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


V.G. Kaburlasos, A. Kehagias, “Fuzzy inference system (FIS) extensions based on lattice theory”, IEEE Transactions on Fuzzy Systemsvol. 22, no. 3, pp. 531-546, 2014.

View on ResearchGate