Series Preface
Volume Preface
Soft and Nature-Inspired Computing
Mathematical Fuzzy Sets and Rough Sets
(Generalized) Topological Computing
Granular Computing (GRC)
Soft and Various Forms of Intelligent Computing
Contents
About the Editor-in-Chief
About the Volume Editors
Contributors
Cooperative Multi-hierarchical Query Answering Systems
Glossary
Definition of the Subject
Introduction
Multi-hierarchical Decision System
Cooperative Query Answering
Future Directions
Bibliography
Dependency and Granularity in Data-Mining
Definition of the Subject
Introduction
Contingency Table from Rough Sets
Notations
Contingency Table (m x n)
Rank of Contingency Table (2 x 2)
Preliminaries
Independence When the Table Is 2 x 2
Rank of Contingency Table (m x n)
Rank and Degree of Dependence
Submatrix and Subdeterminant
Rank and Subdeterminant
Rank and Submatrix
Determinantal Divisors
Divisors and Degree of Dependence
Subdeterminants and Degree of Dependence
Elementary Divisors and Elementary Transformation
Degree of Granularity and Dependence
Conclusion
Acknowledgments
Bibliography
Fuzzy Logic
Glossary
Definition of the Subject
Introduction
Conceptual Structure of Fuzzy Logic
The Basics of Fuzzy Set Theory
The Concept of Granulation
The Concepts of Precisiation and Cointensive Precisiation
The Concept of Cointension
The Concept of a Generalized Constraint
Constrained Variable
Modalities of Generalized Constraints
Possibilistic Constraint
Probabilistic Constraint
Veristic Constraint (Zadeh 1999, 2005a)
Fuzzy Graph Constraint
Usuality Constraint (Zadeh 1999, 2002)
Primary Constraints
Standard Constraints
Generalized Constraint Language (GCL) (Zadeh 1999, 2005a)
Deduction
Principal Contributions of Fuzzy Logic
Fuzzy Logic as the Basis for Generalization of Scientific Theories
A Glimpse of What Lies Beyond Fuzzy Logic
Bibliography
Primary Literature
Books and Reviews
Fuzzy Probability Theory
Glossary
Fuzzy Set and Fuzzy Vector
α-Level Set and Support
σ-Algebra
Definition
Introduction
Mathematical Environment
Fuzzy Random Variables
Fuzzy Probability
Representation of Fuzzy Random Variables
Application Fields
Future Directions
Bibliography
Primary Literature
Books and Reviews
Fuzzy System Models Evolution from Fuzzy Rulebases to Fuzzy Functions
Glossary
Definition of the Subject
Introduction
Type 1 Fuzzy System Models of the Past
Type 1 Fuzzy Rulebases
Type 1 Special Fuzzy Functions´´ of the Recent Past
Special Fuzzy Functions with LSE (SFF-LSE) Method
Support Vector Machines for Regression
Special Fuzzy Functions with SVM (FF-SVM) Method
Future of Fuzzy System Models
Basic Definitions
General Structure of Type 2 Fuzzy System Models
Discrete Interval Valued Type 2 Fuzzy Sets (DIVT2FS)
Discrete Interval Valued Type 2Special Fuzzy Functions´´, (SFF)
Case Study Applications
Daily Stock Price Dataset
Income Prediction Dataset
Desulphurization Dataset
Experimental Design
Sugeno-Yasukawa Models and Takagi-Sugeno Models
Special Fuzzy Functions Models (SFFM)
Experimental Model Results
Conclusions and Future Directions
Bibliography
Primary Literature
Books and Reviews
On Genetic-Fuzzy Data-Mining Techniques
Glossary
Definition of the Subject and Its Importance
Introduction
Data Mining
Fuzzy Sets
Fuzzy Data Mining
Genetic Algorithms
Genetic-Fuzzy Data-Mining Techniques
The Integrated Genetic-Fuzzy Problem for Items with a Single Minimum Support (IGFSMS)
The Integrated Genetic-Fuzzy Problem for Items with Multiple Minimum Supports (IGFMMS)
The Divide-and-Conquer Genetic-Fuzzy Problem for Items with a Single Minimum Support (DGFSMS)
The Divide-and-Conquer Genetic-Fuzzy Problem for Items with Multiple Minimum Supports (DGFMMS)
