An approximate-reasoning system, based on the interval-valued fuzzy logic with one input and one output, is considered. The main goal of the short paper is an extension of the previous definition of an approximate- reasoning system. While the previous definition describes the construction of a “non-weighted” interval-valued inference, the present definition determines the degrees of compatibility of the fuzzy set involved in the antecedent. These degrees are modified by weight functions according to the hierarchy of the credibility or consistency of particular conditional statements in the antecedent. The extended mechanism of the “weighted” interval-valued fuzzy inference is illustrated by a suitable example.