In the paper we propose a new fuzzy interval type-2 C-ordered-means clustering algorithm for incomplete data. The algorithm uses both marginalisation and imputation to handle missing values. Thanks to imputation values in incomplete items are not lost, thanks to marginalisation imputed data can be distinguished from original complete items. The algorithm elaborates rough fuzzy sets (interval type-2 fuzzy sets) to model imprecision and incompleteness of data. For handling outliers the algorithm uses loss functions, ordering technique, and typicalities. Outliers are assigned with low values of typicalities. The paper describes also a new imputation technique–imputation with values from k nearest neighbours.