Fuzzy interpolation and its adaptation

• Main Author: Yang, Longzhi
• Other Authors: Shen, Qiang
• Published: Aberystwyth University 2011
• Online Access: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.767367

Fuzzy inference has been widely used to represent and manage the imprecision and incompleteness in commonsense reasoning with high performance and comprehensibility. Fuzzy interpolation, a particular type of fuzzy inference, strengthens the power of fuzzy inference in two respects. Firstly, it reduces system complexity by omitting those rules that can be approximated by their neighbouring ones. Secondly, it enhances the robustness of fuzzy systems by guaranteeing a certain conclusion always being generated. However, it is possible that multiple object values for a common variable are inferred from complex real-world applications by fuzzy inference. Particularly for fuzzy interpolation, due to the high incompleteness of knowledge bases and the imprecision of observations and rules used for fuzzy interpolation, these values are likely to be inconsistent. Such inconsistencies may result from incorrect observations, incorrect rules in the given rule base or defective interpolation procedures. This PhD work presents, as its main part, a novel approach for identification and correction of multiple simultaneous faults, including incorrect observations, incorrect rules or/and defective interpolation procedures, during the interpolation process in an effort to remove all the inconsistencies. In particular, the assumption-based truth maintenance system (ATMS) is employed to record the dependencies of reasoning conclusions and system inconsistencies, while the underlying technique that the classical general diagnostic engine (GDE) employs for fault localisation is adapted to isolate possible sets of faults. From this, a modification mechanism is introduced to correct a set of identified faults in interpolation, thereby removing inconsistencies. This approach is applied to a real-world problem, which predicates the diarrhoeal disease rates in remote villages, to demonstrate the potential of this work in improving the effectiveness of fuzzy interpolation. The scale and move transformation-based fuzzy interpolation is utilised as the foundation of this work. This approach has been extended to deal with interpolation and extrapolation with multiple multi-antecedent rules. However, the generalised approach may not be able to degenerate back to the basic crisp interpolation and extrapolation based on two rules; and the approximate function of the extended approach may not be continuous. In order to address these limitations, a new approach to generalising the basic fuzzy interpolation techniques is also proposed in this work. Experimental results show that the proposed extension not only successfully removes all the existing shortcomings, but also leads to more reasonable conclusions. In addition, as a supplementary to ordinary fuzzy reasoning, results derived by fuzzy interpolation are expected to be compatible with those obtained by ordinary fuzzy reasoning whenever both approaches are applicable, but this is often not the case. Another further development of fuzzy interpolation made in this work is a different fuzzy interpolation approach based on a direct use of the Extension Principle, which bears a close relationship with the compositional rule of inference, which in turn plays a crucial rule in ordinary fuzzy reasoning. The proposed fuzzy interpolation approach has been demonstrated to be compatible with ordinary fuzzy inference for situations where ordinary fuzzy reasoning can be performed while still entailing interpolative inference for situations where an observation matches no fuzzy rules.