Conventionally, the design of urban water supply and distribution systems is based on the assumption that all the involved parameters are known a priori and remain unaltered throughout the life cycle of the system. However, significant uncertainties do appear during the analysis and design of these systems, such as the equivalent pipe roughness and the actual internal diameters of the pipes. To study these uncertainties, the water supply and the looped water distribution systems are studied separately. For the water supply system, these uncertainties are incorporated in the analysis of the system, using the extension principle of the fuzzy sets and a new operation of the fuzzy subtraction. Based on the calculation of head losses for each branch of the system, the nodal heads are obtained as fuzzy numbers. In regard to the looped water distribution system, a methodology is developed and proposed, based on the extension principle and leading to several optimisation problems with respect to the branches of the system. The aim of the proposed methodology is to determine the α-cuts and finally produce the shape of the membership function of flows in the branches of the system. Both methodologies are illustrated by numerical examples.

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