Multiobjective Genetic-Fuzzy Data Mining
Future Directions
Bibliography
Granular Computing and Data Mining for Ordered Data: The Dominance-Based Rough Set Approach
Glossary
Definition of the Subject and Its Importance
Introduction: Granular Computing and Ordered Data
Philosophical Basis of DRSA Granular Computing
Dominance-Based Rough Set Approach
Fuzzy Set Extensions of the Dominance-Based Rough Set Approach
Variable-Consistency Dominance-Based Rough Set Approach (VC-DRSA)
Dominance-Based Rough Approximation of a Fuzzy Set
Monotonic Rough Approximation of a Fuzzy Set Versus Classical Rough Set
Dominance-Based Rough Set Approach to Case-Based Reasoning
An Algebraic Structure for Dominance-Based Rough Set Approach
Conclusions
Future Directions
Bibliography
Granular Computing, Information Models for
Glossary
Definition of the Subject
Introduction
Candidate Information Models
The Relational Data Model (RDM)
The Attribute-Based Data Model (ABDM)
The Functional Data Model (FDM)
The Extensible Markup Language (XML)
The Resource Description Framework (RDF)
The Web Ontology Language (OWL)
Suitability of Information Models for Granular Computing
Formalism and Theory
Expressive Power
Extensibility and Utility
Future Directions
Bibliography
Introduction to Granular Computing
Granular Computing from Rough Set and Generalized Theory
Granular Computing in Database Theory
Granular Computing in Social Networks
Granular Computing and Fuzzy Set Theory
Grid/Cloud Computing: A New Addition to GrC
General Issues in Granular Computing
Conclusion
Bibliography
Granular Computing and Modeling of the Uncertainty in Quantum Mechanics
Glossary
Definition of the Subject
Introduction
Quantum Postulates and Associated Propositions
0th Postulate of Quantum Mechanics
1st Postulate of Quantum Mechanics
2nd Postulate of Quantum Mechanics
3rd Postulate of Quantum Mechanics
Dirac´s Bra and Ket Notations and the Realization of Wave Function
Realization of q-Representation in Quantum Mechanics
Fourier Transformation and p-Representation
Quantum Uncertainty and Non-compatibility of Observables P and X
Conclusion
Future Directions
Bibliography
Philosophical Foundation for Granular Computing
Glossary
Definition of the Subject and Its Importance
Introduction
The Road to Granular Computing
The Nature of Granule and Granule Computing
The Nature of Granule
The Nature of Granular Computing
Granule Measurement
Granular Structure
Quotient View: Information Hiding
Granular Computing and Ontologies
Information Hiding and Emergence
Granulation Provides a Unified View for Intelligent Problem Solving
Re-examination of Existing Studies from a GrC Perspective
Forming Intelligent Problem Solving Tasks in Terms of Concepts in Granular Computing
Granular Computing and Data Mining/OLAP
Relationship Between These Two Fields
Granular Computing as a Basis for Data Mining and OLAP
Relationship with Soft Computing and Natural Computing
Relationship with Fundamental Issues of Computing and Complex Systems Problem Solving
Granular Computing as Infrastructures for AI-Engineering
Granular Computing and New Computational Models
Temporal Aspects of Information Granules
Today´s Big Challenges from Big Data
Dynamic Granule: Capturing Dynamic Nature of Granules
Temporal Aspects of Time-Varying Data
Importance of Exploring Dynamic Granules at Big Data Era
Other Related Developments
Summary
Future Directions
Acknowledgments
Bibliography
Primary Literature
Granular Computing: Practices, Theories, and Future Directions
Glossary
Definition of the Subject
How Important Is Granular Computing?
What Is Granular Computing?
