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Complexity
Volume 2018, Article ID 8546976, 9 pages
https://doi.org/10.1155/2018/8546976
Research Article

Extension of the Multi-TP Model Transformation to Functions with Different Numbers of Variables

Széchenyi István University, Győr, Hungary

Correspondence should be addressed to Péter Baranyi; moc.liamg@iynarab.retep.forp

Received 18 September 2017; Accepted 29 January 2018; Published 19 March 2018

Academic Editor: Kevin Wong

Copyright © 2018 Péter Baranyi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The tensor product (TP) model transformation defines and numerically reconstructs the Higher-Order Singular Value Decomposition (HOSVD) of functions. It plays the same role with respect to functions as HOSVD does for tensors (and SVD for matrices). The need for certain advantageous features, such as rank/complexity reduction, trade-offs between complexity and accuracy, and a manipulation power representative of the TP form, has motivated novel concepts in TS fuzzy model based modelling and control. The latest extensions of the TP model transformation, called the multi- and generalised TP model transformations, are applicable to a set functions where the dimensionality of the outputs of the functions may differ, but there is a strict limitation on the dimensionality of their inputs, which must be the same. The paper proposes an extended version that is applicable to a set of functions where both the input and output dimensionalities of the functions may differ. This makes it possible to transform complete multicomponent systems to TS fuzzy models along with the above-mentioned advantages.