This paper deals with set-valued classification methods. The aim of these methods is to provide a subset of classes as a prediction that is cautious but not too large. The well known Strong Dominance based set-valued classification algorithm (SD) is a good candidate as a robust method but sometimes the predicted subsets are too large. This paper proposes a flexible method that is a trade-off between SD based method and a point classification method. Indeed, the proposed set-valued classifier within the framework of belief functions, called IC, controls the granularity of the partial order by predicting a compromise between the cautiousness offered by the SD and the precision offered by point prediction classifiers. It is based on a interval criterion that is built from the pignistic criterion to which is associated a threshold. The introduced threshold aims to incorporate the decision-maker preference regarding the data imperfections. The paper shows the management of the interval comparisons and the intransitive binary relations resulting from the introduction of the threshold using graph theory and decision theory. The outputs of the IC are theoretically studied and compared to the prediction of SD and the pignistic criterion. Therefore, its performances regarding five set-valued classification performances measures are compared using fashion mnist image data. Experimental results show that IC gives good performances following trade-off measures.