Illustration of Working Formal Models
Introduction
Classical Examples of Granulation
Ancient Examples
Modern Examples
Further Examples
Formal Models of Granulation
First GrC Models and Ancient Examples
Brief pre-GrC Historical Notes
Second GrC Models and Modern Examples
Third and Fourth GrC Models and Modern Examples
Models for Further Examples
Category Theory Based Models
Overview of Early GrC Models
Granular and Related Structures
Integration - A Dual of Granulation
Simple Examples of Integration
Semantic Views
Future Directions
Bibliography
Principles and Perspectives of Granular Computing
Glossary
Definition of the Subject of Its Importance
Introduction
Perspectives of Granular Computing
Neighborhood System: A Mathematical Structure of Granular Computing
Neighborhood System
Approximation
Rough Set System: An Equivalence Neighborhood System
Partition
Approximation
Information Systems
Quotient Space
Fuzzy Set System: A Fuzzy Neighborhood System
Information Granularity
Approximation
Granular Computing in Data Mining
Granular Computing in Classification and Clustering
Granular Computing in Association Mining
A Framework for Granular Computing in Data Mining
Granular Computing in Software Engineering
User Requirements
System Analysis
System Design
System Implementation
Future Directions
Bibliography
Primary Literature
Granular Computing System Vulnerabilities: Exploring the Dark Side of Social Networking Communities
Glossary
Definition of the Subject
Introduction
Background on Social Networking Communities
Traditional Attacks Targeting Social Networking Communities
Malware Propagation
Worms
Spyware
Adware
Spam
Phishing
New Attacks Against Social Networking Communities
Social Spam
Campaigns
Misinformation
Future Directions
Bibliography
Granular Model for Data Mining
Glossary
Definition of the Subject
Introduction
Granular Model: Syntax and Semantics for Data Mining
Granular Model Definition
Motivation and Examples
Semantic Model
Knowledge Systems and Granularity
Data Mining as Generalization
Data Mining Operators
Data Mining Process
Descriptive Model
K-Descriptive Language
K- Satisfaction and K- Truth
Descriptive Language and Descriptive Model
Granular Model Revisited: Satisfaction and Truth
Future Directions
Bibliography
Granular Neural Networks
Glossary
Definition of the Subject
Introduction
Basic Architecture
First Architecture of Granular Neural Network
Layer 1: Linguistic Feature Extraction Layer
Layer 2: Multi-FNNKD Layer
Layer 3: Output Layer
Second Architecture of Granular Neural Network
Deep Granular Neural Networks
Granular Learning Algorithms
Local Forward-Wave Learning
Procedure of Local Forward-Wave Learning
Global Backward-Wave Learning
Procedure of Global Backward-Wave Learning
Forward-Wave-Backward-Wave Learning
Procedure Genetic Forward-Wave-Backward-Wave Learning
Applications in Bioinformatics
Applications in Computational Web Intelligence
Concepts of Input Data
Overview of Implementation
Performance
Applications in Brain Informatics
Conclusions
Future Directions
Bibliography
Granulation of Knowledge: Similarity Based Approach in Information and Decision Systems
Glossary
Definition of the Subject and Its Importance
Introduction: Basic Ideas
Similarity
Information and Decision Systems
Granulation of Knowledge: General Ideas and Technique of Rough Inclusions
A General Form of Similarity
Granulation: Tools
Granulation by Means of Rough Inclusions
Mereological Theory of Concepts
Rough Inclusions
Calculus on Granules
Some Principal Fields of Applications
Reasoning About Uncertainty
Reasoning in Distributed Systems
Reasoning in Cognitive Schemes: Rough Neural Reasoning
Applications in Data Mining: Granular Classifiers
Granules from Parameterized Variants of Rough Inclusions μh in Classification of Data
Complexity Issues
Future Directions
Bibliography
Primary Literature
Books and Reviews
Multi-Granular Computing and Quotient Structure
Glossary
Definition of the Subject
Introduction
The Granularity Relation
Truth Preserving Property
Falsity Preserving Property
Hierarchy
The Computational Complexity Under Deterministic Model
Combination
The Construction of Quotient-Space Model
The Combination of Quotient Spaces
The Combination of Attribute Functions
Future Directions
Acknowledgments
Bibliography
Non-standard Analysis, an Invitation to
Glossary
Definition of the Subject
Introduction
Differential = Infinitesimal Difference?
