Affiliations: Qingdao University of Science and Technology Qingdao
266061, P. R. China. E-mail: jiangkong@163.net | Chinese Academy of Sciences, Beijing 100080, P. R. China
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.
