In this chapter we discuss soft concept analysis, a study which identifies an enriched notion of "conceptual scale" as developed in formal concept analysis with an enriched notion of "linguistic variable" as discussed in fuzzy logic. The identification "enriched conceptual scale" = "enriched linguistic variable" was made in a previous paper (Enriched interpretation, Robert E. Kent). In this chapter we offer further arguments for the importance of this identification by discussing the philosophy, spirit, and practical application of conceptual scaling to the discovery, conceptual analysis, interpretation, and categorization of networked information resources. We argue that a linguistic variable, which has been defined at just the right generalization of valuated categories, provides a natural definition for the process of soft conceptual scaling. This enrichment using valuated categories models the relation of indiscernability, a notion of central importance in rough set theory. At a more fundamental level for soft concept analysis, it also models the derivation of formal concepts, a process of central importance in formal concept analysis. Soft concept analysis is synonymous with enriched concept analysis. From one viewpoint, the study of soft concept analysis that is initiated here extends formal concept analysis to soft computational structures. From another viewpoint, soft concept analysis provides a natural foundation for soft computation by unifying and explaining notions from soft computation in terms of suitably generalized notions from formal concept analysis, rough set theory and fuzzy set theory.

Conceptual Knowledge Markup Language (CKML) is an application of XML. Earlier versions of CKML followed rather exclusively the philosophy of Conceptual Knowledge Processing (CKP), a principled approach to knowledge representation and data analysis that "advocates methods and instruments of conceptual knowledge processing which support people in their rational thinking, judgment and acting and promote critical discussion." The new version of CKML continues to follow this approach, but also incorporates various principles, insights and techniques from Information Flow (IF), the logical design of distributed systems. Among other things, this allows diverse communities of discourse to compare their own information structures, as coded in logical theories, with that of other communities that share a common generic ontology. CKML incorporates the CKP ideas of concept lattice and formal context, along with the IF ideas of classification (= formal context), infomorphism, theory, interpretation and local logic. Ontology Markup Language (OML), a subset of CKML that is a self-sufficient markup language in its own right, follows the principles and ideas of Conceptual Graphs (CG). OML is used for structuring the specifications and axiomatics of metadata into ontologies. OML incorporates the CG ideas of concept, conceptual relation, conceptual graph, conceptual context, participants and ontology. The link from OML to CKML is the process of conceptual scaling, which is the interpretive transformation of ontologically structured knowledge to conceptual structured knowledge.