Attribute-Weighted Fuzzy Interpolative Reasoning

As exhibited previously, the weights of individual rule antecedent attributes can be computed through a reverse engineering procedure applied to the given fuzzy rule base. As such, the unrealistic assumption that all attributes are of equal significance can be removed in systems modelling, and an enhanced fuzzy rule-based inference mechanism developed. This chapter describes how weights of rule antecedents can be integrated within non-weighted fuzzy rule interpolation (FRI), where attributes are unweighted, to reinforce the performance of fuzzy interpolative reasoning. This enables approximate reasoning to be carried out with unmatched observations, which cannot be implemented using CRI (including newly developed attribute-weighted CRI that was reported in Chap. 5 ). The present chapter describes the innovative approaches in which conventional non-weighted FRI is extended to handling attributes with weights. This covers three popular and commonly used FRI methods, including the most popular scale and move transformation-based FRI (T-FRI). In these extensions, the weights are utilised to modify all components of an FRI computation process systematically, covering the selection of nearest rules and the interpolation of selected rules. This is followed by an in-depth description of attribute-weighted T-FRI and an illustration of its working procedure by continuing the case study of Chap. 4 . It discusses the key differences between the original non-weighted T-FRI method and the attribute-weighted extensions, including two more FRI methods which are not a member of the popular T-FRI family. The chapter further presents a summarised workflow of weighted approximate interpolative reasoning and a generalised framework for fuzzy rule-based inference that is supported by weighted FRI, supported with a suite of application examples.