Combination of the Single-Valued Neutrosophic Fuzzy Set and the Soft Set with Applications in Decision-Making
Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt
School of Mathematics and Physics, Guangxi University of Nationalities, Nanning 530006, China
Department of Mathematics, Faculty of Science and Humanities, Prince Sattam Bin Abdulaziz University, Alkharj 11942, Saudi Arabia
Department of Mathematics, Faculty of Science, New Valley University, Elkharga 72511, Egypt
Department of Mathematics, University of New Mexico, 705 Gurley Ave., Gallup, NM 87301, USA
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
(This article belongs to the Special Issue New Development of Neutrosophic Probability, Neutrosophic Statistics, Neutrosophic Algebraic Structures, and Neutrosophic & Plithogenic Optimizations)
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.