ISBN-10:
3642055966
ISBN-13:
9783642055966
Pub. Date:
12/14/2010
Publisher:
Springer Berlin Heidelberg
Fuzzy Probabilities and Fuzzy Sets for Web Planning / Edition 1

Fuzzy Probabilities and Fuzzy Sets for Web Planning / Edition 1

by James J. Buckley

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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 , #135
Edition description: Softcover reprint of the original 1st ed. 2004
Pages: 190
Product dimensions: 6.10(w) x 9.25(h) x 0.02(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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