Your dilemma is not a dilemma at all. As the name implies Fuzzy method is vague and you cannot base the safety decision on vague conclusions. I have deeped my toes in investigating possible application of Fuzzy approach to the safety cases. It can shed some light on the safety issue, but not much. I have not seen the application of Fuzzy methods in real industrial ( I am in offshore oil and gas industry) cases.
When you rule out everything which is irrelevant, then the remaining item worth perusing.
The context to use Fuzzy number is just to publish paper for the like minded people.
The context for probabilistic method is any situation which involves certitudes. There is a very good track record for it.
Thank your greetings. I looked your profile. and I gather you are primarily academic, hence number of papers are important to you. Producing papers based on Fuzzy logic is easier in comparison with probabilistic methods. But if you wish liaison probabilistic methods takes you along way.
Currently all high risk industry (nuclear, aviation, offshore, to name only a few) use probabilistic methods for their safety assessment. However, the degree of sophistication varies but as time goes by they are catching up with the academic world.
There are also a number of papers that apply Fuzzy numbers to the safety issue with a little success. However, I have yet to see Fuzzy logic applied to actual cases.
Safety cases for the nuclear industry takes a few years to produce and you can bury the author using his/her reports (they are that many). When it finishes they go back to the beginning again and go through another round. All of their calculations are probabilistic.