Adaptive Fuzzy Interpolation and Extrapolation with Multiple-antecedent Rules

Adaptive fuzzy interpolation strengthens the potential of fuzzy interpolative reasoning owning to its efficient identification and correction of defective interpolated rules during the interpolation process. This approach assumes that: i) two closest adjacent rules which flank the observation or a previously inferred result are always available; ii) only single-antecedent rules are involved. In practice, however, variable values of these rules may lie just on one side of the observation or inferred result. Also, there may be certain rules with multiple antecedents in the rule base. This paper extends the adaptive approach, in order to cover fuzzy extrapolation and to support rule base with multiple-antecedent rules. Adaptive fuzzy interpolation and extrapolation complement each other, which jointly improve the applicability of fuzzy interpolative reasoning, as it significantly reduces the restriction over the given rule base

Transformation-Based Fuzzy Rule Interpolation Using Interval Type-2 Fuzzy Sets

In support of reasoning with sparse rule bases, fuzzy rule interpolation (FRI) offers a helpful inference mechanism for deriving an approximate conclusion when a given observation has no overlap with any rule in the existing rule base. One of the recent and popular FRI approaches is the scale and move transformation-based rule interpolation, known as T-FRI in the literature. It supports both interpolation and extrapolation with multiple multi-antecedent rules. However, the difficult problem of defining the precise-valued membership functions required in the representation of fuzzy rules, or of the observations, restricts its applications. Fortunately, this problem can be alleviated through the use of type-2 fuzzy sets, owing to the fact that the membership functions of such fuzzy sets are themselves fuzzy, providing a more flexible means of modelling. This paper therefore, extends the existing T-FRI approach using interval type-2 fuzzy sets, which covers the original T-FRI as its specific instance. The effectiveness of this extension is demonstrated by experimental investigations and, also, by a practical application in comparison to the state-of-the-art alternative approach developed using rough-fuzzy setspublishersversionPeer reviewe

Fuzzy Interpolation Systems and Applications

Fuzzy inference systems provide a simple yet effective solution to complex non-linear problems, which have been applied to numerous real-world applications with great success. However, conventional fuzzy inference systems may suffer from either too sparse, too complex or imbalanced rule bases, given that the data may be unevenly distributed in the problem space regardless of its volume. Fuzzy interpolation addresses this. It enables fuzzy inferences with sparse rule bases when the sparse rule base does not cover a given input, and it simplifies very dense rule bases by approximating certain rules with their neighbouring ones. This chapter systematically reviews different types of fuzzy interpolation approaches and their variations, in terms of both the interpolation mechanism (inference engine) and sparse rule base generation. Representative applications of fuzzy interpolation in the field of control are also revisited in this chapter, which not only validate fuzzy interpolation approaches but also demonstrate its efficacy and potential for wider applications

Adaptive fuzzy interpolation

Fuzzy interpolative reasoning strengthens the power of fuzzy inference by the enhancement of the robustness of fuzzy systems and the reduction of the systems' complexity. However, after a series of interpolations, it is possible that multiple object values for a common variable are inferred, leading 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 interpolative transformations, thereby removing the inconsistencies. In particular, an assumption-based truth-maintenance system (ATMS) is used to record dependences between interpolations, and the underlying technique that the classical 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 realistic problem, which predicates the diarrheal disease rates in remote villages, to demonstrate the potential of this study

Adaptive Fuzzy Interpolation with Prioritized Component Candidates

Adaptive fuzzy interpolation strengthens the potential of fuzzy interpolative reasoning. It first identifies all possible sets of faulty fuzzy reasoning components, termed the candidates, each of which may have led to all the contradictory interpolations. It then tries to modify one selected candidate in an effort to remove all the contradictions and thus restore interpolative consistency. This approach assumes that all the candidates are equally likely to be the real culprit. However, this may not be the case in real situations as certain identified reasoning components may be more liable to resulting in inconsistencies than others. This paper extends the adaptive approach by prioritizing all the generated candidates. This is achieved by exploiting the certainty degrees of fuzzy reasoning components and hence of derived propositions. From this, the candidate with the highest priority is modified first. This extension helps to quickly spot the real culprit and thus considerably improves the approach in terms of efficiency