Fuzzy Probabilities: New Approach and Applications

Professor James J. Buckley (auth.)3540250336, 9783540250333, 9783540323884

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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Table of contents :
Front Matter….Pages i-xi
Introduction….Pages 1-6
Fuzzy Sets….Pages 7-30
Fuzzy Probability Theory….Pages 31-49
Discrete Fuzzy Random Variables….Pages 51-60
Fuzzy Queuing Theory….Pages 61-69
Fuzzy Markov Chains….Pages 71-83
Fuzzy Decisions Under Risk….Pages 85-93
Continuous Fuzzy Random Variables….Pages 95-108
Fuzzy Inventory Control….Pages 109-113
Joint Fuzzy Probability Distributions….Pages 115-123
Applications of Joint Distributions….Pages 125-132
Functions of a Fuzzy Random Variable….Pages 133-137
Functions of Fuzzy Random Variables….Pages 139-144
Law of Large Numbers….Pages 145-146
Sums of Fuzzy Random Variables….Pages 147-150
Conclusions and Future Research….Pages 151-155
Back Matter….Pages 157-166