Preserving piece-wise linearity in fuzzy interpolation

Fuzzy interpolative reasoning plays an important role in fuzzy modelling as it not only helps to reduce the number of rules in a rule base, but also provides an inference mechanism for sparse rule bases. In interpolation, it is desirable to preserve piece-wise linearity as piece-wise linear results can thus be inferred from piece-wise linear rules and observations. This safely ensures the ignorance 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, proposes a new interpolative method which preserves this property.