Abstract
As a substantial extension to fuzzy rule interpolation that works based on two neighboring rules flanking an observation, adaptive fuzzy rule interpolation is able to restore system consistency when contradictory results are reached during interpolation. The approach first identifies the exhaustive sets of candidates, with each candidate consisting of a set of interpolation procedures which may jointly be responsible for the system inconsistency. Then, individual candidates are modified such that all contradictions are removed, and thus, interpolation consistency is restored. It has been developed on the assumption that contradictions may only be resulted from the underlying interpolation mechanism, and that all the identified candidates are not distinguishable in terms of their likelihood to be the real culprit. However, this assumption may not hold for real-world situations. This paper, therefore, further develops the adaptive method by taking into account observations, rules, and interpolation procedures, all as diagnosable and modifiable system components. In addition, given the common practice in fuzzy systems that observations and rules are often associated with certainty degrees, the identified candidates are ranked by examining the certainty degrees of its components and their derivatives. From this, the candidate modification is carried out based on such ranking. This study significantly improves the efficacy of the existing adaptive system by exploiting more information during both the diagnosis and modification processes.
Highlights
Fuzzy inference systems have been successfully applied to many real world applications, but the systems may suffer from either too sparse or too complex rule bases
Given a fuzzy inference problem with a sparse rule base, the interpolator performs inference through fuzzy rule interpolation, and the assumption-based truth maintenance system (ATMS) records the dependencies of contradictions upon the preceding fuzzy interpolation component (FIC)
This paper has presented a generalised framework for adaptive fuzzy rule interpolation
Summary
Fuzzy inference systems have been successfully applied to many real world applications, but the systems may suffer from either too sparse or too complex rule bases. The adaptive approach outlined above assumes that all the contradictory interpolated results are caused by the underpinning interpolation procedures This assumption restricts the applications of AFRI to problems with defective fuzzy interpolation procedures only, but observations and rules in a fuzzy inference system may be ill-specified (to a certain extent). This limitation is not a fundamental restriction of the idea underlying the adaptive approach. Supported by the initial preliminary investigations of [29], this paper further develops the work of [24], to allow the diagnosis and modification of observations and rules This significantly enhances the robustness of the original method as one consistent inference result may still be derived when the original fails, often with intuitively more reasonable interpolated results.
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