Piecewise-linear approximation of non-linear models based on probabilistically/possibilistically interpreted intervals’ numbers (INs)

Linear models are preferable due to simplicity. Nevertheless, non-linear models often emerge in practice. A popular approach for modeling nonlinearities is by piecewise-linear approximation. Inspired from fuzzy inference systems (FISs) of Tagaki–Sugeno–Kang (TSK) type as well as from Kohonen’s self-organizing map (KSOM) this work introduces a genetically optimized synergy based on intervals’ numbers, or INs for short. The latter (INs) are interpreted here either probabilistically or possibilistically. The employment of mathematical lattice theory is instrumental. Advantages include accommodation of granular data, introduction of tunable nonlinearities, and induction of descriptive decision-making knowledge (rules) from the data. Both efficiency and effectiveness are demonstrated in three benchmark problems. The proposed computational method demonstrates invariably a better capacity for generalization; moreover, it learns orders-of-magnitude faster than alternative methods inducing clearly fewer rules.