Analysis and analytical solution of incommensurate fuzzy fractional nabla difference systems in neural networks

Abstract

Uncertain incommensurate fractional nabla difference systems (IFDSs) in recurrent neural networks (RNNs) are analyzed using fuzzy number theory to address input uncertainties. Fuzzy number theory and its operations are re-investigated, and the H-differenceable concept is introduced. The existence of a unique H-differenceable solution for incommensurate RNNs is proved. A recursive algorithm is proposed to obtain fuzzy solutions. Illustrative examples with 2-dimensional IFDSs are provided to validate the framework for integrating fractional calculus, fuzzy dynamics and incommensurate RNNs.

Keywords

Fuzzy numbers / Fuzzy neural networks / Incommensurate systems / Nabla fractional difference / Recurrent neural networks / Uncertainty analysis

Funding

This research is supported by the Neijiang Normal University school-level science and technology project (key project, No. XJ2024008301) and Sharestan retrofit design co.

Declaration of competing interest

The authors declare that they have no conflict of interest to disclose.

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