fuzzy interpolation, fuzzy rule

In this work we consider a theory described in [2] where the fuzzy interpolation is based on similarity relations. From our observations we can say that the method presented in [2] solves an approximation problem instead of interpolation. We focused on triangular fuzzy sets and tried to understand the principle of fuzzy rule base interpolation. In our approach we propose to rewrite the technique in [2] using metric distances. We present compositions between similarity relations and fuzzy sets and their properties. All steps are demonstrated in their graphical representation.