Approximate reasoning systems facilitate fuzzy inference through activating fuzzy if–then rules in which attribute values are imprecisely described. Fuzzy rule interpolation (FRI) supports such reasoning with sparse rule bases where certain observations may not match any existing fuzzy rules, through manipulation of rules that bear similarity with an unmatched observation. This differs from classical rule-based inference that requires direct pattern matching between observations and the given rules. FRI techniques have been continuously investigated for decades, resulting in various types of approach. Traditionally, it is typically assumed that all antecedent attributes in the rules are of equal significance in deriving the consequents. Recent studies have shown significant interest in developing enhanced FRI mechanisms where the rule antecedent attributes are associated with relative weights, signifying their different importance levels in influencing the generation of the conclusion, thereby improving the interpolation performance. This survey presents a systematic review of both traditional and recently developed FRI methodologies, categorised accordingly into two major groups: FRI with non-weighted rules and FRI with weighted rules. It introduces, and analyses, a range of commonly used representatives chosen from each of the two categories, offering a comprehensive tutorial for this important soft computing approach to rule-based inference. A comparative analysis of different FRI techniques is provided both within each category and between the two, highlighting the main strengths and limitations while applying such FRI mechanisms to different problems. Furthermore, commonly adopted criteria for FRI algorithm evaluation are outlined, and recent developments on weighted FRI methods are presented in a unified pseudo-code form, easing their understanding and facilitating their comparisons.

近似推理系统通过激活不精确描述属性值的模糊 if-then 规则来促进模糊推理。模糊规则插值 (FRI) 支持使用稀疏规则库进行这种推理，其中某些观察可能与任何现有模糊规则不匹配，通过操作与不匹配观察具有相似性的规则。这与传统的基于规则的推理不同，后者需要观察和给定规则之间的直接模式匹配。数十年来，FRI 技术一直在不断研究，产生了各种类型的方法。传统上，通常假设规则中的所有先行属性在推导结果时都具有同等重要性。最近的研究对开发增强的 FRI 机制表现出极大的兴趣，其中规则先行属性与相对权重相关联，表示它们在影响结论生成方面的不同重要性级别，从而提高插值性能。本调查对传统和最近开发的 FRI 方法进行了系统回顾，并相应地分为两大类：具有非加权规则的 FRI 和具有加权规则的 FRI。它介绍并分析了从这两个类别中的每一个中选出的一系列常用代表，为这种重要的基于规则的推理的软计算方法提供了全面的教程。在每个类别内和两者之间提供了对不同 FRI 技术的比较分析，强调在将此类 FRI 机制应用于不同问题时的主要优势和局限性。此外，还概述了常用的 FRI 算法评估标准，并以统一的伪代码形式介绍了加权 FRI 方法的最新进展，以简化它们的理解并促进它们的比较。