Interpolation-based Fuzzy Reasoning - a comparison

This paper reviews some important points of sparse rule-bases, the reason of their generation and after that three methods are presented, which allow the approximation of the missing rules with reasonable demand on computing. The delimitations and advantages of these methods are presented, too. Fuzzy systems based on a sparse rule-base do not have rules for all the possible combinations of observations. Thus a system working with classical fuzzy reasoning e.g. based on Compositional Rule of Inference can fire none of the rules by some observed values and will have no output. Fig. 1. As an example let us see a system having an input linguistic variable with a partition as it can be seen in Fig. 1. There are rules for the linguistic terms A 1 and A 2 , but there is no rule for the fuzzy set A* marked by dashed lines. In the case of an observation of x=x* and the lack of a rule with matching antecedent part the system can not produce an output. How can a sparse rule-base emerge? Essentially a sparse rule-base takes its origin from one of the three reasons specified below: 1. The rules generated from information obtained from experts or from other sources (e. g. neural network-based learning techniques) do not cover all the possible observation values. For instance assuming the partition in Fig. 1. on a A 1 1 μ A * A 2 x x *