Theory and Applications of Ordered Fuzzy Numbers : A Tribute to Professor Witold Kosiński

Theory and Applications of Ordered Fuzzy Numbers A Tribute to Professor Witold Kosiński

This book is open access under a CC BY 4.0 license. This open access book offers comprehensive coverage on Ordered Fuzzy Numbers, providing readers with both the basic information and the necessary expertise to use them in a variety of real-world applications. The respective chapters, written by lea...

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Detalles Bibliográficos
Otros Autores: Łukasz Apiecionek (auth), Prokopowicz, Piotr. editor (editor), Czerniak, Jacek. editor, Mikołajewski, Dariusz. editor, Apiecionek, Łukasz. editor, Ślȩzak, Dominik. editor
Formato: Libro electrónico
Idioma:Inglés
Publicado: Cham : Springer Nature 2017
2017.
Edición:1st ed. 2017.
Colección:Studies in Fuzziness and Soft Computing, 356
Materias:
Computational intelligence.
Control engineering.
Operations research.
Decision making.
Management science.
Computational Intelligence.
Control and Systems Theory.
Operations Research/Decision Theory.
Operations Research, Management Science.
fuzzy prediction models
uncertainty modeling
trend processing
propagation of uncertainty
fuzzy arithmetic
analysis
defuzzyfication
Kosinski’s fuzzy numbers
Ver en Biblioteca Universitat Ramon Llull:https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009425407006719
Tabla de Contenidos:
  • Intro
  • Foreword
  • Memories of Professor Witold Kosiński
  • Scientific Development
  • Scientific and Academic Achievements (Part I)
  • Scientific and Academic Achievements (Part II)
  • Scientific Collaboration
  • Teaching and Supervision
  • Scientific and Social Services
  • Personality and Memoires
  • Acknowledgements
  • Contents
  • Part I Background of Fuzzy Set Theory
  • 1 Introduction to Fuzzy Sets
  • 1.1 Classic and Fuzzy Sets
  • 1.2 Fuzzy Sets---Basic Definitions
  • 1.3 Extension Principle
  • 1.4 Fuzzy Relations
  • 1.5 Cylindrical Extension and Projection of a Fuzzy Set
  • 1.6 Fuzzy Numbers
  • 1.7 Summary
  • References
  • 2 Introduction to Fuzzy Systems
  • 2.1 Introduction
  • 2.2 Fuzzy Conditional Rules
  • 2.3 Approximate Reasoning
  • 2.3.1 Compositional Rule of Inference
  • 2.3.2 Approximate Reasoning with Knowledge Base
  • 2.3.3 Fuzzification and Defuzzification
  • 2.4 Basic Types of Fuzzy Systems
  • 2.4.1 Mamdani--Assilan Fuzzy Model
  • 2.4.2 Takagi--Sugeno--Kang Fuzzy System
  • 2.4.3 Tsukamoto Fuzzy System
  • 2.5 Summary
  • References
  • Part II Theory of Ordered Fuzzy Numbers
  • 3 Ordered Fuzzy Numbers: Sources and Intuitions
  • 3.1 Introduction
  • 3.2 Problems with Calculations on Fuzzy Numbers
  • 3.3 Related Work
  • 3.4 Decomposition of Fuzzy Memberships
  • 3.5 Idea of Ordered Fuzzy Numbers
  • 3.6 Summary
  • References
  • 4 Ordered Fuzzy Numbers: Definitions and Operations
  • 4.1 Introduction
  • 4.2 The Ordered Fuzzy Number Model
  • 4.3 Basic Notions for OFNs
  • 4.3.1 Standard Representation of OFNs
  • 4.3.2 OFN Support
  • 4.3.3 OFN Membership Function
  • 4.3.4 Real Numbers as OFN Singletons
  • 4.4 Improper OFNs
  • 4.5 Basic Operations on OFNs
  • 4.5.1 Addition and Subtraction
  • 4.5.2 Multiplication and Division
  • 4.5.3 General Model of Operations
  • 4.5.4 Solving Equations
  • 4.6 Interpretations of OFNs.
