Comprehensive analysis of a new fuzzy rule interpolation method

The first published result in fuzzy rule interpolation was the α-cut based fuzzy rule interpolation, termed as KH fuzzy rule interpolation, originally devoted for complexity reduction. Some deficiencies of this method was presented later, such as subnormal conclusion for certain configuration of the involved fuzzy sets. However, since that several conceptually different fuzzy rule interpolation techniques were proposed, none of those algorithms has such a low computational complexity than the original one. Recently, a modified version of the KH approach has been presented [1], [2], which eliminates the subnormality problem, while at the same time intending to maintain the advantageous computational properties of the original method. This paper presents a comprehensive analysis of the new method, which includes detailed comparison with the original KH fuzzy rule interpolation method concerning the explicit functions of the methods, preservation of piecewise linearity, stability. The fuzziness of the conclusion with respect to the fuzziness of the observation is also investigated in comparison with several interpolation techniques. All these comparisons shows that the new method preserves the advantageous properties of the KH method and alleviates its most significant disadvantage, the problem of subnormality. Keywords—Fuzzy rule interpolation. KH method. Elimination of subnormality. Preservation of piecewise linearity. Stability.