Abstract
In a stochastic homogeneous Poisson process, interarrival times are independent and identically distributed (iid) exponential random variables whose parameter is called the rate of the process. By using fuzzy variables to describe the parameter, a Poisson process whose rates are fuzzy variables is established. Based on the random fuzzy theory, relationship between the renewal number and fuzzy rates is discussed. As an application, a random fuzzy compound Poisson process is investigated.
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Li, S. Poisson process with fuzzy rates. Fuzzy Optim Decis Making 9, 289–305 (2010). https://doi.org/10.1007/s10700-010-9082-1
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DOI: https://doi.org/10.1007/s10700-010-9082-1