Bandler-Kohout subproduct, compositional rule of inference, correctness and continuity of inference, fuzzy relation equations

The compositional rule of inference (CRI) introduced by Zadeh is widely used in approximate reasoning schemes using fuzzy sets. In this work we show that the Bandler-Kohout subproduct does possess all the important properties such as equivalent and reasonable conditions for their solvability, their interpolative properties and the preservation of the indistinguishability that may be inherent in the input fuzzy sets, as cited in favor of using CRI.