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Fuzzy Probabilities New Approach and Applications

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...

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Bibliographic Details
Main Author: Buckley, James J.
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 2005, 2005
Edition:1st ed. 2005
Series:Studies in Fuzziness and Soft Computing
Subjects:
Artificial Intelligence
Probability Theory
Probabilities
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
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505 0 |a Fuzzy Sets -- Fuzzy Probability Theory -- Discrete Fuzzy Random Variables -- Fuzzy Queuing Theory -- Fuzzy Markov Chains -- Fuzzy Decisions Under Risk -- Continuous Fuzzy Random Variables -- Fuzzy Inventory Control -- Joint Fuzzy Probability Distributions -- Applications of Joint Distributions -- Functions of a Fuzzy Random Variable -- Functions of Fuzzy Random Variables -- Law of Large Numbers -- Sums of Fuzzy Random Variables -- Conclusions and Future Research 
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520 |a 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 

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