New Trends in Aggregation Theory

Name: New Trends in Aggregation Theory
Brand: Springer
Price: 171.19 EUR
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Radomír Halas Marek Gagolewski Radko Mesiar(Editor)

Springer (Publisher)

1st Edition

Published on 16. May 2019

IX, 348 pages

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978-3-030-19494-9 (ISBN)

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Content

Intro
Preface
Contents
Invited Speakers
Qualitative Integrals and Cointegrals: A Survey
1 Introduction
2 Motivations
3 Qualitative Integrals and Cointegrals
4 Elementary Properties
4.1 Comparison Between q-Cointegrals and q-Integrals
4.2 Elementary Properties
4.3 Inequalities for q-Integrals
5 Characterization Results
5.1 Characterisation Results for q-Integrals
5.2 Characterisation Theorems for q-cointegrals
6 Upper and Lower Qualitative Possibility Integrals
7 Conclusion
References
The Concave and Decomposition Integrals: A Review and Future Directions
1 Introduction
2 A Motivating Example
3 Capacity and Decompositions of a Random Variable
3.1 The Concave and Choquet Integrals
3.2 The Decomposition-Integral
3.3 Pan Integral and Shilkret Integral
4 Properties of the Decomposition-Integral
5 Future Directions
References
Super Level Measures: Averaging Before Integrating
References
On Extreme Value Copulas with Given Concordance Measures
1 Introduction
2 Notation
3 Dependence Measures
4 Main Results
5 Special Cases
6 Constraints
7 Proofs and Auxiliary Results
7.1 Proof of Theorem 1
7.2 Proofs of Propositions 1,...,6
7.3 Proofs of ``constraints''
References
Some Remarks About Polynomial Aggregation Functions
1 Introduction
2 Preliminaries
3 Polynomial Binary Aggregation Functions with a Non Trivial 0 Region
3.1 The Case of Degree 0 or 1
3.2 The Case of Degree 2
4 Polynomial Binary Aggregation Functions with a Non Trivial 1-region
5 Conclusions and Future Work
References
Other Speakers
Aggregation Through Composition: Unification of Three Principal Fuzzy Theories
1 Introduction
2 Preliminaries
3 Fuzzy Rough Sets
4 F-transform
5 Fuzzy Automata
5.1 Fuzzy Automaton Based on Fuzzy Transition Function
5.2 Fuzzy Relation-Based Fuzzy Automaton
6 Conclusion
References
Pseudo-Additions and Shift Invariant Aggregation Functions
1 Introduction
2 Shift Invariant Aggregation Functions
3 Pseudo-Additions and -Shift Invariant Aggregation Functions
4 Pseudo-Additions that Correspond to Some Fixed Aggregation Functions
5 Concluding Remarks
References
Importation Algebras
1 Introduction
2 Importation Algebra - Definition and Examples
2.1 Importation Algebra
2.2 Examples of Importation Algebra
2.3 Mutual Independence of the Axioms (NP), (QN) and (LI)
3 Order Based on Importation Algebras
3.1 Order on Importation Algebras
4 Importation Algebras When P = [0,1]
4.1 Importation Algebras from Fuzzy Implications
4.2 Importation Algebras Where I Is Not a Fuzzy Implication
5 Recovering the Underlying Order from an Importation Algebra
6 Concluding Remarks
References
On Some Inner Dependence Relationships in Hierarchical Structure Under Hesitant Fuzzy Environment
1 Introduction
2 Hesitant Fuzzy Set and Its Basic Operations
3 Hierarchy of Criteria with Partitioned Structure
3.1 Partial Result for Multi-layer Hierarchical Structure of Criteria in Hesitant Fuzzy Environment
4 Decision Making Under Hesitant Fuzzy Environment
4.1 Application
5 Conclusions and Future Work
References
The Relation Between F-partial Order and Distributivity Equation
1 Introduction
2 Preliminaries
3 Distributivity Equation
4 Concluding Remarks
References
On Properties of Internal Uninorms on Bounded Lattices
1 Basic Notions and Preliminaries
2 Internal Uninorms on Bounded Lattices
3 Concluding Remarks
References
Some Remarks on Generalized Hypothetical Syllogism and Yager's Implications
1 Introduction
2 Preliminaries
3 Aggregation of Fuzzy Implications
4 Yager's Implications Satisfying (GHS)
5 Conclusions
References
Interval-Valued EN-functions and Similarity Measures
1 Introduction
2 Preliminaries
3 Width-Preserving Interval Valued Restricted Equivalence Functions
3.1 Width-Preserving IV Aggregation Functions
4 Width-Based Interval Valued Similarity Measures
5 Conclusions
References
On Some Generalizations of the Choquet Integral
1 Introduction
2 Preliminaries
3 An Overview of Generalizations of the Choquet Integral
