Towards adaptive interpolative reasoning

Fuzzy interpolative reasoning has been extensively studied due to its ability to enhance the robustness of fuzzy systems and to reduce system complexity. However, during the interpolation process, it is possible that multiple object values for a common variable are inferred which may lead to inconsistency in interpolated results. Such inconsistencies may result from defective interpolated rules or incorrect interpolative transformations. This paper presents a novel approach for identification and correction of defective rules in transformations, thereby removing the inconsistencies. In particular, an assumption-based truth maintenance system (ATMS) is used to record dependencies between reasoning results and interpolated rules, while the underlying technique that the general diagnostic engine (GDE) employs for fault localization is adapted to isolate possible faulty interpolated rules and their associated interpolative transformations. From this, an algorithm is introduced to allow for the modification of the original linear interpolation to become first-order piecewise linear. The approach is applied to a carefully chosen practical problem to illustrate the potential in strengthening the power of interpolative reasoning.