Fuzzy Probabilities New Approach and Applications
Title:
Fuzzy Probabilities New Approach and Applications
ISBN:
9783642867866
Personal Author:
Edition:
1st ed. 2003.
Publication Information New:
Heidelberg : Physica-Verlag HD : Imprint: Physica, 2003.
Physical Description:
XII, 165 p. online resource.
Series:
Studies in Fuzziness and Soft Computing, 115
Contents:
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 -- 13.1 Introduction -- 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.
Abstract:
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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Electronic Access:
Full Text Available From Springer Nature Engineering Archive Packages
Language:
English