Tolerance-localized and control-localized solutions of interval linear equations system and their application to course assignment problem

Abstract

There are many approaches to solving a system of interval linear equations. Each of them has different semantics based on the context of the system. We define here two other types of solutions called ‘tolerance-localized’ and ‘control-localized’ solutions. A tolerance-localized solution means that it provides either tolerance, L-localized, or R-localized behavior in each equation of the system. The similar argument serves for a control-localized solution. Theorems are proved to obtain the characterizations of the new solutions. Both sets of tolerance-localized and control-localized solutions could be represented by a system of integer linear equations. An example of application to the course assignment problem is presented, where the teaching workload restriction has been considered as tolerance-localized or control-localized constraints.