Attribute-Weighted Fuzzy Rule-Based Inference

Many computational techniques have been established to perform approximate reasoning, including the popular compositional rule of inference (CRI) [15], approximate analogical reasoning schema (AARS) [11, 12], and Takagi-Sugeno (TS) interpretation [10]. In particular, CRI can effectively implement fuzzy inference by accomplishing generalised modus ponens, as demonstrated by many successful real-world applications, following the pioneering work of Mamdani’s fuzzy logic controller [8]. Recently, the potential benefits of weighting individual domain attributes have been exploited not only in weighted FRI, but in a wide range of alternative multi-attribute decision-making systems (e.g. those following evidential reasoning [14, 16]). Collectively, they showcase the observation that distinguishing different significance levels of individual domain attributes is often necessary to accurately characterise the relationship between the domain input and output. As illustrated in Chap. 4 , both the assessed weights of rule attributes and the formalised attribute-weighted fuzzy rule base help in developing attribute-weighted fuzzy rule-based inference techniques. This chapter first outlines the basic idea and working procedure of CRI inference mechanism, before presenting a mechanism for exploiting the attribute weights to guide the selection of appropriate rules for rule-firing in a process of weighted CRI. Extending this, it further presents in-depth discussions about the determination of the weight of rule consequent attribute. The chapter also includes a set of case studies to evaluate and analyse the performance of attribute-weighted CRI.