Tolerance-localized and control-localized solutions to system of interval linear equations

Abstract

In this thesis, we are interested in a system of interval linear equations Ax=b whose coefficient A and right hand side b vary in some real intervals. We study two types of solutions called tolerance--localized and control--localized solutions of interval linear equations system. The characterizations of each solution are proposed in two main theorems. First, the proposed theorem is stated in terms of center and radius matrices which is directly proved by following their definitions. The other theorem is presented as magnitude sense with new notation. Based on the second theorem, the closed form of all solution sets is released. In addition, we apply the idea of tolerance--localized solution to deal with the course assignment problem. To optimize the preference and over/under workload of the instructors, we formulate the modified integer linear programming model to solve the problem. The obtained result is not significantly different from the original model. Moreover, we found that the obtained result gives higher overall preference of the instructors than actual course assignment in the 2nd semester of 2018.