Preserving Piece-wise Linearity in Fuzzy Interpolation

Fuzzy interpolative reasoning serves as an important role in fuzzy modelling as it does not only help reduce rule number but also provides an inference mechanism for sparse rule bases. The preservation of piece-wise linearity is preferred as piece-wise linear results can be inferred from piece-wise linear rules and observations. This ensures safe ignoring of non-characteristic points in performing interpolations. However, almost all existing fuzzy interpolative reasoning methods do not preserve piecewise linearity for general polygonal fuzzy sets. This paper, based on the work of [1, 2], proposes a new interpolative method which preserves this property.