  • 4.6.1 Direction as a Trend
  • 4.6.2 Validity of Operations
  • 4.6.3 The Meaning of Improper OFNs
  • 4.7 Summary and Further Intuitions
  • References
  • 5 Processing Direction with Ordered Fuzzy Numbers
  • 5.1 Introduction
  • 5.2 Direction Measurement Tool
  • 5.2.1 The PART Function
  • 5.2.2 The Direction Determinant
  • 5.3 Compatibility Between OFNs
  • 5.4 Inference Sensitive to Direction
  • 5.4.1 Directed Inference Operation
  • 5.4.2 Examples
  • 5.5 Aggregation of OFNs
  • 5.5.1 The Aggregation's Basic Properties
  • 5.5.2 Arithmetic Mean Directed Aggregation
  • 5.5.3 Aggregation for Premise Parts of Fuzzy Rules
  • 5.6 Summary
  • References
  • 6 Comparing Fuzzy Numbers Using Defuzzificators on OFN Shapes
  • 6.1 Introduction
  • 6.2 Formal Approach to the Problem
  • 6.3 Defuzzification Methods
  • 6.3.1 Defuzzification Methods for OFN
  • 6.4 Definition of Golden Ratio Defuzzification Operator
  • 6.4.1 Golden Ratio for OFN
  • 6.5 Golden Ratio
  • 6.6 Defuzzification Conditions for GR
  • 6.6.1 Normalization
  • 6.6.2 Restricted Additivity
  • 6.6.3 Homogeneity
  • 6.7 Definition of Mandala Factor Defuzzification Operator
  • 6.8 Mandala Factor
  • 6.9 Defuzzification Conditions for MF
  • 6.9.1 Normalization
  • 6.9.2 Restricted Additivity
  • 6.9.3 Homogeneity
  • 6.10 Catalogue of the Shapes of Numbers in OFN Notation
  • 6.11 Conclusion
  • References
  • 7 Two Approaches to Fuzzy Implication
  • 7.1 Introduction
  • 7.2 Lattice Structure and Implications on SOFNs
  • 7.2.1 Step-Ordered Fuzzy Numbers
  • 7.2.2 Lattice on mathcalRK
  • 7.2.3 Complements and Negation on calN
  • 7.2.4 Fuzzy Implication on BSOFN
  • 7.2.5 Applications
  • 7.3 Metasets
  • 7.3.1 The Binary Tree T and the Boolean Algebra mathfrakB
  • 7.3.2 General Definition of Metaset
  • 7.3.3 Interpretations of Metasets
  • 7.3.4 Forcing
  • 7.3.5 Set-Theoretic Relations for Metasets.
  • 7.3.6 Applications of Metasets
  • 7.3.7 Classical and Fuzzy Implication
  • 7.4 Conclusions and Further Research
  • References
  • Part III Examples of Applications
  • 8 OFN Capital Budgeting Under Uncertainty and Risk
  • 8.1 Introduction
  • 8.2 Ordered Fuzzy Numbers
  • 8.3 Classic Capital Budgeting Methods
  • 8.4 Fuzzy Approach to the Discount Methods
  • 8.5 Computational Example of the Investment Project
  • 8.6 Summary
  • References
  • 9 Input-Output Model Based on Ordered Fuzzy Numbers
  • 9.1 Introduction
  • 9.2 Input-Output Analysis
  • 9.3 Example of Application of OFNs in the Leontief Model
  • 9.4 Conclusions
  • References
  • 10 Ordered Fuzzy Candlesticks
  • 10.1 Introduction
  • 10.2 Ordered Fuzzy Candlesticks
  • 10.3 Volume and Spread
  • 10.3.1 Volume
  • 10.3.2 Spread
  • 10.4 Ordered Fuzzy Candlesticks in Technical Analysis
  • 10.4.1 Ordered Fuzzy Technical Analysis Indicators
  • 10.4.2 Ordered Fuzzy Candlestick as Technical Analysis Indicator
  • 10.5 Ordered Fuzzy Time Series Models
  • 10.6 Conclusion and Future Works
  • References
  • 11 Detecting Nasdaq Composite Index Trends with OFNs
  • 11.1 Introduction
  • 11.2 Application of OFN Notation for the Fuzzy Observation of NASDAQ Composite
  • 11.3 Ordered Fuzzy Number Formulas
  • 11.4 Conclusions
  • References
  • 12 OFNAnt Method Based on TSP Ant Colony Optimization
  • 12.1 Introduction
  • 12.2 Application of Ant Colony Algorithms in Searching for the Optimal Route
  • 12.3 OFNAnt, a New Ant Colony Algorithm
  • 12.4 Experiment
  • 12.4.1 Experiment Execution Method
  • 12.4.2 Software Used for Experiment
  • 12.4.3 Experimental Data
  • 12.5 Results of Experiment
  • 12.6 Summary and Conclusions
  • References
  • 13 A New OFNBee Method as an Example of Fuzzy Observance Applied for ABC Optimization
  • 13.1 Introduction
  • 13.2 ABC (Artificial Bee Colony) Model
  • 13.3 Selected OFN Issues.
