We start with the fuzzy binomial. Then we discuss the fuzzy Poisson probability mass function.

Fuzzy Binomial

Let $E$ be a non-empty, proper subset of $X=\{x_1,x_2,x_3,...,x_n\}$. Let $P(E)=p$ so that $P(E^{‘})=1-p$ where $p\in (0,1)$. Suppose we have $m$ independent repetitions of this experiment. If $P(r)$ is the probability of $r$ successes in the $m$ experiments, then $$P(r)=C^{r}_{m}p^{r}(1-p)^{m-r}$$ for $r=0,1,...,m$ gives the binomial distribution.

We substitute 

Fuzzy Probability Theory---(3)Discrete Random Variables