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TP Grid Structure of Functions

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Dual-Control-Design

Part of the book series: Topics in Intelligent Engineering and Informatics ((TIEI,volume 17))

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Abstract

There are two conceptually important steps of the TS Fuzzy model transformation. One is to extract the TP grid structure of functions. The TP grid structure captures all numerical information that will be important to derive the TP function or TS Fuzzy model variant of a given function or model. The TP grid structure is essentially the component-wise discretized variant of the TP functions or TS Fuzzy models. The role of the other important step of the TS Fuzzy model transformation is to increase the grid density of the TP grid structure to infinity in a numerical sense, which I will refer to as the “refinement” of the TP grid structure. This chapter shows how to transform discretized functions via Higher Order Singular Value Decomposition to a product of a tensor and matrices, which is the tensor product variant of the discretized function. The chapter also discusses how to control the trade-off between the complexity and accuracy of the decomposition and gives further practical hints. The chapter presents numerical examples to show how to easily determine the TP grid structure.

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Authors and Affiliations

  1. University of Pannonia, Veszprém, Hungary

    Péter Baranyi

  2. HUN-REN Hungarian Research Network, Budapest, Hungary

    Péter Baranyi

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  1. Péter Baranyi
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Correspondence to Péter Baranyi .

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Baranyi, P. (2023). TP Grid Structure of Functions. In: Dual-Control-Design. Topics in Intelligent Engineering and Informatics, vol 17. Springer, Cham. https://doi.org/10.1007/978-3-031-44575-0_5

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