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Zeroing Neural Network Based on Neutrosophic Logic for Calculating Minimal-Norm Least-Squares Solutions to Time-Varying Linear Systems

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Abstract

This paper presents a dynamic model based on neutrosophic numbers and a neutrosophic logic engine. The introduced neutrosophic logic/fuzzy adaptive Zeroing Neural Network dynamic is termed NSFZNN and represents an improvement over the traditional Zeroing Neural Network (ZNN) design. The model aims to calculate the matrix pseudo-inverse and the minimum-norm least-squares solutions of time-varying linear systems. The improvement of the proposed model emerges from the advantages of neutrosophic logic over fuzzy and intuitionistic fuzzy logic in solving complex problems associated with predictions, vagueness, uncertainty, and imprecision. We use neutrosphication, de-fuzzification, and de-neutrosophication instead of fuzzification and de-fuzzification exploited so far. The basic idea is based on the known advantages of neutrosophic systems compared to fuzzy systems. Simulation examples and engineering applications on localization problems and electrical networks are presented to test the efficiency and accuracy of the proposed dynamical system.

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Acknowledgements

Predrag Stanimirović is supported by the Ministry of Education, Science and Technological Development, Republic of Serbia, Contract No. 451-03-68/2020-14/200124. Predrag Stanimirović is supported by the Science Fund of the Republic of Serbia, #GRANT No 7750185, Quantitative Automata Models: Fundamental Problems and Applications—QUAM. This work was supported by the Ministry of Science and Higher Education of the Russian Federation (Grant No. 075-15-2022-1121).

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Authors and Affiliations

  1. Department of Economics, Division of Mathematics-Informatics and Statistics-Econometrics, National and Kapodistrian University of Athens, Sofokleous 1 Street, 10559, Athens, Greece

    Vasilios N. Katsikis & Spyridon D. Mourtas

  2. University of Athens Master of Business Administration, National and Kapodistrian University of Athens, Athens, Greece

    Vasilios N. Katsikis

  3. Administration of Businesses and Organizations Department, Hellenic Open University, 26335, Patras, Greece

    Vasilios N. Katsikis

  4. Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, Niš, 18000, Serbia

    Predrag S. Stanimirović

  5. Laboratory “Hybrid Methods of Modelling and Optimization in Complex Systems”, Siberian Federal University, Prosp. Svobodny 79, Krasnoyarsk, Russia, 660041

    Predrag S. Stanimirović & Spyridon D. Mourtas

  6. Hunan Provincial Key Laboratory of Intelligent Computing and Language Information Processing, Changsha, 410081, China

    Lin Xiao

  7. Technical Faculty at Bor, University of Belgrade, Vojske Jugoslavije 12, Bor, 19210, Serbia

    Dragiša Stanujkić

  8. Faculty of Applied Management, Economics and Finance, University Business Academy in Novi Sad, Jevrejska 24, Belgrade, 11000, Serbia

    Darjan Karabašević

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  1. Vasilios N. Katsikis
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Correspondence to Vasilios N. Katsikis.

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The authors Vasilios N. Katsikis, Predrag S. Stanimirović, Spyridon D. Mourtas, Lin Xiao, Dragiša Stanujkić and Darjan Karabašević of the paper entitled “Zeroing Neural Network based on Neutrosophic Logic for Calculating Minimal-norm Least-squares Solutions to Time-varying Linear Systems,” declare that there is no conflict of interest.

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Katsikis, V.N., Stanimirović, P.S., Mourtas, S.D. et al. Zeroing Neural Network Based on Neutrosophic Logic for Calculating Minimal-Norm Least-Squares Solutions to Time-Varying Linear Systems. Neural Process Lett 55, 8731–8753 (2023). https://doi.org/10.1007/s11063-023-11175-7

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