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An approach which uses fuzzy variables to solve the capacitor-switching (CS) problem in radial distribution systems is proposed. CS is an important measure for loss minimisation of distribution systems via an optimal capacitor dispatch schedule. Uncertainty of forecasted load values are represented as trapezoidal fuzzy numbers via fuzzy sets. The principles of fuzzy set theory are applied to form a methodology suitable for calculations of fuzzy complex numbers while maintaining a fast computational speed. An approach based on successive linear integer programming with fuzzy variables is exploited to optimise the on-off status of each switchable capacitor bank. A computer program has been developed according to this approach, and numerical studies on a radial distribution system are verified in detail.