4 A New Approach to Generalization of the Choquet Integral
5 Concluding Remarks
References
Penalty-Based Data Aggregation in Real Normed Vector Spaces
1 Introduction
2 Existence and Uniqueness Results
3 Noteworthy Aggregation Theory Properties
3.1 Internalities
3.2 Stability of the Solution
4 The Limiting Case p=
5 Conclusions
References
Gravitational Clustering Algorithm Generalization by Using an Aggregation of Masses in Newton Law
1 Introduction
2 Preliminaries
2.1 Aggregation Functions
2.2 Algorithm of Gravitational Clustering
3 New Gravitational Clustering Algorithm
3.1 Description and Actuating of the Proposed Gravitational Clustering Algorithm
3.2 Study of Convergence. Single Particle Movement. Governing Mapping Contraction
4 Conclusion
References
Uninorms on Bounded Lattices with Given Underlying Operations
1 Introduction
2 Basic Notations and Some Known Facts and Notions
3 Uninorms with Given Underlying t-norm and t-conorm
4 Conclusions
References
Description and Properties of Curve-Based Monotone Functions
1 Introduction
2 Preliminaries
3 Curve-Based Monotonicity
4 Properties of Curve-Based Monotone Functions
5 Curve-Based Monotonicity with Respect to the Composition of Curves
6 Conclusion
References
A Construction Method for t-norms on Bounded Lattices
1 Introduction
1.1 Preliminaries
2 Construction of Triangular Norm
3 Concluding Remarks
References
Penalty-Based Aggregation of Strings
1 Introduction
2 The Framework of Penalty-Based Data Aggregation
3 Strings of the Same Length
3.1 The Discrete Distance Metric
3.2 The Hamming Distance Metric
3.3 The Lexicographic Distance Metric
3.4 The Baire Distance Metric
4 Strings of Different Length
5 Conclusions
References
On Some Properties of Generalized Convex Combination of Triangular Norms
1 Introduction
2 Basic Notions
3 Generalized Convex Combination of Triangular Norms
4 Concluding Remarks
References
Analysis of Relationship Among V4 Countries and Germany by Their Gross Domestic Products and Copula Models
1 Introduction
2 Theory
2.1 Copula
2.2 Inference
3 Application
3.1 Data Overview
3.2 Overall Dependence
3.3 Dependence Evolution
4 Conclusion
References
Aggregation via Clone Theory Approach
1 Introduction
2 Clones
3 Aggregation Clones and Their Generators
References
Mixture Functions Based on Deviation and Dissimilarity Functions
1 Introduction
2 Preliminaries
2.1 Mixture Functions
2.2 Penalty Based Function
2.3 Deviation and Dissimilarity Functions
3 Mixture Functions as Penalty Based Functions
3.1 Mixture Function Based on Special Dissimilarity and Deviation Functions
3.2 Properties of Selected Quasi-mixture Function
4 Conclusion
References
F-transform and Dimensionality Reduction: Common and Different
1 Introduction
2 Preliminaries
2.1 Laplacian Eigenmaps for Dimensionality Reduction
2.2 F-transforms
3 Dimensionality Reduction by the F-transform
3.1 Numerical Experiments
4 Conclusion
References
Note on Aggregation Functions and Concept Forming Operators
1 Introduction
2 Aggregation Functions, Residuated Mappings, Concept Lattices
3 General Concept Structures
4 Conclusion
References
Ordinal Sums of t-norms and t-conorms on Bounded Lattices
1 Preliminaries
2 Ordinal sum of t-norms and t-conorms
3 Ordinal Sums of t-representable t-norms and t-conorms
4 Conclusion
References
Aggregation of Fuzzy Conformances
1 Introduction
2 The Conformance Measures in Brief
3 The Aggregation of Atomic Conformances
3.1 Conjunctive Aggregation
3.2 Disjunctive Aggregation
3.3 The Hybrid Aggregation
3.4 The Ordinal Sums of Aggregated Conformances
3.5 Averaging Aggregation Considering Groups of Conformances
4 Discussion
5 Conclusion
References
Construction of Fuzzy Implication Functions Based on F-chains
1 Introduction
2 Preliminaries
3 F-chains Based Construction of Fuzzy Implication Functions
4 F-chain-based Ordinal Sums of Fuzzy Implication Functions
5 Conclusion
References
Modalities Based on Double Negation
1 Introduction
2 Basic Considerations of Negation
3 Modalities Induced by Two Different Negation Operators
4 Conclusions
References
Condorcet Winners on Bounded and Distributive Lattices
1 Introduction
2 Compatible Preference on a Lattice
3 Voting Rules
4 Characterization of Voting Rules
5 Condorcet Winners
6 Concluding Remarks
References
Author Index

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