Fuzzy interpolation with generalized representative values

Fuzzy interpolative reasoning offers the potential to model problems using sparse rule bases, as opposed to dense rule bases deployed in traditional fuzzy systems. It thus supports the simplification of complex fuzzy models in terms of rule number and facilitates inferences when limited knowledge is available. This paper presents an interpolative reasoning method by means of scale and move transformations. It can be used to interpolate fuzzy rules involving arbitrarily complex polygonal fuzzy sets. In particular, the paper introduces the general definition on representative values (RVs) employed by fuzzy interpolation and presents three useful implementations of this definition. This provides a degree of freedom to choose appropriate RVs to meet different requirements. The interpolation mechanism associated with the general RV definition is outlined and a comparative study of the interpolation results over different RV implementations is given.