 Fuzzy set theory interprets \(\mu_{T}(178cm)\) as the degree to which the vague statement “someone measuring 178cm is tall” is true. Degrees of truth belong to the philosophy of language. They do not (yet) have anything to do with degrees of belief, which belong to epistemology. The epistemological thesis of possibility theory is that your subjective degrees of possibility should reflect semantic facts about degree of membership. Suppose you learn that Sophia is tall. Then, your degree of possibility for the statement “Sophia is 178cm” should equal \(\mu_{T}(178\text{cm})\). That may handle borderline heights elegantly, but it has somewhat unintuitive consequences at the extremes. Since, presumably, \(\mu_T(190\text{cm})=\mu_T(210\text{cm})=1\), you must find it maximally possible that Sophia is 190 and 210cm tall. 