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Towards granular calculus of single-valued neutrosophic functions under granular computing

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Abstract

Neutrosophic theory studies objects whose values vary in the sets of elements and are not true or false, but in between, that can be called by neutral, indeterminate, unclear, vague, ambiguous, incomplete or contradictory quantities. In this paper, we firstly introduce preliminaries on granular calculus and analysis related to single-valued neutrosophic functions. Based on horizontal membership functions approach, we establish some basic arithmetic operations of single-valued neutrosophic numbers, that red allow us to directly introduce the terms of neutrosophic function in usual mathematical formulas. Additionally, we build metrics on the space of single-valued neutrosophic numbers induced from Hamming distance. Then, we define some backgrounds on the limit, derivative and integral of single-valued neutrosophic functions. Finally, in order to demonstrate the usable of our theoretical results, we present some applications to well-known problems arising in engineering such as logistic model, the inverted pendulum system, Mass - Spring - Damper model.

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Acknowledgements

The authors would like to thank the editor-in-chief, associate editor, and the anonymous referees for their helpful comments and valuable suggestions, which greatly improved this paper. This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.02-2018.311.

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Authors and Affiliations

  1. Faculty of Natural Science, Hanoi Metropolitan University, Hanoi, Vietnam

    Nguyen Thi Kim Son

  2. Department of Mathematics, Hanoi Pedagogical University 2, Hanoi, Vietnam

    Nguyen Phuong Dong

  3. VNU Information Technology Institute, Vietnam National University, Hanoi, Vietnam

    Le Hoang Son

  4. Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Hoang Viet Long

  5. Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Hoang Viet Long

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  1. Nguyen Thi Kim Son
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Son, N.T.K., Dong, N.P., Son, L.H. et al. Towards granular calculus of single-valued neutrosophic functions under granular computing. Multimed Tools Appl 79, 16845–16881 (2020). https://doi.org/10.1007/s11042-019-7388-8

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