Kooperativer Bibliotheksverbund

UID:

Format: 1 Online-Ressource (XXI, 173 p. 56 illus., 50 illus. in color)

Edition: 1st ed. 2021

ISBN: 9783030722807

Series Statement: Studies in Fuzziness and Soft Computing 408

Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-3-030-72279-1

Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-3-030-72281-4

Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-3-030-72282-1

Language: English

DOI: 10.1007/978-3-030-72280-7

URL: Volltext  (URL des Erstveröffentlichers)

URL: Buchcover

UID:

Format: 1 online resource (186 pages)

ISBN: 9783030722807 , 3030722805

Series Statement: Studies in fuzziness and soft computing ; Volume 408

Note: Intro -- Foreword -- Preface -- Introduction-Aggregation and Intelligent Decision -- Contents -- List of Figures -- List of Tables -- Elements of Nilpotent Fuzzy Logic -- 1 Connectives: Conjunctions, Disjunctions and Negations -- 1.1 Introduction -- 1.2 Preliminaries -- 1.2.1 Negations -- 1.2.2 Triangular Norms and Conorms -- 1.3 Characterization of Strict Negation Operators -- 1.4 Nilpotent Connective Systems -- 1.4.1 Structural Properties of Connective Systems -- 1.4.2 Consistent Connective Systems -- 1.5 Summary -- References -- 2 Implications -- 2.1 Introduction -- 2.2 Preliminaries -- 2.3 R-Implications in Bounded Systems -- 2.4 S-Implications in Bounded Systems -- 2.4.1 Properties of iSn, iSd and iSc -- 2.4.2 S-Implications and the Ordering Property -- 2.5 A Comparison of Implications in Bounded Systems -- 2.6 Min and Max Operators in Nilpotent Connective Systems -- 2.7 Summary -- References -- 3 Equivalences -- 3.1 Introduction -- 3.2 Preliminaries -- 3.3 Equivalences in Bounded Systems -- 3.3.1 Properties of ec(x,y) and ed(x,y) -- 3.4 Dual Equivalences -- 3.4.1 Properties of bared and barec -- 3.5 Arithmetic Mean Operators in Bounded Systems -- 3.6 Aggregated Equivalences -- 3.6.1 Properties of the Aggregated Equivalence Operator -- 3.7 Applications -- 3.8 Summary -- References -- 4 Modifiers and Membership Functions in Fuzzy Sets -- 4.1 Introduction -- 4.2 Unary Operators in Nilpotent Logical Systems -- 4.2.1 Possibility and Necessity as Unary Operators Derived from Multivariable Operators -- 4.2.2 Drastic Unary Operators -- 4.2.3 Composition Rules -- 4.2.4 Multivariable Operators Derived from Unary Operators -- 4.2.5 A General Framework: The α, β, γ- Model -- 4.3 Unary Operators Induced by Negation Operators -- 4.4 Membership Functions -- 4.5 Non-membership Functions -- 4.6 Summary -- References -- Decision Operators. , 5 Aggregative Operators -- 5.1 Introduction -- 5.2 Preliminaries -- 5.3 Shifting Transformations on the Generator Functions - A General Parametric Formula -- 5.4 The Weighted General Operator -- 5.5 Properties of the General and the Weighted General Operator -- 5.5.1 The De Morgan Property -- 5.5.2 Bisymmetry -- 5.6 The Two-Variable General and Weighted Aggregative Operator -- 5.7 Summary -- References -- 6 Preference Operators -- 6.1 Introduction -- 6.2 Operators of Nilpotent Systems - A General Framework -- 6.2.1 Normalization of the Generator Functions -- 6.2.2 The General Parametric Operator -- 6.2.3 The Unary Operators: Negation, Modifiers and Hedges -- 6.3 Preference Modeling -- 6.4 Properties of the Preference Operator -- 6.4.1 Basic Properties -- 6.4.2 Ordering Properties -- 6.4.3 Preference and Negation -- 6.4.4 Preference, Conjunction and Disjunction -- 6.4.5 Preference and Aggregation -- 6.4.6 Additive Transitivity -- 6.4.7 Bisymmetry and the Common Base Property -- 6.4.8 Preference and Unary Operators -- 6.5 Summary -- References -- Learning and Neural Networks -- 7 Squashing Functions -- 7.1 Introduction -- 7.2 Łukasiewicz Operators -- 7.3 Approximation of the Cutting Function -- 7.3.1 The Sigmoid Function -- 7.3.2 The Interval [a,b] Squashing Function -- 7.3.3 The Error of the Approximation -- 7.4 Approximation of Piecewise Linear Membership Functions -- 7.5 Summary -- References -- 8 Learning Rules -- 8.1 Introduction -- 8.2 Problem Definition and Solution Outline -- 8.3 Preliminaries -- 8.4 The Structure and Representation of the Rules -- 8.5 The Optimization Process -- 8.5.1 Rule Optimization by GA -- 8.5.2 A Gradient-Based Local Optimization of Memberships -- 8.6 Applications -- 8.7 Summary -- References -- 9 Interpretable Neural Networks Based on Continuous-Valued Logic and Multi-criteria Decision Operators -- 9.1 Introduction. , 9.2 Related Work -- 9.3 Nilpotent Logical Systems and Multicriteria Decision Tools -- 9.4 Nilpotent Logic-Based Interpretation of Neural Networks -- 9.5 Playground Examples -- 9.5.1 XOR -- 9.5.2 Preference -- 9.6 Summary -- References -- 10 Conclusions.

Additional Edition: ISBN 9783030722791

Additional Edition: ISBN 3030722791

Language: English

Keywords: Llibres electrònics ; Llibres electrònics

UID:

Format: XXI, 173 p. 56 illus., 50 illus. in color. , online resource.

Edition: 1st ed. 2021.

ISBN: 9783030722807

Series Statement: Studies in Fuzziness and Soft Computing, 408

Content: The research presented in this book shows how combining deep neural networks with a special class of fuzzy logical rules and multi-criteria decision tools can make deep neural networks more interpretable - and even, in many cases, more efficient. Fuzzy logic together with multi-criteria decision-making tools provides very powerful tools for modeling human thinking. Based on their common theoretical basis, we propose a consistent framework for modeling human thinking by using the tools of all three fields: fuzzy logic, multi-criteria decision-making, and deep learning to help reduce the black-box nature of neural models; a challenge that is of vital importance to the whole research community.

Note: Chapter 1: Connectives: Conjunctions, Disjunctions and Negations -- Chapter 2: Implications -- Chapter 3: Equivalences -- Chapter 4: Modifiers and Membership Functions in Fuzzy Sets -- Chapter 5: Aggregative Operators -- Chapter 6: Preference Operators.

In: Springer Nature eBook

Additional Edition: Printed edition: ISBN 9783030722791

Additional Edition: Printed edition: ISBN 9783030722814

Additional Edition: Printed edition: ISBN 9783030722821

Language: English

DOI: 10.1007/978-3-030-72280-7

URL: https://doi.org/10.1007/978-3-030-72280-7