Singular Fuzzy Linear Systems and the W-weighted Drazin Inverse

摘要

The linear system of equations Ax = b wherein A is a crisp singular matrix X and b are vectors of fuzzy numbers in paremetric form is called a singular fuzzy linear system of equations. Let A ∈ C~(m×n), W ∈ C~(n×m), the rectangular crisp matrix A has the unique W-weighted Drazin inverse, denoted by A~(D,W),which satisfies AWX = XWA, XWAWX= X, (AW)~(k+1) XW = (AW)~k , where ind(AW)=k. The W-weighted Drazin inverse in solving the crisp linear system WAWx= b has been used. In this paper, some new results on the W-weighted Drazin inverse are given. This results in solving singular fuzzy linear system, constrained linear systems and etc, would be applied.