Fuzzy Probabilities and Fuzzy Sets for Web Planning

2004
ISBN: 978-3-540-00473-8
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 135, 190 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1030 g

Reihe: Studies in Fuzziness and Soft Computing

1.1 Introduction This book is written in five major divisions. The first part is the introduc­ tory chapters consisting of Chapters 1-3. In part two, Chapters 4-10, we use fuzzy probabilities to model a fuzzy queuing system. We switch to employ­ ing fuzzy arrival rates and fuzzy service rates to model the fuzzy queuing system in part three in Chapters 11 and 12. Optimization models comprise part four in Chapters 13-17. The final part has a brief summary and sug­ gestions for future research in Chapter 18, and a summary of our numerical methods for calculating fuzzy probabilities, values of objective functions in fuzzy optimization, etc., is in Chapter 19. First we need to be familiar with fuzzy sets. All you need to know about fuzzy sets for this book comprises Chapter 2. Two other items relating to fuzzy sets, needed in Chapters 13-17, are also in Chapter 2: (1) how we plan to handle the maximum/minimum of a fuzzy set; and (2) how we will rank a finite collection of fuzzy numbers from smallest to largest.

Zielgruppe

Research

Autoren/Hrsg.

Buckley, James J.

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Mathematik | Informatik EDV | Informatik Technische Informatik Externe Speicher & Peripheriegeräte
• Wirtschaftswissenschaften Betriebswirtschaft Wirtschaftsinformatik, SAP, IT-Management
• Technische Wissenschaften Elektronik | Nachrichtentechnik Nachrichten- und Kommunikationstechnik Funktechnik
• Technische Wissenschaften Technik Allgemein Computeranwendungen in der Technik
• Mathematik | Informatik EDV | Informatik Business Application Unternehmenssoftware SAP
• Mathematik | Informatik EDV | Informatik Angewandte Informatik Computeranwendungen in Wissenschaft & Technologie
• Technische Wissenschaften Technik Allgemein Technik: Allgemeines
• Mathematik | Informatik EDV | Informatik Technische Informatik Systemverwaltung & Management
• Mathematik | Informatik EDV | Informatik Professionelle Anwendung Computer-Aided Design (CAD)
• Mathematik | Informatik EDV | Informatik Digital Lifestyle Internet, E-Mail, Social Media

Inhaltsverzeichnis

1 Introduction.- 1.1 Introduction.- 1.2 Fuzzy Probabilities.- 1.3 Fuzzy Arrival/Service Rates.- 1.4 Optimization Models.- 1.5 Notation.- 1.6 References.- 2 Fuzzy Sets.- 2.1 Introduction.- 2.2 Fuzzy Sets.- 2.3 Fuzzy Arithmetic.- 2.4 Fuzzy Functions.- 2.5 Finding the Min/Max of a Fuzzy Number.- 2.6 Ordering/Ranking Fuzzy Numbers.- 2.7 References.- 3 Fuzzy Probabilities/Arrival Rates.- 3.1 Introduction.- 3.2 Fuzzy Probabilities from Confidence Intervals.- 3.3 Fuzzy Arrival/Service Rates.- 3.4 Fuzzy Numbers from Expert Opinion.- 3.5 Restricted Fuzzy Arithmetic.- 3.6 Computations.- 3.7 Figures.- 3.8 References.- 4 Fuzzy Markov Chains.- 4.1 Introduction.- 4.2 Fuzzy Regular Markov Chains.- 4.3 Fuzzy Absorbing Markov Chains.- 4.4 Other Fuzzy Markov Chains.- 4.5 References.- 5 Fuzzy Queuing Theory.- 5.1 Introduction.- 5.2 Queuing Theory.- 5.3 Fuzzy Queuing Theory.- 6 Computations: One Sever.- 6.1 Introduction.- 6.2 Calculations.- 6.3 References.- 7 Example: One Sever.- 7.1 Introduction.- 7.2 Computations.- 7.3 References.- 8 Computations: Two Servers.- 8.1 Introduction.- 8.2 Calculations.- 9 Example: Two Servers.- 9.1 Introduction.- 9.2 Computations.- 9.3 References.- 10 Computations: Three or More Servers.- 10.1 References.- 11 Fuzzy Arrival/Service Rates.- 11.1 Introduction.- 11.2 Fuzzy Steady State Probabilities.- 11.3 Fuzzy System Parameters.- 11.4 References.- 12 Example: Fuzzy Arrival/Service Rates.- 12.1 Introduction.- 12.2 One Server.- 12.3 Two Servers.- 12.4 Three or More Servers.- 12.5 References.- 13 Optimization: Without Revenue/Costs.- 13.1 Introduction.- 13.2 Fuzzy Probabilities.- 13.3 Fuzzy Arrival/Service Rates.- 13.4 References.- 14 Optimization: With Revenue/Costs.- 14.1 Introduction.- 14.2 Fuzzy Probabilities.- 14.3 Fuzzy Arrival/Service Rates.- 14.4 References.- 15 Burstiness.- 15.1 Introduction.- 15.2 Fuzzy Probabilities.- 15.3 Fuzzy Arrival/Service Rates.- 15.4 References.- 16 Long Tailed Distributions.- 16.1 Introduction.- 16.2 Fuzzy Probabilities.- 16.3 Fuzzy Arrival/Service Rates.- 16.4 References.- 17 Putting It All Together.- 17.1 Introduction.- 17.2 Fuzzy Probabilities.- 17.3 Fuzzy Arrival/Service Rates.- 18 Summary and Future Research.- 18.1 Introduction.- 18.2 Fuzzy Probabilities.- 18.3 Fuzzy arrival/Service Rate.- 18.4 Future Research.- 18.5 References.- 19 Computational Algorithms.- 19.1 Introduction.- 19.2 Computations: Fuzzy Probabilities.- 19.3 Computations: Fuzzy Arrivals and Service Rates.- 19.4 References.- List of Figures.- List of Tables.