Shadowed Type-2 Fuzzy Logic Systems

摘要

General Type-2 Fuzzy Logic Systems (GT2 FLSs) are an extension to Type-1 (T1) FLS where at least one Fuzzy Set (FS) is a GT2 FS. However, due to the high computational complexity of operations on GT2 FSs, GT2 FLSs have been rarely used in practical applications. Instead, Interval Type-2 (IT2) FLSs which employ constrained IT2 FSs, have been widely used. Despite their superior computational complexity, IT2 FLSs lack the expressive power of GT2 FSs when describing various sources of uncertainty. Further, it is unclear how to derive an IT2 FLS from a specific GT2 FLS. To alleviate these issues, this paper outlines a novel concept of Shadowed Type-2 Fuzzy Logic Systems (ST2 FLS). The ST2 FLS consists of previously proposed ST2 FSs, which are T2 FSs with secondary membership functions represented as Shadowed Sets (SSs). Because ST2 FSs are directly induced by GT2 FSs, the entire design of the ST2 FLS can be automatically derived from a specific GT2 FLS. Furthermore, the proposed ST2 FLS was shown to approximate GT2 FLS more accurately compared to IT2 FLS, while maintaining the computational efficiency of IT2 FLS.