Weighted Generalized M-P Inverse of Quantale Matrix

As an analogy of morphism or ring involution operation,Quantale involution operation is defined in this paper.The definitions of weighted generalized M-P inverse of a Quantale matrix and generalized left(right) cancellable property are given.Under these definitions,it is proved that if a Quantale matrix has a weighted generalized M-P inverse,then the inverse is unique.Based on this result,by using the method of ring theory,some characterizations for a Quantale matrix to possess a weighted generalized M-P inverse are obtained.Our results are new and generalize some recent results in this field.