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.
Author(s): Professor James J. Buckley (auth.)
Series: Studies in Fuzziness and Soft Computing 115
Edition: 1
Publisher: Physica-Verlag Heidelberg
Year: 2003
Language: English
Pages: 165
City: Berlin, New York
Tags: Artificial Intelligence (incl. Robotics)
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
