Abstract
The TP and the TS Fuzzy model transformation investigated in the previous chapters transform a given function to the tensor product of a core tensor and weighting functions defined per each dimension. This chapter introduces the Pseudo TP or TS Fuzzy model transformation concept, an inverse process of the TP or TS Fuzzy model transformations, designed for cases where the weighting / membership functions are already defined over at least some of the dimensions, meaning that only the core tensor and the remaining weighting functions need to be found. If a TP representation of the function doesn’t exist, the Pseudo TP/TS Fuzzy model transformation constructs a core tensor (and remaining weighting functions) that provides the best \(L_2\) norm approximation of the given function using predefined weighting functions. The term “Pseudo” originates from “Pseudo inverse”, reflecting the transformation’s inverse nature. The chapter provides numerical examples and MATLAB codes to demonstrate this transformation’s effectiveness.
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Baranyi, P. (2023). Pseudo TP/TS Fuzzy Model Transformation. In: Dual-Control-Design. Topics in Intelligent Engineering and Informatics, vol 17. Springer, Cham. https://doi.org/10.1007/978-3-031-44575-0_8
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DOI: https://doi.org/10.1007/978-3-031-44575-0_8
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