I don't know if this is the right forum to ask this, but I'm currently reviewing a paper that uses arithmetic on fuzzy numbers to propagate uncertainty.

As I understand the authors, they claim that fuzzy numbers are a more natural way for domain experts to express uncertainty: for example, an expert can say that the base temperature of a building is "about" 17C. This can then be represented by a fuzzy number centred on 17C, and used in subsequent calculations.

I am no expert, and I suppose fuzzy numbers and fuzzy set theory in general can be immensely useful elsewhere, but this particular use of fuzzy numbers as a simplified uncertainty propagation strikes me as odd. But I have very limited access to a decent library and could not find any literature confirming or refuting this point of view.

Could someone please point me in the right direction? A similar question has been asked before on this site (Reasons not to use fuzzy numbers instead of pds to represent uncertainty), but I'm not convinced that question has been satisfactorily answered.

  • $\begingroup$ While I am not sure I would believe that fuzziness is about different degrees of truth which is completely different from different degrees of uncertainty about something that will be either true or false. In other words probability measures uncertainty, while fuzziness measures vagueness. To me they seem possible complements, but never substitutes. $\endgroup$
    – gwr
    Commented Feb 14, 2018 at 13:53
  • $\begingroup$ I just love the harsh look E.T. Jaynes took on Fuzzy Sets here (p. 268). ;-) $\endgroup$
    – gwr
    Commented Feb 14, 2018 at 14:00


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