Lattice Computing: A Mathematical Modelling Paradigm for Cyber-Physical System Applications

By “model”, we mean a mathematical description of a world aspect. Mathematical models, implemented in software, are often engaged to drive hardware. Models are typically developed in the Euclidean space RN, for an integer number N, where R is the totally ordered lattice of real numbers. Note that modelling in RN is inherently related to the physical world, where the conventional measurement process gives rise to the set, R, of real numbers. Nevertheless, alternative spaces for modelling, even in physics, have been proposed, such as a probability space whose “event space” suggests a mathematical lattice. The interest here is in explicit, rigorous modelling in a mathematical lattice data domain. Mathematical lattices emerged in the mid-19th century as a spin-off of work on the formalizing of propositional logic. Furthermore, it was Birkhoff’s work in the mid-1930s that started the general development of mathematical lattice theory. The proliferation of computers has triggered a growing interest in mathematical lattices, including Boolean algebra for computer design as well as for software verification. As a result of the proliferation of computers, cyber–physical systems (CPSs) have emerged as devices with both sensing and reasoning capacities, which may also interact with humans. Notably, in addition to numerical (multimodal) sensory data during their interactions with one another, humans engage non-numerical data such as spoken language, gestures, rules, moral principles, concepts, symbols, etc. Therefore, for seamless interactions with humans, CPSs are also expected to cope with non-numerical data. Lately, the “Lattice Computing (LC) information processing paradigm” has been proposed in CPS applications for mathematical modelling based on lattice theory by rigorously unifying (and fusing), in a Cartesian product, lattice-ordered numerical data and/or non-numerical data. Especially promising is the capacity of mathematical lattices for knowledge representation. For instance, mathematical lattices may suggest useful alternatives for representing human intensions/emotions and other. Part of the interest of lattice theory is still in mathematics. However, the interest in practical applications is growing. This Special Issue presents recent advances in the LC paradigm, including studies in abstract/applied mathematics, formal concept analysis (FCA), mathematical morphology and image processing, machine learning, and computational intelligence, including both neural computing and fuzzy classifier designs