Investigating a relevance of fuzzy mappings

The study introduces a concept of relevance of fuzzy mappings regarded as f undamental constructs of granular computing and rule-based systems, in part icular. The notion of relevance of the fuzzy mappings is instrumental in th e quantification of the quality of such mappings prior to their detailed co nstruction. For the purposes of such quantification, we introduce shadowed sets and discuss as an algorithmic framework to be instrumental in expressi ng and quantifying the property of relevance of the fuzzy mappings, It is r evealed that shadowed sets provide an interesting three-valued quantificati on of this property (such as acceptable mapping, marginal mapping, and a la ck of mapping). The paper includes a number of detailed calculations concer ning two commonly exploited classes of triangular and Gaussian fuzzy sets. Numerical studies are discussed as well.