Abstract
The Neutrosophic set (NS) has grasped concentration by its ability for handling indeterminate, uncertain, incomplete, and inconsistent information encountered in daily life. Recently, there have been various extensions of the NS, such as single valued neutrosophic sets (SVNSs), Interval neutrosophic sets (INSs), bipolar neutrosophic sets (BNSs), Refined Neutrosophic Sets (RNSs), and triangular fuzzy number neutrosophic set (TFNNs). This paper contains an extended overview of the concept of NS as well as several instances and extensions of this model that have been introduced in the last decade, and have had a significant impact in literature. Theoretical and mathematical properties of NS and their counterparts are discussed in this paper as well. Neutrosophic-set-driven decision making algorithms are also overviewed in detail.
Highlights
The Neutrosophic set (NS) originates from neutrosophy, which is a branch of philosophy that provides a means to imitate the possibility and neutralities that refer to the grey area between the affirmative and the negative common to most real-life situations [1]
This paper presents an overview of NSs and some of the most significant instances and extensions of NS, as well as the application of these models in multiple attribute decision-making (MADM) problems
We gave an overview of a neutrosophic set, its extensions, and other hybrid frameworks of neutrosophic sets, fuzzy based models soft sets, and the application of these neutrosophic models in (MADM) problems
Summary
The Neutrosophic set (NS) originates from neutrosophy, which is a branch of philosophy that provides a means to imitate the possibility and neutralities that refer to the grey area between the affirmative and the negative common to most real-life situations [1]. For addressing many decision making problems that involve human knowledge, which is often pervaded with uncertainty, indeterminacy, and inconsistency in information, the concept of NS can be useful. In the extent of natural science, operations research, economics, management science, military affairs, and urban planning, NSs have a broad application They can be applied todecision making problems when the ambiguity and complexity of the attributes make the problems impossible to be expressed or valued with real numbers. This paper presents an overview of NSs and some of the most significant instances and extensions of NS, as well as the application of these models in multiple attribute decision-making (MADM) problems.
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