Poisson process with fuzzy rates (Q707723)

The author uses the setting of credibility theory introduced by Liu (which is questionable, however, since the typical and fruitful fuzzy thinking is suppressed by self-duality in favour of a probability-like theory) and defines a Poisson process \(N(t)\) with fuzzy rates, also called renewal number. He proves theorems which relate the first two moments of \(N(t)\) with the moments of the fuzzy rate, and he presents formulas for computing the average chance of some interesting random fuzzy events. Finally, compound Poisson processes are investigated.