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Unexpected conditions are often encountered by practitioners in the navigation of autonomous guided vehicles (AGV). In dynamic circumstances, traditional fuzzy controller using simple type-1 fuzzy sets may not be robust enough to overcome uncertainties caused by noise-corrupted sonar signals. For this reason, an interval type-2 fuzzy wall-following controller (IT2FWFC) is developed to improve the resilience to inaccuracies that can hinder the normal operation of an AGV. The antecedent part of the proposed IT2FWFC is made up of type-2 fuzzy sets and its consequent part is formed from fuzzy singletons. Furthermore, the non-sensitiveness property of the IT2FWFC for noise-elimination is also analyzed in this paper. In order to reduce computational loads during practical control, a simplified center-of-sets (COS) type-reduction procedure with clearly marked rule indices is also developed. Experiment results are included to illustrate the robustness of an AGV when detecting objects with uneven surfaces and exhibiting its wall-following behavior at the same time. The wall-following behavior of the IT2FWFC outperforms that of the type-1 fuzzy wall-following controller (T1FWFC) designed previously by the same framework of this paper.