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Open AccessArticle

Combination of the Single-Valued Neutrosophic Fuzzy Set and the Soft Set with Applications in Decision-Making

1
Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt
2
School of Mathematics and Physics, Guangxi University of Nationalities, Nanning 530006, China
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Department of Mathematics, Faculty of Science and Humanities, Prince Sattam Bin Abdulaziz University, Alkharj 11942, Saudi Arabia
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Department of Mathematics, Faculty of Science, New Valley University, Elkharga 72511, Egypt
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Department of Mathematics, University of New Mexico, 705 Gurley Ave., Gallup, NM 87301, USA
6
Physics Department, Faculty of Science, University of Jeddah, Jeddah 23890, Saudi Arabia
*
Author to whom correspondence should be addressed.
Symmetry 2020, 12(8), 1361; https://doi.org/10.3390/sym12081361
Received: 16 July 2020 / Revised: 3 August 2020 / Accepted: 8 August 2020 / Published: 14 August 2020
In this article, we propose a novel concept of the single-valued neutrosophic fuzzy soft set by combining the single-valued neutrosophic fuzzy set and the soft set. For possible applications, five kinds of operations (e.g., subset, equal, union, intersection, and complement) on single-valued neutrosophic fuzzy soft sets are presented. Then, several theoretical operations of single-valued neutrosophic fuzzy soft sets are given. In addition, the first type for the fuzzy decision-making based on single-valued neutrosophic fuzzy soft set matrix is constructed. Finally, we present the second type by using the AND operation of the single-valued neutrosophic fuzzy soft set for fuzzy decision-making and clarify its applicability with a numerical example. View Full-Text
Keywords: single-valued neutrosophic fuzzy set; soft set; Algorithm 1; Algorithm 2; decision-making single-valued neutrosophic fuzzy set; soft set; Algorithm 1; Algorithm 2; decision-making
MDPI and ACS Style

Khalil, A.M.; Cao, D.; Azzam, A.; Smarandache, F.; Alharbi, W.R. Combination of the Single-Valued Neutrosophic Fuzzy Set and the Soft Set with Applications in Decision-Making. Symmetry 2020, 12, 1361. https://doi.org/10.3390/sym12081361

AMA Style

Khalil AM, Cao D, Azzam A, Smarandache F, Alharbi WR. Combination of the Single-Valued Neutrosophic Fuzzy Set and the Soft Set with Applications in Decision-Making. Symmetry. 2020; 12(8):1361. https://doi.org/10.3390/sym12081361

Chicago/Turabian Style

Khalil, Ahmed M.; Cao, Dunqian; Azzam, Abdelfatah; Smarandache, Florentin; Alharbi, Wedad R. 2020. "Combination of the Single-Valued Neutrosophic Fuzzy Set and the Soft Set with Applications in Decision-Making" Symmetry 12, no. 8: 1361. https://doi.org/10.3390/sym12081361

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Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

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