Reconstruction problem and information granularity

The paper elaborates on the representation and reconstruction of numerical and nonnumerical data in fuzzy modeling. Proposed are general criteria leading to the distortion-free interfacing mechanisms that help transform information between the systems (or modeling environments) operating at different levels of information granularity. Distinguished are three basic categories of information: numerical, interval-valued, and linguistic (fuzzy). Since all of them are dealt with here, the paper subsumes the current studies concentrated exclusively on representing fuzzy sets through their numerical representatives (prototypes). The algorithmic framework in which the distortion-free interfacing is completed is realized through neural networks. Each category of information is treated separately and gives rise to its own specialized architecture of the neural network. Similarly, these networks require carefully designed training sets that fully capture the specificity of the reconstruction problem. Several carefully selected numerical examples are aimed at the illustration of the key ideas.