We　investigate　the　representation　theory　of　the　positively　based　algebra　A(m,d),　which　is　a　generalization　of　the　noncommutative　Green　algebra　of　weak　Hopf　algebra　corresponding　to　the　generalized　Taft　algebra.　It　turns　out　that　A(m,d)　is　of　finite　representative　type　if　d　＜=　4,　of　tame　type　if　d　=　5,　and　of　wild　type　if　d　＞　6.　In　the　case　when　d　＜=　4,　all　indecomposable　representations　of　A(m,d)　are　constructed.　Furthermore,　their　right　cell　representations　as　well　as　left　cell　representations　of　A(m,d)　are　described.