Fuzzy rule interpolation Matlab toolbox-FRI toolbox. Fuzzy systems use fuzzy rule base to make inference. A fuzzy rule base is fully covered (at level α), if all input universes are covered by rules at level α . Such fuzzy rule bases are also called dense or complete rule bases. In practice, it means that for all the possible observations there exists at least one firing rule, whose antecedent part overlaps the input data at least partially at level α . If this condition is not satisfied, the rule base is considered sparse rule base, i.e. containing gaps. The classical fuzzy reasoning techniques like Zadeh’s, Mamdani’s, Larsen’s or Sugeno’s cannot generate an acceptable output for such cases. Fuzzy rule based interpolation (FRI) techniques were introduced to generate inference for sparse fuzzy rule base, thus extend the usage of fuzzy inference mechanisms for sparse fuzzy rule base systems. Basically, FRI techniques perform interpolative approximate reasoning by taking into consideration the existing fuzzy rules for cases where there is no fuzzy rules to fire.