In this paper ill-posed linear inverse problems that arises in many applications is considered. The instability of special kind of these problems and it's relation to the kernel, is described. For finding a stable solution to these problems we need some kind of regularization that is presented. The results have been applied for a singular equation.

Linear equality systems with fuzzy parameters and crisp variables defined by the Zadeh’s extension principle are called possibilistic linear equality systems. This study focuses on the problem of stability (with respect to small changes in the membership function of fuzzy parameters) of the solution in these systems.

Many statistical problems, including some of the most important for physical applications, have long been regarded as underdetermined from the standpoint of a strict frequency de nition of probability; yet they may appear well posed or even overdetermined by the principles of maximum entropy and transformation groups. Furthermore, the distributions found by these methods turn out to have a de n...