Numeric data to information granules and computing with words

Abstract

The underlying intent of this study is to show how numeric data, fuzzy sets (and information granules, in general) as well as information granules of higher type build a knowledge-based conceptual hierarchy. The bottom-up organization of the paper starts with a concept and selected techniques of data compactification. Compactification is the process, which involves information granulation and in successive phases may give rise to higher type constructs (say, type-2 fuzzy sets, interval-valued fuzzy sets and alike). The detailed algorithmic investigations are provided where we show how membership grades of higher type constructs are formed. In the sequel, we focus on Computing with Words (CW) which in this context is regarded as a general paradigm of processing information granules. We stress the relationships between numeric computing and processing information granules of well-defined semantics (which constitutes the essence of Computing with Words).