The grey extensible set

The grey system theory is a new subject to handl systems with missing information and extenics is also a new one to solve contradictory problems. The extensible set is the set theory of extenics and it includes the researched object, the dependent criterion and the extensible vary. Under the information-missing situation, the values of the researched object are grey. Then we propose the grey extensible set. The decision-makers can utilize it to solve the contradictory problems with missing information and it would be the set theory of grey extenics.