A novel method for new membership function calculation in HOSVD-based reduction to improve the operation needs

Complexity reduction techniques should be used in those kinds of complex systems in which the evaluation time has a critical importance. Although the hierarchical clustered structure can reduce the number of the rules in contrast to the single-staged models, a further reduction technique is recommended to use in the subsystems to improve the evaluation time. A possible method among the several available ones is the widely used Higher Order Singular Value Decomposition (HOSVD), which is used to reduce the number of the rules in fuzzy logic-based systems. The authors studied this method and a novel pre-processing procedure was developed. This procedure can be used in HOSVD rule base reduction as an offline process to calculate the new membership function values belongs to crisp inputs. Due to offline processing the operation needs are reduced at all levels and all groups of the hierarchy where the reduction is performed separately. The novel method is based on the equidistant division of the input's domain, where the division is based on the accuracy of the input factor.