Aggregation Functions in Theory and in Practise, 1st Edition

  • Published By:
  • ISBN-10: 3642391656
  • ISBN-13: 9783642391651
  • DDC: 515.724
  • Grade Level Range: College Freshman - College Senior
  • 552 Pages | eBook
  • Original Copyright 2013 | Published/Released June 2014
  • This publication's content originally published in print form: 2013

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This volume collects the extended abstracts of 45 contributions of participants to the Seventh International Summer School on Aggregation Operators (AGOP 2013), held at Pamplona in July, 16-20, 2013. These contributions cover a very broad range, from the purely theoretical ones to those with a more applied focus. Moreover, the summaries of the plenary talks and tutorials given at the same workshop are included.Together they provide a good overview of recent trends in research in aggregation functions which can be of interest to both researchers in Physics or Mathematics working on the theoretical basis of aggregation functions, and to engineers who require them for applications.

Table of Contents

Front Cover.
Editorial Board.
Title Page.
Copyright Page.
Invited Speakers.
1: Invited Talks.
2: Functional Equations Involving Fuzzy Implications and Their Applications in Approximate Reasoning.
3: Aggregation Operators and Observable Properties of Human Reasoning.
4: Copulas, Tail Dependence and Applications to the Analysis of Financial Time Series.
5: On Quadratic Constructions of Copulas.
6: Compatible Group Decisions.
7: A Review of the Relationships between Aggregation, Implication and Negation Functions.
8: Copulas.
9: On Some Construction Methods for Bivariate Copulas.
10: On the Construction of Semiquadratic Copulas.
11: Copulas and Self-affine Functions.
12: Diagonal Copulas.
13: R Package to Handle Archimax or Any User-Defined Continuous Copula Construction: Acopula.
14: How to Prove Sklar's Theorem.
15: Ordered Aggregation.
16: OM3: Ordered Maxitive, Minitive, and Modular Aggregation Operators: Axiomatic Analysis under Arity-Dependence (I).
17: OM3: Ordered Maxitive, Minitive, and Modular Aggregation Operators. A Simulation Study (II).
18: Duplication in OWA-Generated Positional Aggregation Rules.
19: Application of OWA Operators in the L-Fuzzy Concept Analysis.
20: Norm Aggregations and OWA Operators.
21: T-norms.
22: Migrativity of Uninorms over T-norms and T-conorms.
23: Additive Generators of Overlap Functions.
24: Continuous T-norms and T-conorms Satisfying the Principle of Inclusion and Exclusion.
25: On Mulholland Inequality and Dominance of Strict Triangular Norms.
26: Distributivity Equation in the Class of Noncommutative T-Operators.
27: On Some Classes of Discrete Additive Generators.
28: Multi-criteria Decision Making.
29: The Consensus Functional Equation in Agreement Theory.
30: A Discriminative Dynamic Index Based on Bipolar Aggregation Operators for Supporting Dynamic Multi-criteria Decision Making.
31: Social Choice Voting with Linguistic Preferences and Difference in Support.
32: Calibration of Utility function.
33: Uncertain Choices: A Comparison of Fuzzy and Probabilistic Approaches.
34: Bayes Theorem, Uninorms and Aggregating Expert Opinions.
35: Applications.
36: On the Induction of New Fuzzy Relations, New Fuzzy Operators and Their Aggregation.
37: Comparison of Different Algorithms of Approximation by Extensional Fuzzy Subsets.
38: On the Symmetrization of Quasi-metrics: An Aggregation Perspective.
39: Aggregation Operators and Quadric Hypersurfaces.
40: An Analysis of Bilevel Linear Programming Solving Parameters Based on Factoraggregation Approach.
41: Upper Bounding Overlaps by Groupings.
42: A Preliminary Study of the Usage of Similarity Measures to Detect Singular Points in Fingerprint Images.
43: Fuzzy Transforms.
44: F-transform in View of Aggregation Functions.
45: Fuzzy Hit-or-Miss Transform Using the Fuzzy Mathematical Morphology Based on T-norms.
46: Image Reduction Operators as Aggregation Functions: Fuzzy Transform and Undersampling.
47: Implications.
48: Implications Satisfying the Law of Importation with a Given T-norm.
49: Fuzzy Implication Classes Satisfying a Boolean-Like Law.
50: Implications Generated by Triples of Monotone Functions.
51: A Generalization of a Characterization Theorem of Restricted Equivalence Functions.
52: Integrals.
53: Some New Definitions of Indicators for the Choquet Integral.
54: Exponential Family of Level Dependent Choquet Integral Based Class-Conditional Probability Functions.
55: Axiomatic Foundations of the Universal Integral in Terms of Aggregation Functions and Preference Relations.
56: Incomplete Data.
57: Aggregation of Incomplete Qualitative Information.
58: Consistency and Stability in Aggregation Operators: An Application to Missing Data Problems.
59: Aggregation on Lattices.
60: Quasi-OWA Operators on Complete Lattices.
61: Obtaining Multi-argument Fuzzy Measures on Lattices.
62: Aggregation of Convex Intuitionistic Fuzzy Sets.