Structure of This Article
Pre-Robinson Infinitesimals
Recap: Naive Set Notations
Ordered Field Extension
Classical Augmented Infinities
Non-Archimedean Infinitesimal
Hyperreals
The Construction of Ultimate-Reals
Star-Extensions
NS View of Continuous Functions
NS Calculus
NS Integral Calculus
NS-ODE
General Idea of NSA
The Set-Terminology
Naive Set Operations
The Ultra-Power Construction
Some Consequences of Transference
Loeb Construction
Measure
Loeb Measure
Anderson´s Wiener Process
A Future for Non-standard Analysis?
Bibliography
Information System Design Using Fuzzy and Rough Set Theory
Glossary
Definition of the Subject and Its Importance
Introduction
Fuzzy Sets and Rough Sets
Fuzzy Set Theory
Rough Set Theory
Rough Relational Database
Information Theory
Entropy and the Rough Relational Database
Rough Fuzzy Relational Database
Fuzzy Rough Relational Operators
Difference
Union
Intersection
Select
Project
Join
Rough Set Modeling of Spatial Data
Data Mining in Rough Databases
Aggregation of Uncertain Information
Future Directions
Acknowledgments
Bibliography
Primary Literature
Books and Reviews
Rough Set Data Analysis
Introduction
Focusing Mechanism
Definition of Rules
Rough Sets
Classification Accuracy and Coverage
Probabilistic Rules
Positive Rules
Negative Rules
Algorithms for Rule Induction
Experimental Results
Performance of Rules Obtained
What Is Discovered?
Interesting Rules Are Very Few
Positive Rules in Differential Diagnosis of Headache
Negative Rules in Differential Diagnosis of Headache
Positive Rules in Meningitis
Positive and Negative Rules in CVD
Rule Discovery as Knowledge Acquisition and Decision Support
Expert System: RH
Evaluation of RH
Discussion
Hierarchical Rules for Decision Support
Relations Between Rules
Conclusions
Bibliography
Rule Induction, Missing Attribute Values, and Discretization
Glossary
Discretization
LEM2 Algorithm
LERS Machine Learning/Data Mining System
Missing Attribute Values
Rule Induction
Definition of the Subject and Its Importance
Introduction
Discretization
LEM2 Algorithm
Procedure LEM2
Inconsistent Data
Missing Attribute Values
Lower and Upper Approximations
Probabilistic Approximations
MLEM2
Classification System
Validation
Future Directions
Bibliography
Social Networks and Granular Computing
Glossary
Definition of the Subject and Its Importance
Introduction
Mathematical Preliminaries
Sets
Multisets
Relations
Rough Set Theory: Functional Granulation
Positional Analysis: Relational Granulation
Modal Logic: The Bridge
Propositional Multi-modal Logic
Graded Modal Logic
Hybrid Logic
From Relational Granulation to Functional Granulation
Structural Equivalences and Hybrid Logics
Regular Equivalences and Multi-modal Logics
Exact Equivalences and Graded Modal Logics
Observational Equivalences
Related Work
Conclusion and Future Directions
Bibliography
Rough Sets in Decision-Making
Entry Outline
Glossary
Definition of the Subject and Its Importance
Introduction to Decision Support Using Rough Set Concept
Classical Rough Set Approach to Classification Problems of Taxonomy Type
Data Table and Indiscernibility Relation
Approximations
Dependence and Reduction of Attributes
Decision Table and Decision Rules
Explanation of the Classical Rough Set Approach by an Example
Dominance-Based Rough Set Approach to Ordinal Classification Problems
Dominance-Based Rough Set Approach (DRSA)
Example Illustrating DRSA in the Context of Ordinal Classification
Robust Ordinal Regression for DRSA
DRSA on a Pairwise Comparison Table for Multiple Criteria Choice and Ranking Problems
Multiple Criteria Choice and Ranking Problems
The Pairwise Comparison Table
Approximation by Means of Graded Dominance Relations
