James J. Buckley

Fuzzy Probabilities

New Approach and Applications

• Broschiertes Buch

Produktbeschreibung

In probability and statistics we often have to estimate probabilities and parameters in probability distributions using a random sample. Instead of using a point estimate calculated from the data we propose using fuzzy numbers which are constructed from a set of confidence intervals. In probability calculations we apply constrained fuzzy arithmetic because probabilities must add to one. Fuzzy random variables have fuzzy distributions. A fuzzy normal random variable has the normal distribution with fuzzy number mean and variance. Applications are to queuing theory, Markov chains, inventory control, decision theory and reliability theory.

Produktdetails

• Studies in Fuzziness and Soft Computing 115
• Verlag: Physica / Physica-Verlag / Physica-Verlag HD
• Artikelnr. des Verlages: 978-3-642-86788-0
• Softcover reprint of the original 1st ed. 2003
• Seitenzahl: 180
• Erscheinungstermin: 1. Juni 2012
• Englisch
• Abmessung: 235mm x 155mm x 11mm
• Gewicht: 282g
• ISBN-13: 9783642867880
• ISBN-10: 364286788X
• Artikelnr.: 38033560

Inhaltsangabe

1 Introduction.- 1.1 Introduction.- 1.2 References.- 2 Fuzzy Sets.- 2.1 Introduction.- 2.2 Fuzzy Sets.- 2.3 Fuzzy Arithmetic.- 2.4 Fuzzy Functions.- 2.5 Finding the Minimum of a Fuzzy Number.- 2.6 Ordering Fuzzy Numbers.- 2.7 Fuzzy Probabilities.- 2.8 Fuzzy Numbers from Confidence Intervals.- 2.9 Computing Fuzzy Probabilities.- 2.10 Figures.- 2.11 References.- 3 Fuzzy Probability Theory.- 3.1 Introduction.- 3.2 Fuzzy Probability.- 3.3 Fuzzy Conditional Probability.- 3.4 Fuzzy Independence.- 3.5 Fuzzy Bayes' Formula.- 3.6 Applications.- 3.7 References.- 4 Discrete Fuzzy Random Variables.- 4.1 Introduction.- 4.2 Fuzzy Binomial.- 4.3 Fuzzy Poisson.- 4.4 Applications.- 4.5 References.- 5 Fuzzy Queuing Theory.- 5.1 Introduction.- 5.2 Regular, Finite, Markov Chains.- 5.3 Fuzzy Queuing Theory.- 5.4 Applications.- 5.5 References.- 6 Fuzzy Markov Chains.- 6.1 Introduction.- 6.2 Regular Markov Chains.- 6.3 Absorbing Markov Chains.- 6.4 Application: Decision Model.- 6.5 References.- 7 Fuzzy Decisions Under Risk.- 7.1 Introduction.- 7.2 Without Data.- 7.3 With Data.- 7.4 References.- 8 Continuous Fuzzy Random Variables.- 8.1 Introduction.- 8.2 Fuzzy Uniform.- 8.3 Fuzzy Normal.- 8.4 Fuzzy Negative Exponential.- 8.5 Applications.- 8.6 References.- 9 Fuzzy Inventory Control.- 9.1 Introduction.- 9.2 Single Period Model.- 9.3 Multiple Periods.- 9.4 References.- 10 Joint Fuzzy Probability Distributions.- 10.1 Introduction.- 10.2 Continuous Case.- 10.3 References.- 11 Applications of Joint Distributions.- 11.1 Introduction.- 11.2 Political Polls.- 11.3 Fuzzy Reliability Theory.- 11.4 References.- 12 Functions of a Fuzzy Random Variable.- 12.1 Introduction.- 12.2 Discrete Fuzzy Random Variables.- 12.3 Continuous Fuzzy Random Variables.- 13 Functions of Fuzzy Random Variables.- 13.1Introduction.- 13.2 One-to-One Transformation.- 13.3 Other Transformations.- 14 Law of Large Numbers.- 15 Sums of Fuzzy Random Variables.- 15.1 Introduction.- 15.2 Sums.- 16 Conclusions and Future Research.- 16.1 Introduction.- 16.2 Summary.- 16.3 Research Agenda.- 16.4 Conclusions.- List of Figures.- List of Tables.