Weighted Fuzzy Interpolative Reasoning

Unlike classical rule-based inference that performs direct pattern matching between observations and the given rules, fuzzy rule interpolation (FRI) supports approximate reasoning with sparse rule bases where the rules available do not cover the entire problem space. That is, it works for situations where certain observations may not match any existing fuzzy rules, through approximate knowledge interpolation by manipulating rules that bear similarity with an unmatched observation. In conventional fuzzy interpolative reasoning systems, multiple rules are generally involved with each concerning multiple rule antecedent attributes. However, these antecedent attributes are assumed to have equal significance within the rule interpolation process. Recent studies have shown great interest in developing enhanced FRI methods where the rule antecedent attributes are associated with relative weights, signifying their different importance levels in deriving the conclusion, thereby improving the interpolative inference performance. Research from this viewpoint essentially opens a wide avenue, including the inevitable point of attribute evaluation and attribute weight computation. This chapter reviews such advances in the development of weighted fuzzy interpolative reasoning systems. It first summarises the common nature of each typical existing approach, followed by presenting a brief comparison amongst them. It finishes with a qualitative, overall comparison between the weighted FRI techniques and their original counterparts, namely, the unweighted approaches that were outlined in Chap. 2 . In particular, weighted FRI methods are reformulated and presented in a unified pseudocode form, easing their understanding and facilitating their comparisons.