Liu in 2007 has introduced the theory of uncertainty [[20]](#ref-0020). The structure of the present paper is to define some new type of generalized ∆- operator on this theory of uncertainty by employing the notion of sequence spaces. Some basic structures will be computed. Also, some sharp inclusion relations with counter examples concerning to the newly constructed spaces of this paper will be computed. Mathematical Subject Classification 2010: 46A45; 60F17.