Relational Contexts and Relational Concepts

  • Authors:

  • Feng Jiang;Yuefei Sui;Cungen Cao

  • 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;Chinese Academy of Sciences, Beijing 100080, P. R. China

  • Venue:
  • Fundamenta Informaticae
  • Year:
  • 2010

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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.