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" New trends in aggregation theory / "
editors, Radomír Halaš, Marek Gagolewski and Radko Mesiar.
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BL
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| Record Number
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862001
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| Main Entry
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International Summer School on Aggregation Operators(2019 :, Olomouc, Czech Republic)
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| Title & Author
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New trends in aggregation theory /\ editors, Radomír Halaš, Marek Gagolewski and Radko Mesiar.
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| Publication Statement
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Cham :: Springer,, 2019.
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| Series Statement
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Advances in intelligent systems and computing ;; 981
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1 online resource
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| ISBN
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3030194949
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: 9783030194949
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9783030194932
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Includes bibliographical references and index.
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| Contents
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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
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2 A Motivating Example3 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
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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
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5.1 Fuzzy Automaton Based on Fuzzy Transition Function5.2 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
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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
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| Abstract
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This book collects the contributions presented at AGOP 2019, the 10th International Summer School on Aggregation Operators, which took place in Olomouc (Czech Republic) in July 2019. It includes contributions on topics ranging from the theory and foundations of aggregation functions to their various applications. Aggregation functions have numerous applications, including, but not limited to, data fusion, statistics, image processing, and decision-making. They are usually defined as those functions that are monotone with respect to each input and that satisfy various natural boundary conditions. In particular settings, these conditions might be relaxed or otherwise customized according to the users needs. Noteworthy classes of aggregation functions include means, t-norms and t-conorms, uninorms and nullnorms, copulas and fuzzy integrals (e.g., the Choquet and Sugeno integrals). This book provides a valuable overview of recent research trends in this area.
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Aggregation operators, Congresses.
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Mathematical statistics, Congresses.
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Soft computing, Congresses.
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Aggregation operators.
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Mathematical statistics.
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MATHEMATICS-- Calculus.
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MATHEMATICS-- Mathematical Analysis.
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Soft computing.
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| Dewey Classification
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515/.724
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| LC Classification
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QA329.I58 2019
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| Added Entry
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Gagolewski, Marek
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Halaš, Radomír
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Mesiar, Radko
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