APPLICATION OF SUPER INTERVAL MATRICES AND SET LINEAR ALGEBRAS BUILT USING SUPER INTERVAL MATRICES

Chapter Six

Super interval matrices are obtained by replacing the entries in super matrices by intervals of the form [0, a] where a ∈ Zn or Z+ ∪ {0} or Q+ ∪ {0} or R+ ∪ {0}. Also it can equally be realized as usual interval matrices which are partitioned in different ways to get different types of super interval matrices. Thus given any m × n super interval matrix M by partitioning M we can get several m × n super interval matrices. Also for each type of partition we have a collection and that collection can have nice algebraic structure. So in the place of one algebraic structure we get several of them with same natural order which is not possible in usual interval matrices. Hence in applying them to fields like mathematical / fuzzy modeling and in finite element methods using intervals one can get better results saving economy and time. Further when in super interval matrices if we replace the real intervals by fuzzy intervals we get super fuzzy interval matrices which can find its application in all problems where fuzzy interval solution is expected.

Certainly these new structures will be a boon to finite interval analysis were usual interval matrices can be replaced by super interval matrices and the results can be accurate time saving and the expert can experiment with different partitions of the interval matrix to obtain the expected or the best solution.