# Why Fuzzy Rule Interpolation is important?

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.

# News

Version 1.1.13 of the FRIT Matlab Toolbox has been released on 19.10.2013.Version 1.1.6 of the SFMI Sparse Fuzzy Model Identification Matlab Toolbox has been released on 19.10.2013.