Reasoning by analogy with fuzzy rules

In sparse systems rules do not cover the complete observation space and, in the general case, observations do not match with any of the rule antecedents, i.e. there is no direct way to compute a conclusion. A solution to this problem is presented if reasoning by analogy is applied. The basic case of reasoning by analogy is the interpolation of two rules. An extension of this method is extrapolation, another is interpolation of 2k rules. The generalization including all these methods uses an approximation covering the whole space where the complete rule system or an arbitrary subset of it can be used as the basis for the calculation of the conclusion. This generalized algorithm is sketched, and a few examples are presented