Singular Fuzzy Linear Systems and the W-weighted Drazin Inverse

The linear system of equations A (x) over tilde = (b) over tilde wherein A is a crisp singular matrix (x) over tilde and (b) over tilde are vectors of fuzzy numbers in paremetric form is called a singular fuzzy linear system of equations. Let A is an element of C-mxn, W is an element of C-nxm, 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+1XW = (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.