The paper presents an attempt to adapt resolution-based theorem proving techniques to fuzzy modelling of uncertainty. Within the first two sections, some general arguments are supplied to justify the approach. The FOpL calculus (Fuzzy Operator Logic) is introduced in the next section. Then, the resolution principle is redefined in the context of the FOpL calculus, and its completeness property is proved. Some additional results and examples are presented in the final part of the paper. The reported research could be an important step toward developing an appropriate theoretical framework allowing the design of new theorem provers for uncertain knowledge bases.