基于模糊规则的插值推理算法综述

Fuzzy rule-based approximate reasoning system, established with support of the fuzzy set theory and fuzzy logic, has gained rapid developments in a variety of scientific areas, including mathematics, engineering, and computer science. It works by the use of a set of fuzzy if-then rules, as an effective tool to address the issues of imprecision and vagueness in modelling and reasoning. The conventional reasoning mechanism can only perform inference with dense rule bases where any input observation is able to match the existing fuzzy rules. Fuzzy rule interpolation (FRI) facilitates fuzzy rule-based inference system to make reasoning when incomplete (or sparse) rule bases are available, where an estimation is able to be made by computing an interpolated consequent for the observation which matches no rules. This paper systematically reviews the fuzzy interpolative reasoning technique where FRI is involved. In particular, the existing methodologies of FRI are generically categorised into two groups, which are the α-cut based interpolation and the intermediate rule based interpolation, respectively. The main body of this survey reviews each of the two groups of method, where individual representative approaches are described in detail to demonstrate the basic idea of their implementations of FRI. Also, other alternative FRI methods and practical applications of fuzzy interpolative reasoning systems are briefly outlined. In addition, the most commonly used evaluation criteria over FRI algorithms are collected and presented, supported by the comparison and discussion among the typical methods. This paper finally points out potential work of future study in this area.