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An alternative approach is using fuzzy-numbers. If evaluated with interval arithmetic you can do very long calculations involving uncertain numbers very fast and with strong mathematical guarantees.

It would especially outperform the Monte-Carlo approach drastically.

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sixo 4 days ago | parent [-]

This assumes the inputs are uniform distributions, or perhaps normals depending on what exactly fuzzy numbers mean. M-C is not so limited.

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constantcrying 4 days ago | parent [-]

No. It assumes the numbers aren't random at all.

Although fuzzy-number can be used to model many different kinds of uncertainties.

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filiph 3 days ago | parent [-]

I'm familiar with fuzzy numbers (e.g. see my https://filiph.net/fuzzy/ toy) but I didn't know there's arithmetic with fuzzy numbers. How is it done? Do you have a link?

	▲	constantcrying 3 days ago \| parent [-]
		There is a book by Hanss on it. It focuses on the sampling approach (he calls it "transformation method") though. If you want to do arithmetic and not a black box approach you just have to realize that you can perform them on the alpha-cuts with ordinary interval arithmetic. Then you can evaluate arbitrary expressions involving fuzzy numbers, keeping the strengths and weaknesses of interval arithmetic. The sampling based approach is very similar to Monte-Carlo, but you sample at certain well defined points.