It is known that interval-valued fuzzy sets [m(x)] provide a more adequate description of expert uncertainty than the more traditional "type-1" (number-valued) fuzzy techniques. Specifically, an interval-valued fuzzy set can be viewed as a class of possible fuzzy sets m(x) from [m(x)]. In this case, as a result of defuzzification, it is natural to return the range [u] of all possible values u(m) that can be obtained by defuzzifying membership functions m(x) from this class. In practice, it is reasonable to restrict ourselves only to fuzzy numbers m(x), i.e., to "unimodal" fuzzy sets. Under this restriction, in general, we get a narrower range [a] of possible values of u(m). In this paper, we describe a feasible algorithm for computing the new range [a].