Error calculation of the HOSVD-based rule base reduction in hierarchical fuzzy systems

In real time evaluation systems the decision should be made in time to avoid the serious consequences. In the literature there are several techniques which aim to reduce the computational complexity of these kinds of systems. Among others the Higher Order Singular Value Decomposition (HOSVD) based reduction method is a useful tool for handling this problem. In the case when only non-exact reduction can be performed, the error calculation is also essential, because the reduction degree is based on the calculated error in these systems. In this paper the authors present the HOSVD reduction error calculation in hierarchical fuzzy systems using Mamdani-type inference and define a general formula which includes the propagated error from the previous levels of the hierarchy; in which the error bound, calculated by different ways, can be used and takes into account the case when not all the inputs contain a propagated error but only a few of them. Furthermore a greedy algorithm is presented for reduction optimization.