A knowledge reduction approach for linguistic concept formal context

Abstract Formal concept analysis (FCA) has been widely studied as an important tool for data processing and knowledge discovery. The present work focuses on FCA under uncertainty while the attributes are described with linguistic terms or attribute description are incomplete. Accordingly, a linguistic concept formal context is introduced first. With an attempt of knowledge reduction, the multi-granularity similarity relationship between linguistic concepts is defined on the basis of granular computing which further divides the linguistic concept set into three parts under λ-granularity (i.e., core linguistic concept, unnecessary linguistic concept, and relative necessary linguistic concept). A multi-granularity linguistic reduction algorithm of incomplete linguistic concept formal context is then introduced. To handle the incompleteness, a new algorithm to complete the incomplete linguistic concept formal context based on the closeness degree between fuzzy objects is proposed. Finally, based on the Boolean matrix and Boolean factor analysis method, the linguistic concept knowledge reduction algorithm to extract the core linguistic concept and reduce the scale of linguistic concept lattice is proposed to handle the complexity, which is achieved by computing the similarity of linguistic concept knowledge in order to handle different types of linguistic information and concept knowledge. The effectiveness and practicability of the proposed model are illustrated by examples.