Decision Rules
Application of the Decision Rules and Final Recommendation
Approximation by Means of Multi-graded Dominance Relations
Dominance Without Degrees of Preference
Example Illustrating DRSA in the Context of Multiple Criteria Choice and Ranking
DRSA for Decision Under Uncertainty
Basic Concepts
Example Illustrating DRSA in the Context of Decision Under Uncertainty
Multiple Criteria Decision Analysis Using Association Rules
Interactive Multiobjective Optimization Using DRSA (IMO-DRSA)
Example Illustrating IMO-DRSA in the Context of Multiobjective Optimization
Characteristics of the IMO-DRSA
Some Dedicated Applications of the IMO-DRSA: Financial Portfolio and Project Portfolio
An Abstract Algebra for Reasoning About Multiple Criteria Decisions: The Bipolar Pawlak-Brouwer-Zadeh Lattice
Conclusions
Prospective Directions of Applications
Bibliography
Knowledge Engineering from Email Archives
Glossary
Definition of the Subject
Introduction
Email Format History
Email System
Email Security and SPAM Prevention
Email Clients
Email Archiving
Compliance/Surveillance
eDiscovery
Archiving Modes
Archiving Tasks
Mail Parsing
Storing of Mails
User Association
Indexing and Querying
Implicit/Hidden Knowledge in Email Archives
Future Directions
Bibliography
Fuzzy Similarity for Parallel Function Computation Model
Background
OpenCL (Open Computing Language)
Fuzzy Similarity for Natural Language Processing (NLP)
Introduction
word2vec
Mathematical Transformations
Book Cataloging
Translations in Natural Language Processing
Bibliography
Mereology
Glossary
Introduction
First-Order Logic
First-Order Mereological Axioms and Theories
Alternative Formulations
Models of Mereological Theories
Decidability Concerning First-Order Mereological Theories
Fuzzification of Mereology
Future Directions
Acknowledgments
Bibliography
Primary Literature
Books and Reviews
Variable Precision Approximations of Rough Sets
Introduction
Basics of Pawlak´s Rough Sets
Approximation Space
Set Approximation Regions
Variable Precision Rough Set Model
Set Frequency and Conditional Frequency
Approximation Regions in the VPRSM
Absolute Set Approximation Regions
Decision Tables Learned from Data
Attributes
Deterministic and Nondeterministic Decision Tables
Probabilistic Decision Tables
Dependencies in Probabilistic Decision Tables
γ - Dependency Measure
λ - Dependency Measure
Reduction and Significance of Attributes
Attribute Reduct
Significance of Attributes
Final Remarks
Bibliography
Algebraic Models and Granular Computing
Glossary
Definition of the Subject
Introduction: Algebraic Models
Example: Boolean Algebras and Classical Logic
Example: Some Non-Boolean Algebras and Nonclassical Logics
E1. Positive Implication Algebras
Equational Definability of PIA
Positive Implication Algebra of Sets
E2. Implication Algebras
Implication Algebra IA
Equational Definability of IA
Implication Algebra of Sets
E3. Peirce Algebras
Peirce Algebra PA
Equational Definability of PA
Peirce Algebra of Sets
Filters in Peirce Algebras
E4. Quasi-Boolean Algebras and De Morgan Lattices
Quasi-Boolean Algebra
De Morgan Lattice
QBA of Sets
Granular Computing
S5 Rough Algebra
Construction of Modal Lindenbaum-Tarski Algebra
Modal Lindenbaum-Tarski Algebra
S5 Rough Algebra Construction
Properties of the S5 Rough Algebra
Questions and Observations
Topological Rough Algebras
Generalized Rough Sets, L-Fuzzy, and LT-Fuzzy Sets
LT-Fuzzy Sets
Generalized Rough Sets
Approximation Space
Topological Space
Approximation Topological Space
Topological and Rough Equalities
Rough, L-Fuzzy, and LT-Fuzzy Sets
Bibliography
Set-Valued Mapping for Generalized Rough Approximation and Application to Clustering Algorithm
