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An introduction to single-valued neutrosophic soft topological structure

  • Fuzzy systems and their mathematics
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Abstract

Fuzzy soft set theory presented by Maji et al. (J Fuzzy Math 9(3):589–602, 2001) and soft set theory presented by Molodtsov (Comput Math Appl 37(3):19–31, 1999) are important ideas in decision-making problems. They can be used to model uncertainty and make decisions under uncertainty. A single-valued neutrosophic soft set (svnf-set) is a hybrid model of a single-valued neutrosophic set and fuzzy soft set that is shown in this paper. The novel concept of single-valued neutrosophic soft topology (svnft) is defined to discuss topological structure of (svnf-set). Some fundamental properties of svnft and their related results are studied. It is good to use the proposed models of svnf-sets and svnft to figure out how to deal with uncertainty in real life. Thus, svnft is a generalization of fuzzy soft topology and fuzzy intuitionistic soft topology. Moreover, after giving the definition of a single-valued neutrosophic soft base svnf-base, we also added the concept of svnft. Finally, we set up the concept of single-valued neutrosophic soft closure spaces and show that the initial single-valued neutrosophic soft closure structures are real, which is what we did. From this fact, the category SVNSC is considered as a topological category over SET.

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Acknowledgements

The authors would like to thank Deanship of Scientific Research at Majmaah University for supporting this work under Project Number No: R-2022-125. The authors would also like to express their sincere thanks to the referees for their useful suggestions and comments.

Funding

This research was supported by Majmaah University.

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Authors and Affiliations

  1. Department of Mathematics, College of Science and Human Studies, Hotat Sudair, Majmaah University, Majmaah, 11952, Saudi Arabia

    Yaser Saber

  2. Department of Mathematics, Faculty of Science Al-Azhar University, Assiut, 71524, Egypt

    Yaser Saber

  3. Department of Mathematics, College of Science and Arts, Jouf University, Gurayat, 77455, Saudi Arabia

    Fahad Alsharari

  4. Department of Mathematics, University of New Mexico, Gallup, NM, 87301, USA

    Florentin Smarandache

Authors
  1. Yaser Saber
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  2. Fahad Alsharari
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  3. Florentin Smarandache
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Correspondence to Fahad Alsharari.

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Saber, Y., Alsharari, F. & Smarandache, F. An introduction to single-valued neutrosophic soft topological structure. Soft Comput 26, 7107–7122 (2022). https://doi.org/10.1007/s00500-022-07150-4

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