A new method for avoiding abnormal conclusion for /spl alpha/-cut based rule interpolation

The first published result in fuzzy rule interpolation was the /spl alpha/-cut based fuzzy rule interpolation, termed as KH-interpolation, originally devoted for complexity reduction. Some deficiencies of this method were presented, such as abnormal conclusion for a certain configuration of the involved fuzzy sets. This inspired several authors to propose various conceptually different fuzzy interpolation approaches, however, none of those algorithms has such a low computational complexity as the KH-method. In the frequent practical cases of using piecewise linear sets only with three of four characteristic points the new methods maintain their relatively high complexity. The goal of this paper is to modify properly the original /spl alpha/-cut based interpolation approach to eliminate the abnormality problem and to ensure normal conclusion in the practical case when the fuzzy sets are of a finite number of characteristic points, while at the same time maintaining the advantageous properties of the original method. A concise analysis of the proposed method is also presented.