  The theory introduced, presented and developed in this paper, is concerned
with an enriched extension of the theory of Rough Sets pioneered by Zdzislaw
Pawlak. The enrichment discussed here is in the sense of valuated categories as
developed by F.W. Lawvere. This paper relates Rough Sets to an abstraction of
the theory of Fuzzy Sets pioneered by Lotfi Zadeh, and provides a natural
foundation for "soft computation". To paraphrase Lotfi Zadeh, the impetus for
the transition from a hard theory to a soft theory derives from the fact that
both the generality of a theory and its applicability to real-world problems
are substantially enhanced by replacing various hard concepts with their soft
counterparts. Here we discuss the corresponding enriched notions for
indiscernibility, subsets, upper/lower approximations, and rough sets.
Throughout, we indicate linkages with the theory of Formal Concept Analysis
pioneered by Rudolf Wille. We pay particular attention to the all-important
notion of a "linguistic variable" - developing its enriched extension,
comparing it with the notion of conceptual scale from Formal Concept Analysis,
and discussing the pragmatic issues of its creation and use in the
interpretation of data. These pragmatic issues are exemplified by the
discovery, conceptual analysis, interpretation, and categorization of networked
information resources in WAVE, the Web Analysis and Visualization Environment
currently being developed for the management and interpretation of the universe
of resource information distributed over the World-Wide Web.
