A Lattice-Computing ensemble for reasoning based on formal fusion of disparate data types, and an industrial dispensing application

By “fusion” this work means integration of disparate types of data including (intervals of) real numbers as well as possibility/probability distributions defined over the totally-ordered lattice (R, ⩽) of real numbers. Such data may stem from different sources including (multiple/multimodal) electronic sensors and/or human judgement. The aforementioned types of data are presented here as different interpretations of a single data representation, namely Intervals’ Number (IN). It is shown that the set F of INs is a partially-ordered lattice (F, ⪯) originating, hierarchically, from (R, ⩽). Two sound, parametric inclusion measure functions σ:FN × FN → [0, 1] result in the Cartesian product lattice (FN, ⪯) towards decision-making based on reasoning. In conclusion, the space (FN, ⪯) emerges as a formal framework for the development of hybrid intelligent fusion systems/schemes. A fuzzy lattice reasoning (FLR) ensemble scheme, namely FLR pairwise ensemble, or FLRpe for short, is introduced here for sound decision-making based on descriptive knowledge (rules). Advantages include the sensible employment of a sparse rule base, employment of granular input data (to cope with imprecision/uncertainty/vagueness), and employment of all-order data statistics. The advantages as well as the performance of our proposed techniques are demonstrated, comparatively, by computer simulation experiments regarding an industrial dispensing application.

► The mathematical lattice of Intervals’ Numbers (INs) stems from real numbers. ► INs integrate (granular) data stemming from either sensors or human judgment. ► Fuzzy lattice reasoning (FLR) is employed for tunable decision-making. ► The novel FLRpe scheme is applied on INs for robust decision-making by voting. ► Computer simulation experiments demonstrate comparatively advantages of FLRpe.