Subsethood measures for interval-valued fuzzy sets based on the aggregation of interval fuzzy implications

The connection between fuzzy subsethood measures and fuzzy implications straightforwardly follows from the definition of inclusion for (crisp) sets. In accordance with this connection we introduce a new constructive method for (weak) fuzzy subsethood measures for interval-valued fuzzy sets based on the aggregation of fuzzy interval implications. For this purpose we generalize aggregation functions and propose a technique for aggregation of intervals. The benefit of our approach lies in the wide range of obtained fuzzy subsethood measures for interval-valued fuzzy sets. Moreover, the method gives the possibility to construct new fuzzy subsethood measures with properties that are appropriate to the situation under investigation. Another advantage of the method is its clear semantic interpretation.