Fuzzy Inference System (FIS) Extensions Based on the Lattice Theory

摘要: A fuzzy inference system (FIS) typically implements a function $f: {\BBR}^{N} \rightarrow {\mathfrak T}$ , where the domain set ${\BBR}$ denotes totally ordered of real numbers, whereas range ${\mathfrak may be either T} = {\BBR}^{M}$ (i.e., FIS regressor) or labels classifier), etc. This study considers complete lattice $({\BBF},\preceq)$ Type-1 Intervals’ Numbers (INs), an IN $F$ can interpreted as possibility distribution probability distribution. In particular, this concerns matching degree (or satisfaction degree, firing degree) part FIS. Based on inclusion measure $\sigma : {\BBF} \times [0,1]$ we extend traditional design toward implementing {\BBF}^{N} with following advantages: 1) accommodation granular inputs; 2) employment sparse rules; and 3) introduction tunable (global, rather than solely local) nonlinearities explained in manuscript. New theorems establish that $\sigma$ is widely (though implicitly) used by FISs trivial point) input vectors. preliminary industrial application demonstrates advantages our proposed schemes. Far-reaching extensions are also discussed.