Fuzzy Set Approximation Based on Linguistic Term Shifting

Fuzzy systems working with a sparse rule base apply special reasoning techniques in order to ensure the acceptable output in case of observations hitting the gap between the antecedent parts of the rules, too. The methods that follow the generalized methodology of the fuzzy rule interpolation (GM) [1] produce the conclusion in two steps. First a new rule is interpolated in the position determined by the reference point(s) of the observation followed by the estimation of the conclusion by firing this rule. The new fuzzy set approximation method (FEAT-α) proposed in this paper offers a solution for the task of the first step of the GM. Its main features are its low computational complexity, its ability to take into consideration all the sets belonging to the partition and the fact that the calculations are based on α-cuts.