Fuzzy Probabilities [electronic resource] : New Approach and Applications / by James J. Buckley.Material type: TextLanguage: English Series: Studies in Fuzziness and Soft Computing: 115Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2005Description: XII, 164 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783540323884Subject(s): Computer science | Artificial intelligence | Computer Science | Artificial Intelligence (incl. Robotics)Additional physical formats: Printed edition:: No titleDDC classification: 006.3 LOC classification: Q334-342TJ210.2-211.495Online resources: Click here to access online
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.
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.