Fuzzy Probabilities and Fuzzy Sets for Web Planning / Edition 1

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Overview

This book presents important applications of soft computing and fuzziness to the growing field of web planning. A new method of using fuzzy numbers to model uncertain probabilities and how these can be used to model a fuzzy queuing system is demonstrated, as well as a method of modeling fuzzy queuing systems employing fuzzy arrival rates and fuzzy service rates. All the computations needed to get to the fuzzy numbers for system performance are described starting for the one server case to more than three servers. A variety of optimization models are discussed with applications to the average response times, server utilization, server and queue costs, as well as to phenomena identified with web sites such as "burstiness" and "long tailed distributions".

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Product Details

  • ISBN-13: 9783642055966
  • Publisher: Springer Berlin Heidelberg
  • Publication date: 12/14/2010
  • Series: Studies in Fuzziness and Soft Computing Series , #135
  • Edition description: Softcover reprint of the original 1st ed. 2004
  • Edition number: 1
  • Pages: 190
  • Product dimensions: 9.21 (w) x 6.14 (h) x 0.43 (d)

Table of Contents

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.- 2.2.1 Fuzzy Numbers.- 2.2.2 Alpha-Cuts.- 2.2.3 Inequalities.- 2.2.4 Discrete Fuzzy Sets.- 2.3 Fuzzy Arithmetic.- 2.3.1 Extension Principle.- 2.3.2 Interval Arithmetic.- 2.3.3 Fuzzy Arithmetic.- 2.4 Fuzzy Functions.- 2.4.1 Extension Principle.- 2.4.2 Alpha-Cuts and Interval Arithmetic.- 2.4.3 Differences.- 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.- 3.3.1 Fuzzy Arrival Rate.- 3.3.2 Fuzzy Service Rate.- 3.4 Fuzzy Numbers from Expert Opinion.- 3.5 Restricted Fuzzy Arithmetic.- 3.5.1 Probabilities.- 3.5.2 Restricted Arithmetic: General.- 3.5.3 Restricted Fuzzy Arithmetic: Book.- 3.6 Computations.- 3.6.1 First Problem.- 3.6.2 Second Problem.- 3.6.3 Another Fuzzy Computation.- 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.- 13.2.1 Minimize % MathType!MTEF!2!1!+-
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% WGvbaaaaaa!36DF!$$\overline U $$.- 13.3.3 Ranking the Fuzzy Sets.- 13.4 References.- 14 Optimization: With Revenue/Costs.- 14.1 Introduction.- 14.2 Fuzzy Probabilities.- 14.2.1 Ranking the Fuzzy Sets.- 14.3 Fuzzy Arrival/Service Rates.- 14.3.1 Ranking the Fuzzy Sets.- 14.4 References.- 15 Burstiness.- 15.1 Introduction.- 15.2 Fuzzy Probabilities.- 15.2.1 Ranking the Fuzzy Numbers.- 15.3 Fuzzy Arrival/Service Rates.- 15.3.1 Ranking the Fuzzy Numbers.- 15.4 References.- 16 Long Tailed Distributions.- 16.1 Introduction.- 16.2 Fuzzy Probabilities.- 16.2.1 Ranking the Fuzzy Numbers.- 16.3 Fuzzy Arrival/Service Rates.- 16.3.1 Ranking the Fuzzy Numbers.- 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.- 18.4.1 CD-ROM.- 18.4.2 Simulation.- 18.5 References.- 19 Computational Algorithms.- 19.1 Introduction.- 19.2 Computations: Fuzzy Probabilities.- 19.2.1 Premium Solver Problem.- 19.2.2 Genetic Algorithm.- 19.2.3 Optimization Models.- 19.3 Computations: Fuzzy Arrivals and Service Rates.- 19.4 References.- List of Figures.- List of Tables.

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