Introduction
Rough Approximation and Generalizations
A Class of Generalizations
A Set-Valued Mapping and Rough Approximations
The Case of Neighborhood
Soft Boundary in an Euclidean Space
Application to K-Means Clustering
K-Means Algorithm
Allocation Rule
Rough Approximations
Optimization Problem
An Illustrative Example
Conclusion
Bibliography
Fuzzy System Representations of Stochastic Systems
Glossary
Definition of the Subject
Introduction
Background of Stochastic Systems
Fuzzy Reasoning Meaning of Continuous Stochastic Systems
Fuzzy Reasoning Representations of Double-Inputs and Single-Output Continuous Stochastic Systems
Fuzzy Reasoning Representations of Discrete Stochastic Systems
Reducibility in the Transformations Between Fuzzy Systems and Stochastic Systems
The Uncertainty Systems with One-Dimensional Random Variable and Their Representations
Typical Case 1: Pure Certainty Systems
Typical Case 2: Pure Stochastic Systems
Typical Case 1
Typical Case 2
Unification on Uncertainty Systems
Conclusions
Bibliography
Function Approximation Property of Fuzzy Systems and Its Error Analysis
Glossary
Definition of the Subject
Introduction
Structures of Fuzzy Systems
Function Approximation Property of Fuzzy Systems
The Approximate Remainder Formula of fn(x) to Continuous Function s(X)
The Error Estimation Between Fuzzy System and fn(x)
Simulation Example
Conclusions
Bibliography
Issues in Access Control and Privacy for Big Data
Glossary
Definition of the Subject
Introduction
Access Control and Privacy
Access Control
Privacy
Access Control Versus Privacy
4 Vs of Big Data
Volume
Variety
Velocity
Veracity
Putting it All Together
Summary and Future Directions
Bibliography
Security Situational Awareness: A Practical Approach for a Complex Heterogeneous Environment
Glossary
Definition of the Subject
Introduction
Security-Relevant Data That Is Useful for Protecting a Data Center
Vulnerability Data
Network Flow Data
DNS Data
Intrusion Detection System Data
Centralized Log Data
Risk-Partitioning the Mountain of Data
Partitioning Based on Acceptable Risk
Partitioning Based on High Risk
Partitioning Based on Unknown Risk
Results of Partitioning
Data Enrichment to Facilitate Actionable Security Event Detection
Detecting Actionable Security Events
Vulnerabilities
System´s Software Vulnerability
Vulnerabilities Due to Misconfiguration of Computer Systems or Networks
Vulnerability-Related Policy Violation
Intrusions
Intrusion Detection System Events
Brute-Force Attacks
Suspicious Logins
APTs, Malware Beacons, and Back Doors
Suspicious DNS Activity
Policy Violations
Insider Threats and Data Exfiltration
Future Directions
Bibliography
Security with Privacy
Introduction
Privacy Enhancing Techniques for Security
Privacy-Preserving Data Matching
Privacy-Preserving Collaborative Data Mining
Privacy-Preserving Biometrics Authentication
Privacy-Preserving Fine-Grained Access Control for Cloud Data
Future Directions
Concluding Remarks
Acknowledgments
Glossary
References
Privacy Preservation in Big Data Analytics
Definition of Subject
Glossary
Introduction
What Is Big Data
Open Data for Governments
Big Data: Issues and Challenges
Privacy Law
Privacy Preservation Data Publishing
Well-Known Examples for Privacy Preservation in Re-identification Problems
Techniques for Privacy Preserving Data Publishing
k-Anonymity on Relational Data
l-Diversity and t-Closeness on Relational Data
Anonymization Methods on Transactional Data
Anonymization Methods on Social Network Data
Privacy Versus Utility
Differential Privacy
The Challenges on Big Data Privacy Preservation
Current Techniques for Privacy Preservation on Big Data
Opening Issues to Privacy Preservation on Big Data
