The techniques for formal manipulation of fuzzy rule bases introduced in the previous chapter facilitate the complexity management in fuzzy systems. These techniques allow the compressed information about the fuzzy system contained in the Boolean matrix and the binary relation to be reorganised for the purpose of analysis or synthesis. This reorganisation is carried out by representing a single operand rule base with a couple of product rule bases, or alternatively, by representing a couple of operand rule bases with a single product rule base. In either case, no special requirements are usually placed on the corresponding operand or product rule bases, i.e. the latter may be any arbitrary rule bases.