Formal concept attribute partial-order structure diagram and applications

Abstract

Formal-Concept Attribute Partial-Order Structure Diagram (FC-APOSD) is proposed on the basis of formal concept analysis and Attribute Partial-Order Structure Diagram (APOSD) theory, which inherits the advantage of good visualisation of APOSD and can reveal relationships among formal concepts at the same time. This paper focuses on the mathematical description of FC-APOSD, how to use FC-APOSD to explore knowledge from a formal context and the applications of FC-APOSD. Specifically, our work mainly includes the following points: 1. FC-APOSD is described in mathematical formal language; 2. After giving a necessary and sufficient condition for an attribute set of a node to be the intension of a formal concept, a method to find pseudo-intensions using FC-APOSD is provided; 3. The relationship among objects is discussed using groups and subgroups in FC-APOSD; 4. A method to find exclusive attributes from a formal context is provided by using FC-APOSD; 5. With the help of classical Chinese medicinal formulae related to emotional diseases from 'Treatise on Febrile and Miscellaneous Diseases', the syndrome-treatment pattern of emotional diseases is explored using the FC-APOSD method.