Fuzzy Probabilities, 2005
New Approach and Applications
Studies in Fuzziness and Soft Computing Series, Vol. 115

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.

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.

New method of dealing with imprecise probabilities, most of which not published before