Granular Encoding-Decoding for the Design of Granular Architectures

Fuzzy constructs (models) interact with numeric entities. This communication is realized through mechanisms of encoding and decoding. Encoding realizes a representation of input data through a collection of information granules and, as such, can be viewed as a nonlinear transformation of the original numeric entity to some internal (granular) format. The decoding is carried out in the opposite direction: the result at the level of information granules is brought back to the numeric entity. This study provides a unified view of the functionalities and design of these mechanisms by studying their components information granules. The optimization concerns a minimization of loss functions guided by criteria of minimal reconstruction error and a retention of semantics of the codebooks (landmarks) encountered in the encoding and decoding procedures. The role of triangular fuzzy sets is discussed along with associated learning mechanisms. Illustrative applications to hierarchical models and fuzzy cognitive maps are covered.