Definability of concept in incomplete information systems

Shunliang Huang 

Business School, Shandong University of Technology, No.88, Gongqingtuan Rd., Zibo 255000, China

An incomplete information table (a set) can be expressed as a family of complete information tables (sets). The family of complete information sets maybe constructs an interval set. A concept in incomplete information situation, called partially known concept, is said to be definable if its extension can be expressed as an interval set. The new definition of definability proposed in this paper, named interval definable, is different from its usual meaning in the rough sets theory where a concept is definable means that its extension is a definable set, which is the union of some equivalence classes. The new definition of definability not only provides a new interpretation of interval sets, but also endows more general meaning and deeper understanding of definability.