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[null,"1.","Record Nr.",null,"UNINA9910231246403321"]
[null,null,"Autore",null,"Łukasz Apiecionek"]
[null,null,"Titolo",null,"Theory and Applications of Ordered Fuzzy Numbers [[electronic resource] ] : A Tribute to Professor Witold Kosiński / / edited by Piotr Prokopowicz, Jacek Czerniak, Dariusz Mikołajewski, Łukasz Apiecionek, Dominik Ślȩzak"]
[null,null,"Pubbl/distr/stampa",null,"Springer Nature, 2017"]
[{"$nulls":4},"Cham : , : Springer International Publishing : , : Imprint : Springer, , 2017"]
[null,null,"ISBN",null,"3-319-59614-4"]
[null,null,"Edizione",null,"[1st ed. 2017.]"]
[null,null,"Descrizione fisica",null,"1 online resource (XVIII, 322 p. 156 illus., 106 illus. in color.)"]
[null,null,"Collana",null,"Studies in Fuzziness and Soft Computing, , 1434-9922 ; ; 356"]
[null,null,"Disciplina",null,"006.3"]
[null,null,"Soggetti",null,"Computational intelligence"]
[{"$nulls":4},"Control engineering"]
[{"$nulls":4},"Operations research"]
[{"$nulls":4},"Decision making"]
[{"$nulls":4},"Management science"]
[{"$nulls":4},"Computational Intelligence"]
[{"$nulls":4},"Control and Systems Theory"]
[{"$nulls":4},"Operations Research/Decision Theory"]
[{"$nulls":4},"Operations Research, Management Science"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,"Nota di contenuto",null,"Intro -- Foreword -- Memories of Professor Witold Kosiński -- Scientific Development -- Scientific and Academic Achievements (Part I) -- Scientific and Academic Achievements (Part II) -- Scientific Collaboration -- Teaching and Supervision -- Scientific and Social Services -- Personality and Memoires -- Acknowledgements -- Contents -- Part I Background of Fuzzy Set Theory -- 1 Introduction to Fuzzy Sets -- 1.1 Classic and Fuzzy Sets -- 1.2 Fuzzy Sets---Basic Definitions -- 1.3 Extension Principle -- 1.4 Fuzzy Relations -- 1.5 Cylindrical Extension and Projection of a Fuzzy Set -- 1.6 Fuzzy Numbers -- 1.7 Summary -- References -- 2 Introduction to Fuzzy Systems -- 2.1 Introduction -- 2.2 Fuzzy Conditional Rules -- 2.3 Approximate Reasoning -- 2.3.1 Compositional Rule of Inference -- 2.3.2 Approximate Reasoning with Knowledge Base -- 2.3.3 "]
[{"$nulls":4},"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."]
[{"$nulls":4},"4.6.1 Direction as a Trend -- 4.6.2 Validity of Operations -- 4.6.3 The Meaning of Improper OFNs -- 4.7 Summary and Further Intuitions -- References -- 5 Processing Direction with Ordered Fuzzy Numbers -- 5.1 Introduction -- 5.2 Direction Measurement Tool -- 5.2.1 The PART Function -- 5.2.2 The Direction Determinant -- 5.3 Compatibility Between OFNs -- 5.4 Inference Sensitive to Direction -- 5.4.1 Directed Inference Operation -- 5.4.2 Examples -- 5.5 Aggregation of OFNs -- 5.5.1 The Aggregation's Basic Properties -- 5.5.2 Arithmetic Mean Directed Aggregation -- 5.5.3 Aggregation for Premise Parts of Fuzzy Rules -- 5.6 Summary -- References -- 6 Comparing Fuzzy Numbers Using Defuzzificators on OFN Shapes -- 6.1 Introduction -- 6.2 Formal Approach to the Problem -- 6.3 Defuzzification Methods -- 6.3.1 Defuzzification Methods for OFN -- 6.4 Definition of Golden Ratio Defuzzification Operator -- 6.4.1 Golden Ratio for OFN -- 6.5 Golden Ratio -- 6.6 Defuzzification Conditions for GR -- 6.6.1 Normalization -- 6.6.2 Restricted Additivity -- 6.6.3 Homogeneity -- 6.7 Definition of Mandala Factor Defuzzification Operator -- 6.8 Mandala Factor -- 6.9 Defuzzification Conditions for MF -- 6.9.1 Normalization -- 6.9.2 Restricted Additivity -- 6.9.3 Homogeneity -- 6.10 Catalogue of the Shapes of Numbers in OFN Notation -- 6.11 Conclusion -- References -- 7 Two Approaches to Fuzzy Implication -- 7.1 Introduction -- 7.2 Lattice Structure and Implications on SOFNs -- 7.2.1 Step-Ordered Fuzzy Numbers -- 7.2.2 Lattice on mathcalRK -- 7.2.3 Complements and Negation on calN -- 7.2.4 Fuzzy Implication on BSOFN -- 7.2.5 Applications -- 7.3 Metasets -- 7.3.1 The Binary Tree T and the Boolean Algebra mathfrakB -- 7.3.2 General Definition of Metaset -- 7.3.3 Interpretations of Metasets -- 7.3.4 Forcing -- 7.3.5 Set-Theoretic Relations for Metasets."]
[{"$nulls":4},"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 "]
[{"$nulls":4},"Candlestick as Technical Analysis Indicator -- 10.5 Ordered Fuzzy Time Series Models -- 10.6 Conclusion and Future Works -- References -- 11 Detecting Nasdaq Composite Index Trends with OFNs -- 11.1 Introduction -- 11.2 Application of OFN Notation for the Fuzzy Observation of NASDAQ Composite -- 11.3 Ordered Fuzzy Number Formulas -- 11.4 Conclusions -- References -- 12 OFNAnt Method Based on TSP Ant Colony Optimization -- 12.1 Introduction -- 12.2 Application of Ant Colony Algorithms in Searching for the Optimal Route -- 12.3 OFNAnt, a New Ant Colony Algorithm -- 12.4 Experiment -- 12.4.1 Experiment Execution Method -- 12.4.2 Software Used for Experiment -- 12.4.3 Experimental Data -- 12.5 Results of Experiment -- 12.6 Summary and Conclusions -- References -- 13 A New OFNBee Method as an Example of Fuzzy Observance Applied for ABC Optimization -- 13.1 Introduction -- 13.2 ABC (Artificial Bee Colony) Model -- 13.3 Selected OFN Issues."]
[{"$nulls":4},"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."]
[{"$nulls":4},"18.3.1 Data Ladder -- 18.3.2 Models of a Single Neuron -- 18.3.3 Models of Biologically Relevant Neural Networks -- 18.3.4 Models of Human Behavior -- 18.4 Traditional versus Fuzzy Approach -- 18.5 OFN as an Alternative Approach to Fuzziness -- 18.6 Patterns and Examples -- 18.6.1 Intuitive Modeling of the Complex Functions -- 18.6.2 Improving Policy Gradient Method -- 18.6.3 Modeling Learning Rate with the OFNs -- 18.7 Discussion -- 18.7.1 Results of Other Scientists -- 18.7.2 Limitations of Our Approach and Directions  for Further Research -- 18.8 Conclusions -- References."]
[null,null,null,"Sommario/riassunto","This book is open access under a CC BY 4.0 license. This open access book offers comprehensive coverage on Ordered Fuzzy Numbers, providing readers with both the basic information and the necessary expertise to use them in a variety of real-world applications. The respective chapters, written by leading researchers, discuss the main techniques and applications, together with the advantages and "]
[{"$nulls":4},"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."]