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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

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Theory and Applications of Ordered Fuzzy Numbers

Pubblicazione:  Cham : Springer International Publishing : Imprint : Springer, 2017 
Estensione:  1 online resource (XVIII, 322 pages 156 illustrations, 106 illustrations in color.) : online resource. 
Tipo formato:  computer 
Tipo contenuto:  text 
Tipo supporto:  online resource 
Disciplina:  006.3 
Titolo uniforme di collana:  Studies in fuzziness and soft computing ; 356. 14349922 
Genere/Forma:  Electronic book 
Electronic books  
Classificazione LOC:  Q342 
Creatori/Collaboratori:  Prokopowicz, Piotr, [editor.] 
Czerniak, Jacek, [editor.]  
Mikołajewski, Dariusz, [editor.]  
Apiecionek, Łukasz, [editor.]  
Ślȩzak, Dominik. [editor.]  
Nota di contenuto:  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 Systems2.1 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 Memberships3.5 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 Operations4.6.3 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 Shapes6.1 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.  
Restrizioni accesso:  Access is restricted to users affiliated with licensed institutions. 
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 realworld 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 easytounderstand reference guide to their applications for advanced undergraduate students, operations researchers, modelers and managers alike. 
Collana:  Studies in Fuzziness and Soft Computing, 14349922 ; 356 
ISBN:  9783319596143 
3319596144  
9783319596136  
3319596136  
Formato:  Materiale a stampa 
Livello bibliografico  Monografia 
Lingua di pubblicazione:  Inglese 
Record Nr.:  006481404 
Localizzazioni e accesso elettronico  https://ebookcentral.proquest.com/lib/nyulibraryebooks/detail.action?docID=5591904 
Collocazione:  Electronic access 
Lo trovi qui:  New York University 