In this paper, we use parametric form of fuzzy number and we converta fuzzy linear system to two linear system in crisp case. Conditions for the existence of a minimal solution to $mtimes n$ fuzzy linear equation systems are derived and a numerical procedure for calculating the minimal solution is designed. Numerical examples are presented to illustrate the proposed method.

Granuloma annulare(GA) is an inflammatory benign cutaneous disease of unknown etiology that may manifest different clinical features. The most common presentation or classic form of the disease is manifested as flesh colored, annular grouped papules, commonly involving the hands and feet. Various skin injuries and infections have been reported to trigger GA, including insect bites, warts,...

We first introduce matrix concepts in linear programming by developing a variation of the simplex method called the revised simplex method. This algorithm, which has become the basis of all commercial computer codes for linear programming, simply recognizes that much of the information calculated by the simplex method at each iteration, as described in Chapter 2, is not needed. Thus, efficienci...


 Linear Contrasts 
 Week 4 Prof. Patrick Bennett Omnibus vs. Focussed F tests • A significant omnibus F test supports a very general hypothesis not all means are equal not all group effects are zero • Significant F doesn’t tell us how group means differ • Generality of omnibus F often comes at cost of reduced power Bennett, PJ PSY710 Chapter 3 Ȳ u is simply the mean of the group means; di↵eren...

in this work‎, ‎an iterative method based on a matrix form of lsqr algorithm is constructed for solving the linear operator equation $mathcal{a}(x)=b$‎ ‎and the minimum frobenius norm residual problem $||mathcal{a}(x)-b||_f$‎ ‎where $xin mathcal{s}:={xin textsf{r}^{ntimes n}~|~x=mathcal{g}(x)}$‎, ‎$mathcal{f}$ is the linear operator from $textsf{r}^{ntimes n}$ onto $textsf{r}^{rtimes s}$‎, ‎$ma...