms by Strengthening of the Second Premise
5 Example of Logical Syllogism in Finite Model
6 Conclusion and Future Directions
References
Comparing Hexagons of Opposition in Probabilistic Rough Set Theory
1 Introduction
2 Preliminaries
3 Comparing Hexagons of Opposition
3.1 Relations of Opposition When 0 < ' < ' < 1
3.2 Relations of Opposition When 0 < ' < ' < < 1
3.3 Relations of Opposition When 0 < ' ' < 1
4 Conclusions and Future Directions
References
Analysis of Peterson's Rules for Syllogisms with Intermediate Quantifiers
1 Introduction
2 Preliminaries
2.1 Fuzzy Type Theory
2.2 Evaluative Linguistic Expressions
3 The Theory of Intermediate Quantifiers
3.1 Syntactic Definition of Intermediate Quantifiers
4 Generalized Syllogisms with Intermediate Quantifiers
4.1 Formalization of Syllogisms
4.2 Peterson's Rules for Intermediate Syllogisms
4.3 Formalization of Extended Peterson's Rules
5 Conclusion and Future Directions
References
On Modeling of Fuzzy Peterson's Syllogisms Using Peterson's Rules
1 Introduction
1.1 Main Goals
2 Preliminaries
2.1 Peterson's Square
2.2 Categorical Syllogism
3 Peterson Rules for Aristotle's Syllogisms
3.1 Example of Fuzzy Syllogisms with Classical Quantifiers
4 Peterson Rules for Syllogism with Intermediate Quantifiers
5 An Example of Fuzzy Non-trivial Syllogism
6 Future Work and Ideas
7 Conclusion
References
Mathematical Fuzzy Logics
Cutting of Partial Fuzzy Relations and Their Compositions – The Case of the Dragonfly Operations
1 Introduction and Motivation
2 Preliminaries
2.1 Dragonfly Algebra Dealing with Missing Values
2.2 Compositions of Partial Fuzzy Relations
3 Cutting of Partial Fuzzy Relations
4 Compositions of Cutting Partial Fuzzy Relations
4.1 Properties
4.2 Cutability of Compositions of Partial Fuzzy Relations
5 Conclusions
References
Rotations of Gödel Algebras with Modal Operators
1 Introduction
2 Gödel and Nilpotent Minimum Algebras
3 Towards NM-Algebras with Modal Operators
3.1 The Case of NM+-Algebras with Operators
3.2 The Case of NM–Algebras with Operators
4 Conclusion and Future Work
References
On Operations of Restriction and Freezing on Monadic Fuzzy Quantifiers Over Fuzzy Domains
1 Introduction
2 Preliminaries
2.1 Algebraic Structures of Truth Values
2.2 Fuzzy Sets
2.3 Fuzzy Domains
3 NL-quantifiers and Generalized Quantifiers
3.1 Generalized Quantifiers
3.2 Restriction and Freezing
4 Fuzzy Quantifiers
4.1 Fuzzy Quantifiers Over Fuzzy Domains
4.2 Restriction and Freezing for Fuzzy Quantifiers over Fuzzy Domains
5 Conclusion
References
Involutions on Different Goguen L-fuzzy Sets
1 Introduction
2 Involutions on ([0,1], ) and on (A, A )
3 Involutions on (A, A) and on (I, I)
4 Involutions on (I, I*) and on (I2, I2)
5 Involutions on ([0,1], ) and on (I2, I2)
6 Conclusions
References
On the Order-Compatibility of Fuzzy Logic Connectives on the Generated Clifford Poset
1 Introduction
1.1 Motivation for This Work
2 Clifford Poset and Some Functional Equations
2.1 FLCs that Give Rise to Clifford Posets
2.2 Conditional Functional Equations
3 FLCs and Multiplicative Clifford's Relation
3.1 On the Boundedness of Multiplicative Clifford Poset
3.2 On the Monotonicity of F on the Induced Clifford Poset
3.3 Multiplicative Clifford Posets from FLCs
4 FLCs and Additive Clifford's Relation
4.1 On the Boundedness of Additive Clifford Poset
4.2 On the Monotonicity of F on the Induced Clifford Poset
4.3 Additive Clifford Posets from FLCs
4.4 Additive Clifford Posets from Fuzzy Implications
5 Some Concluding Remarks
References
Theoretical and Applied Aspects of Imprecise Probabilities
Decision Making with State-Dependent Preference Systems
1 Introduction
2 Preliminaries
3 State-Dependent Decision Systems
3.1 The Basic Model
3.2 Criteria for Decision Making
3.3 Generalizing the Criteria to Imprecise Probabilities
4 Algorithms for Determining Optimal Acts
4.1 Two Basic Linear Programs
4.2 Approximating the Linear Programs by Grouping the States
4.3 Different Choices for the Partition
5 An Illustrative Toy Example
6 Outlook
References
Inner Approximations of Credal Sets by Non-additive Measures
1 Introduction
2 Inner Approximations of Coherent Lower Probabilities
3 Incenters of Credal Sets
3.1 Inner Approximations in CLV
3.2 Inner Approximations in CPMM
3.3 Inner Approximations in CTV
3.4 Incenters of Credal Sets
4 Comparison of Decision Rules
5 Concluding Remarks
References
A Robust Bayesian Estimation Approach for the Imprecise Plackett–Luce Model
1 Introduction
2 Our Robust PL Model
2.1 The Plackett-Luce Model
2.2 Hierarchical Model
3 Parameter Estimation
3.1 Maximum a Posteriori Estimation
3.2 Imprecise MAP Estimation
4 Illustration
4.1 Synthetic Dataset
4.2 NASCAR Dataset
5 Conclusion
References
A Discussion About Independence and Correlation in the Framework of Coherent Lower Conditional Probability
1 Introduction
2 The Reference Framework
2.1 Coherent Conditional Probability
2.2 Zero-Layers
2.3 Coherent Lower Conditional Probability
3 Independence and Correlation in the Framework of Coherent Conditional Probabilities
4 Independence and Correlation in the Framework of Coherent Lower Conditional Probabilities
5 Conclusion
References
Markov and Time-Homogeneity Properties in Dempster-Shafer Random Walks
1 Introduction
2 Preliminaries
3 Dempster-Shafer Random Walks
4 Construction of Dempster-Shafer Random Walks
5 Conclusion
References
Correlated Boolean Operators for Uncertainty Logic
1 Introduction
2 Correlated and as a Copula
3 Interval Probabilities
3.1 Other Boolean Operations
4 Probability Boxes
4.1 Two Levels of Dependence
5 Application
5.1 Interval Scenario
5.2 P-Box Scenario
6 Conclusion
References
Author Index