Privacy Preservation Big Data Publishing Issues
Privacy Preservation Big Data Mining Issues
Summary
Bibliography
Access Control for XML Big Data Applications
Introduction
Use-Case Background
UML Extensions for Document Modeling
Extensions for Document Security Policy Modeling and Integration
Integrating Local Security Policies into a Global Security Policy
Assumptions and Equivalence Finding
Integration Process for Local Security Policy Sets
Resolving Conflicts of Integrated Security Rule Sets
Creating the Global Security Policy
Related Work
Conclusion
Bibliography
A Theory of Approximate Arithmetic for Numerical Analysis: A Mathematical Foundation
Glossary
Definition of the Subject
Introduction
SRNC: Approximation for Numerical Computing
SRNC: A Paradox? In Approximate Addition
Backgrounds: Lemmas, Notations, and Conventions
Approximations, Metersticks, and Topologies
Measuring Functions and Topologies
Approximate Arithmetic
Semi-group
Semi-group
Topological Fields
Isomorphisms of Ordered Fields
Conclusions
References
Interval Computing
Definition of Interval Computing
Introduction
Motivation
Early History
Modern History
Key Information
Basic Definitions and Properties
Current Uses
Reference Resources
General and Introductory Books
Applications
Software
Other Resources
Future Directions
References
Aggregation Operators and Soft Computing
Glossary
Definition of the Subject
Introduction
Applications
Aggregation, Integration, and Fusion
Aggregation Operators and Their Construction
Some Aggregation Operators
Quasi-Arithmetic Means
Weighted Means and Quasi-Weighted Means
Losonczi´s Means
Linear Combination of Order Statistics and OWA Operators
The WOWA Operator
Fuzzy Integrals
Future Directions
Bibliography
Primary Literature
Books and Reviews
Evolving Fuzzy Systems
Glossary
Definition of the Subject
Introduction
Evolving Clustering
Evolving TS Fuzzy Systems
Evolving Fuzzy Classifiers
Evolving Fuzzy Controllers
Application Case Studies
Self-Calibrating Intelligent Sensors for Process Industries
Adaptive Real-Time Classifiers (Image, Land-Mark, Robotic)
Predictive Models (Air-Conditioning, Financial Time-Series, Benchmark Data Sets)
Fault Detection and Prognostics
Speech Signal Reconstruction
Future Directions
Acknowledgments
Bibliography
Primary Literature
Books and Reviews
Fuzzy Logic, Type-2 and Uncertainty
Glossary
Definition of the Subject
Introduction
Imprecision
Vagueness or Linguistic Uncertainty
Type-2 Fuzzy Systems
Union of Type-2 Fuzzy Sets
Intersection of Type-2 Fuzzy Sets
Generalized Type-2 Fuzzy Systems
Interval Type-2 Fuzzy Sets and Systems
Interval Type-2 Fuzzy Sets
Interval Type-2 Fuzzy Logic Systems
Applications
Future Directions
Bibliography
Fuzzy Optimization
Glossary
Definition of the Subject
Introduction
Basics of Fuzzy Set Theory
Extension Principles
Basics of Possibility Theory
Semantics of Fuzzy Sets and Possibility Distributions in Fuzzy Optimization
Fuzzy Relations
Basics of Fuzzy Sets and Possibility Theory in Optimization
Classical Approaches to Fuzzy Optimization
Fuzzy Programming
Possibilistic Programming
Programming with Fuzzy and Possibilistic Components
Possibilistic, Interval, Cloud, and Probabilistic Optimization Utilizing IVPM
Future Directions
Bibliography
Foundations of Fuzzy Sets Theory
Glossary
Definition of the Subject
Introduction
Fuzzy Sets: Basic Definition and Properties
The Idea of a Fuzzy Set
Some Extensions of the Concept of Zadeh´s Fuzzy Set
Basic Definition and Properties Related to Fuzzy Sets
Basic Operations on Fuzzy Sets
Fuzzy Relations
Linguistic Variable, Fuzzy Conditional Statement, and Compositional Rule of Inference
The Extension Principle
Fuzzy Numbers
