Neutrosophic sets (NSs) and logic are one of the influential mathematical tools to manage various uncertainties. Among diverse models for analyzing neutrosophic information, rough set theory (RST) provides an effective way in the field of neutrosophic information analysis, and a multitude of scholars have focused on neutrosophic fusion of RST in recent years. At present, there are not comprehensive literature reviews and statistics of these generalized rough set theories and applications. This review study first explores a summarization of current neutrosophic fusion of RST from five basic aspects, i.e., rough neutrosophic sets (RNSs) and neutrosophic rough sets (NRSs), soft rough neutrosophic sets (SRNSs) and neutrosophic soft rough sets (NSRSs), mathematical foundations of RNSs and NRSs, RNSs and NRSs-based decision making, RNSs and NRSs-based other applications. Then, on the basis of the overview from five fundamental perspectives, a systematic bibliometric overview of current works with respect to neutrosophic fusion of RST is further conducted. Finally, in light of the results of this review, different challenging issues related to the main topics are listed, which are beneficial to future studies of NSs and logic. © 2019 Elsevier B.V.

Arun Kumar S

Department of Information Security

School of Computer Science and Engineering

Vellore Campus

Zhang C

Li D

Kang X

Song D

Broumi S.

Vellore Institute of Technology (VIT) is a private university located in&nbsp;Tamil Nadu, India. Founded in 1984, as Vellore Engineering College, the institution offers 20 undergraduate, 34 postgraduate, four integrated and four research programs. It has campuses in Vellore, Amravati, Bhopal and Chennai.

VIT is one of the top ranked private universities in India according to NIRF, THE and QS Rankings.&nbsp;Govt. of India has recognized&nbsp;VIT, Vellore as an&nbsp;Institution of Eminence. This has allowed VIT to take independent quality initiatives and move up in world ranking.

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VIT University

Computers in Industry

In group decision-making (GDM) model, experts often evaluate their opinion by using triangular fuzzy numbers. The preference relations with triangular fuzzy numbers are in consistent in nature, so we turned to neutrosophic in this paper. It is very important to take into account consistency of expert opinion and consensus degree in GDM. In order to distinguish the typical consistency, the concept of additive approximation consistency is proposed for triangular neutrosophic additive reciprocal matrices. The properties of triangular neutrosophic additive reciprocal matrices with additive approximation consistency are studied in detail. Second, by using (n- 1) restricted preference values, a triangular neutrosophic additive reciprocal preference relation with additive approximation consistency is constructed. The differences among expert’s opinions are measured using consensus degree. For generating a collective triangular neutrosophic additive reciprocal matrix with additive approximation consistency, the neutrosophic triangular weighted aggregation operator is used. Finally, a novel algorithm for the group decision-making problem with triangular neutrosophic additive reciprocal preference relations is presented. A numerical example is carried out to illustrate the proposed definitions and algorithm. © 2017, Springer-Verlag GmbH Germany.

Soft Computing

A novel group decision-making model based on triangular neutrosophic numbers

In real-world diagnostic procedures, due to the limitation of human cognitive competence, a medical expert may not conveniently use some crisp numbers to express the diagnostic information, and plenty of research has indicated that generalized fuzzy numbers play a significant role in describing complex diagnostic information. To deal with medical diagnosis problems based on generalized fuzzy sets (FSs), the notion of single-valued neutrosophic multisets (SVNMs) is firstly used to express the diagnostic information in this article. Then the model of probabilistic rough sets (PRSs) over two universes is applied to analyze SVNMs, and the concepts of single-valued neutrosophic rough multisets (SVNRMs) over two universes and probabilistic rough single-valued neutrosophic multisets (PRSVNMs) over two universes are introduced. Based on SVNRMs over two universes and PRSVNMs over two universes, single-valued neutrosophic probabilistic rough multisets (SVNPRMs) over two universes are further established. Next, a three-way decisions model by virtue of SVNPRMs over two universes in the context of medical diagnosis is constructed. Finally, a practical case study along with a comparative study are carried out to reveal the accuracy and reliability of the constructed three-way decisions model. © 2018 by the authors.

Fulltext

Symmetry

Medical Diagnosis Based on Single-Valued Neutrosophic Probabilistic Rough Multisets over Two Universes

Mathematical Methods in the Applied Sciences

Boundary blow‐up rate of solutions to elliptic cooperative systems

Information Sciences

Interval-valued hesitant fuzzy multi-granularity three-way decisions in consensus processes with applications to multi-attribute group decision making

Artificial Intelligence Review

A bibliometric analysis of neutrosophic set: two decades review from 1998 to 2017

Neutrosophic fusion of rough set theory: An overview

Journal	Data powered by TypesetComputers in Industry
Publisher	Data powered by TypesetElsevier BV
ISSN	0166-3615
Open Access	0