Consistency of interval judgment matrix

The consistency problem of the interval judgment matrix is studied.Existing definitions on the consistency in some papers are firstly summarized and analyzed,and the invalidity in these definitions are pointed out.Furthermove,some definitions concerning the consistency of interval judgement matrix including perfect consistency,strong consistency,consistency and satisfactory consistency are proposed,and the relations between these definitions and the existing ones in some papers are discussed.The validity of these definitions is confirmed.Moreover,a method for testing consistency is given,and two examples show the effectiveness and potential practicality of this method.