Fuzzy Events and Their Probabilities
Defuzzification of Fuzzy Sets
Fuzzy Logic: Basic Issues
Bellman and Zadeh´s General Approach to Decision-Making Under Fuzziness
Multistage Decision-Making (Control) Under Fuzziness
Concluding Remarks
Bibliography
Hybrid Soft Computing Models for Systems Modeling and Control
Glossary
Definition of the Subject
Introduction
Genetic Algorithm for Optimization
Genetic Algorithm for Optimization
Evolution of Fuzzy Systems
Application to Anesthesia Control
Anesthesia Control Using Fuzzy Logic
Characteristics of the Fuzzy Controller
Genetic Algorithm Specification
Representation of the Chromosome
Simulation Results for the Case of Anesthesia Control
Application to the Control of the Bar and Ball System
Simulation Results with the Complete HGA
Simulation Results with a Method Dased Only on Mutation
Simulation Results with a Method Based Only on Crossover
Comparison of the Simulation Results
Hierarchical Genetic Algorithms for Neural Networks
Experimental Results for Time Series Prediction
Prediction with a Neural Network
Prediction with an Adaptive Neuro-Fuzzy Inference System (ANFIS)
Prediction with an Interval Type-2 TSK Fuzzy Model
Prediction with a Neuro-Genetic Model
Prediction with Type-1 Fuzzy Models Optimized with Genetic Algorithms
Conclusions
Future Directions
Bibliography
Neuro-fuzzy Systems
Glossary
Definition of the Subject
Introduction
Fuzzy Reasoning
Logical Approach to Fuzzy Inference Reasoning
Mamdani Approach to Fuzzy Inference Reasoning
Description of Fuzzy Inference Systems
Logical-Type Neuro-fuzzy Systems
Mamdani-Type Neuro-fuzzy Systems
Simplified Neuro-fuzzy Systems
Takagi-SugenoNeuro-fuzzy Systems
Neuro-fuzzy Systems with Weights
Neuro-fuzzy Systems for Pattern Classification
Learning
Criteria Isolines Method
Future Directions
Acknowledgments
Bibliography
Possibility Theory
Glossary
Definition of the Subject and Its Importance
Introduction
Historical Background
G. L. S. Shackle
D. Lewis
L. J. Cohen
L. A. Zadeh
Basic Notions of Possibility Theory
Qualitative Possibility Theory
Nonmonotonic Inference
Possibilistic Logic
Decision-Theoretic Foundations
Quantitative Possibility Theory
Possibility as Upper Probability
Conditioning
Probability-Possibility Transformations
From Possibility to Probability
From Objective Probability to Possibility
Possibility Distributions Induced by Prediction Intervals
Subjective Possibility Distributions
Mean Values in Possibility Theory
Applications and Future Directions
Bibliography
Rough Sets: Foundations and Perspectives
Glossary
Definition of the Subject
Introduction
Approximation Spaces
Framework for an Approximation Space
Rough Sets
Information Tables
Decision Systems and Decision Rules
Dimensionality Reduction
Summary
Future Directions
Acknowledgments
Bibliography
Primary Literature
Further Readings - Books
Further Readings - Transactions on Rough Sets
Further Readings - Special Issues of Journals
Further Readings - Proceedings of International Conferences
Introduction to Soft Computing
Statistics with Imprecise Data
Glossary
Definition of the Subject
Introduction
Mathematical Modeling of Imprecise Data
Fuzzy Random Variables
Statistical Analysis of Fuzzy Data Corresponding to Fuzzy Perceptions of Existing Real-Valued Data
Fuzzy Estimation
Fuzzy Statistical Tests
Statistical Analysis of Existing Fuzzy-Valued Data
Fuzzy Estimation
Statistical Tests
Future Directions
Bibliography
Primary Literature
Books and Reviews
Some Remarks on the Foundations of Numerical Analysis
Glossary
Definition of Numerical Analysis
Introduction
Early History
Modern History
Cn Modern Numerical Analysis
Classical References
Future Directions
References
Index