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