User-driven summarization of data based on gradual rules

A procedure is presented here for building a summarized, but faithful, description of a set of data which are supposed to belong to the graph of a function, or more generally to the graph of a multiple-valued function, whose possible values, at any point, remain ''close'' enough to each other. This description is expressed by means of fuzzy gradual rules which: i) are meaningful for a human operator (because their conditional parts are expressed using fuzzy sets which belong to partitions into linguistic categories provided by the user), and ii) have a clear and not ambiguous semantics in order to be usable by an approximate reasoning system.