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Pseudoinversion Through an Innovative Noise-Resilient Neutrosophic Logic Activated Zeroing Neural Network: Application to Mobile Object Localization
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DOI：10.1109/tfuzz.2026.3690694.png)
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Abstract
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The efficient calculation of the time-varying matrix (TVM) pseudoinverse, or Moore–Penrose inverse, is a fundamental requirement for solving dynamic problems in diverse fields. To address this issue, this research proposes a novel zeroing neural network model, termed ZMPC, that is specifically designed for TVM pseudoinverse computation. The ZMPC model, in contrast to traditional frameworks, simultaneously enforces all four Penrose equations to ensure that the computed solution remains the unique TVM pseudoinverse with improved tracking accuracy and reduced computational load. Another significant theoretical contribution of this research is the integration of a novel finite-time noise-resilient adaptive activation function (NAF), which uses neutrosophic logic principles to enhance convergence and robustness. To evaluate these developments, the proposed NAF-based ZMPC framework is compared with state-of-the-art formulations through three numerical examples and a practical mobile object localization task. The results demonstrate that the proposed framework achieves improved effectiveness, consistent finite-time convergence, and high noise robustness across arbitrary matrix dimensions, outperforming prevalent methodologies in TVM pseudoinversion.
Keywords:
Activation function (AF)
fuzzy system
mobile object localization
Moore–Penrose inverse
neutrosophic logic
zeroing neural network (ZNN)
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