Relational Contexts and Relational Concepts

Abstract

Formal concept analysis (FCA) is a mathematical description and theory of concepts implied in formal contexts. And the current formal contexts of FCA aim to model the binary relations between individuals (objects) and attributes in the real world. In the real world we usually describe each individual by some attributes, which induces the relations between individuals and attributes. But there also exist many relations between individuals, for instance, the parent-children relation in a family. In this paper, to model the relations between individuals in the real world, we propose a new context -relational context for FCA, which contains a set U of objects and a binary relation r on U. Corresponding to the formal concepts in formal contexts, we present different kinds of relational concepts in relational contexts, which are the pairs of sets of objects. First we define the standard relational concepts in relational contexts. Moreover, we discuss the indirect relational concepts and negative relational concepts in relational contexts, which aim to concern the indirection and negativity of the relations in relational contexts, respectively. Finally, we define the hybrid relational concepts in relational contexts, which are the combinations of any two different kinds of relational concepts. In addition, we also discuss the application of relational contexts and relational concepts in the supply chain management field.

Concept Lattices in Green Farmland Databases and Concept Intent Reduction for the Mass Food Production

“…A node of concept lattices is an objects/attributes pair, called a formal concept, consisting of two parts: the extent (objects the concept covers) and intent (attributes describing the concept). Concept lattices have already been applied to a wide range of disciplines such as knowledge discovery (Belohlavek et al, 2014;Berghammer and Winter, 2013;Huchard et al, 2007;Jiang and Deogun, 2007;Lei et al, 2009;Missaoui et al, 2012;Poelmans et al, 2010), information retrieval, software engineering (Jay et al, 2008;Tilley and Eklund, 2007), rough set theory (Jiang et al, 2010;Qu et al, 2007;Yao, 2004;Wei and Qi, 2010;Zhou and Yao, 2010), knowledge ontology (Ge et al, 2012;Chunping and Liu, 2012) and the connections with description logics (Bazin and Ganascia, 2012;Ma et al, 2012).…”

“…Recently, a main axis of research on FCA has aimed at extending the classical FCA, either by scaling methods (Ganter and Wille, 1999;Lei et al, 2009) or by extending the definition of the Galois connection (Huchard et al, 2007;Jiang et al, 2010). One of the disadvantages of scaling methods is that it is very sensitive to user's selection of scale attributes.…”