978-1-4244-7316-8/11/$26.00 ©2011 IEEE Adaptive Fuzzy Interpolation with Uncertain Observations and Rule Base

Abstract—Adaptive fuzzy interpolation strengthens the po-tential of fuzzy interpolative reasoning. It views interpolation procedures as artificially created system components, and iden-tifies all possible sets of faulty components that may each have led to all detected contradictory results. From this, a modification procedure takes place, which tries to modify each of such components, termed candidates, in an effort to remove all the contradictions and thus restore consistency. This approach assumes that the employed interpolation mechanism is the only cause of contradictions, that is all given observations and rules are believed to be true and fixed. However, this may not be the case in certain real situations. It is common in fuzzy systems that each observation or rule is associated with a certainty degree. This paper extends the adaptive approach by taking into consideration both observations and rules also, treating them as diagnosable and modifiable components in addition to interpolation procedures. Accordingly, the modification procedure is extended to cover the cases of modifying observations or rules in a given rule base along with the modification of fuzzy reasoning components. This extension significantly improves the robustness of the existing adaptive approach. Index Terms—Fuzzy interpolation, uncertain observations, uncertain rules. I