A comparison of arithmetical operations with $f$ correlated fuzzy numbers

Abstract: We present a brief introduction to a class of interactive fuzzy numbers, called $f$-correlated fuzzy numbers, which consist of pairs of fuzzy numbers where one is dependent on the other by a continuous monotone injective function. We have deduced some equations that can directly calculate the results of the sums and products of $f$-correlated fuzzy numbers, using only basic operations with real numbers, intervals on the real line and the function that relates the fuzzy numbers being considered. We proved that their correlated and standard sum coincide, and that in a certain sense, the correlated product is contained in the standard product.