A proposal for a new fuzzy probability distribution function

This paper proposes a new fuzzy probability distribution function containing fuzzy numbers as its parameters. Concretely, the normal distribution which is widely used in the field of stochastic processes and statistics is developed into the fuzzy probability distribution function defined by the fuzzy numbers of the mean and the standard deviation respectively. The following points are studied: 1) the fuzzy distribution function defines the probability as a fuzzy number; 2) the fuzzy distribution function grows closer to the usual one if the fuzziness gets smaller; 3) a method for calculating the probability of crisp and fuzzy events by the fuzzy probability distribution is proposed; and 4) the hybrid number defined by Kaufmann (1983) is one of random variables obeying the proposed fuzzy one.