Between Dog and Wolf: A Continuous Transition from Fuzzy to Probabilistic Estimates
Martine C. Ceberio, Olga M. Kosheleva, Владик Крейнович, Luc Longpré · 2019
Often, we use original expert estimates to compute estimates of related quantities. In many practical situations, it is desirable to know how accurate is the resulting estimate. There are many techniques for computing this accuracy: we can use simple probabilistic ideas and we can use simple fuzzy ideas. Strangely enough, these two reasonable techniques lead to drastically different results. Which of them is correct? Our practical tests show that none of these two methods is perfect: probabilistic approach usually underestimates uncertainty, while the fuzzy approach overestimates it. This looks similar to many cases that motivated Zadeh to promote the idea of soft computing – a combination of different uncertainty techniques. To get a more adequate combination technique, we analyzed the general problem of combining accuracy estimates and came up with a 1-parametric family of techniques that contains probabilistic and fuzzy as particular cases – and that indeed works better on several practical examples that each of the original two techniques.