  • 13.4 New Hybrid OFNBee Method
  • 13.5 Experimental Results
  • 13.6 Conclusion
  • References
  • 14 Fuzzy Observation of DDoS Attack
  • 14.1 Introduction
  • 14.2 DDoS Attack Description and Recognition
  • 14.3 The Idea of Attack Recognition and Prevention
  • 14.4 Attack Observation Using OFNs
  • 14.5 Experiment Test Results
  • 14.5.1 Test Description
  • 14.5.2 Attack Detection Using Proposed Method
  • 14.6 Conclusions-Method Comparision
  • References
  • 15 Fuzzy Control for Secure TCP Transfer
  • 15.1 Introduction
  • 15.2 Multipath TCP
  • 15.3 Multipath TCP Schedulers
  • 15.3.1 Multipath TCP Standard Scheduler
  • 15.3.2 Multipath TCP Secure Scheduler
  • 15.3.3 Multipath TCP Scheduler with OFN Usage
  • 15.3.4 OFN for Problem Detection
  • 15.4 OFN Scheduler Algorithm
  • 15.5 Simulation Test Results
  • 15.6 Conclusions
  • References
  • 16 Fuzzy Numbers Applied to a Heat Furnace Control
  • 16.1 Introduction
  • 16.2 Selected Definitions
  • 16.2.1 The Essence of Ordered Fuzzy Numbers
  • 16.2.2 Fuzzy Controller
  • 16.2.3 Control of the Stove on Solid Fuel
  • 16.3 Classic Fuzzy Controller
  • 16.4 The Controller for the OFNs
  • 16.4.1 Directed OFN as a Combustion Trend
  • 16.5 Modeling Trend in the Inference Process
  • 16.6 Conclusions
  • References
  • 17 Analysis of Temporospatial Gait Parameters
  • 17.1 Introduction
  • 17.2 Methods
  • 17.2.1 Subjects
  • 17.2.2 Methods
  • 17.2.3 Statistical Analysis
  • 17.2.4 Fuzzy-Based Tool for Gait Assessment
  • 17.2.5 Main Ideas of the OFN Model
  • 17.2.6 OFN Model in Gait Assessment
  • 17.3 Results
  • 17.4 Discussion
  • 17.5 Conclusions
  • References
  • 18 OFN-Based Brain Function Modeling
  • 18.1 Introduction
  • 18.2 State of the Art
  • 18.2.1 Theory
  • 18.2.2 Modeling Complex Ideas with Fuzzy Systems
  • 18.2.3 Clinical Practice
  • 18.2.4 Models for Linking Hypotheses and Experimental Studies
  • 18.3 Concepts.
  • 18.3.1 Data Ladder
  • 18.3.2 Models of a Single Neuron
  • 18.3.3 Models of Biologically Relevant Neural Networks
  • 18.3.4 Models of Human Behavior
  • 18.4 Traditional versus Fuzzy Approach
  • 18.5 OFN as an Alternative Approach to Fuzziness
  • 18.6 Patterns and Examples
  • 18.6.1 Intuitive Modeling of the Complex Functions
  • 18.6.2 Improving Policy Gradient Method
  • 18.6.3 Modeling Learning Rate with the OFNs
  • 18.7 Discussion
  • 18.7.1 Results of Other Scientists
  • 18.7.2 Limitations of Our Approach and Directions for Further Research
  • 18.8 Conclusions
  • References.

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