Fuzzy interpolation with Cartesian representation and extensibility functions

This paper summaries the application of the recently proposed Cartesian representation of membership functions to the problem of fuzzy interpolation. It is shown that under this formulation the problem can be according to whether the observation lies within or outside the antecedent spanning set. For the former, the observation contains the same geometric properties as the given antecedents, and interpolation can be conducted based on the given rules using the extensibility function concept. On the other hand, observation lying outside the antecedent spanning set contains new geometric properties beyond those of the given rules, and heuristic reasoning must therefore be applied. A two step approach with flexibility to accommodate additional criteria and design objectives is presented for this case.