Theory and Applications of Ordered Fuzzy Numbers : A Tribute to Professor Witold Kosiński / edited by Piotr Prokopowicz, Jacek Czerniak, Dariusz Mikołajewski, Łukasz Apiecionek, Dominik Ślȩzak.

Format:

Book

Author/Creator:

Łukasz Apiecionek

Contributor:

Prokopowicz, Piotr, Editor.

Czerniak, Jacek, Editor.

Mikołajewski, Dariusz, Editor.

Apiecionek, Łukasz, Editor.

Ślęzak, Dominik, Editor.

Series:

Studies in Fuzziness and Soft Computing, 1434-9922 ; 356

Language:

English

Subjects (All):

Computational intelligence.

Automatic control.

Operations research.

Decision making.

Management science.

Computational Intelligence.

Control and Systems Theory.

Operations Research/Decision Theory.

Operations Research, Management Science.

Local Subjects:

Computational Intelligence.

Control and Systems Theory.

Operations Research/Decision Theory.

Operations Research, Management Science.

Physical Description:

1 online resource (XVIII, 322 p. 156 illus., 106 illus. in color.)

Edition:

1st ed. 2017.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2017.

Language Note:

English

Summary:

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 leading researchers, discuss the main techniques and applications, together with the advantages and shortcomings of these tools in comparison to other fuzzy number representation models. Primarily intended for engineers and researchers in the field of fuzzy arithmetic, the book also offers a valuable source of basic information on fuzzy models and an easy-to-understand reference guide to their applications for advanced undergraduate students, operations researchers, modelers and managers alike.

Contents:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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.

Notes:

CC BY

Description based on publisher supplied metadata and other sources.

ISBN:

9783319596143

3319596144

OCLC:

1076234313