Multi-attribute decision making (MADM). Play an important role in many applications, due to the efficiency to handle indeterminate and inconsistent information, single valued neutrosophic sets is widely used to model indeterminate information. In this paper, a new MADM method based on neutrosophic trapezoid linguistic weighted arithmetic averaging aggregation SVNTrLWAA operator and neutrosophic trapezoid linguistic weighted geometric aggregation SVNTrLWGA operator is presented. A numerical example is presented to demonstrate the application and efficiency of the proposed method.

Uncertainties play a dominant role during the aggregation process and hence their corresponding decisions are made fuzzier. Single-value neutrosophic numbers (SVNNs) contain the three ranges: truth, indeterminacy, and falsity membership degrees, and are very useful for describing and handling the uncertainties in the day-to-day life situations. In this study, some operations of SVNNs such as sum, product, and scalar multiplication are defined under Frank norm operations and, based on it, some averaging and geometric aggregation operators have been developed. We further establish some of its properties. Moreover, a decision-making method based on the proposed operators is established and illustrated with a numerical example.

A single-valued neutrosophic set has king power to express uncertainty characterized by indeterminacy, inconsistency and incompleteness. Most of the existing single-valued neutrosophic cross entropy bears an asymmetrical behavior and produces an undefined phenomenon in some situations.

In this paper, we first introduce single valued trapezoidal neutrosophic (SVTN) numbers with their properties. We then define some operations and distances of the SVTN-numbers. Based on these new operations, we also define some aggregation operators, including SVTN-ordered weighted geometric operator, SVTN-hybrid geometric operator, SVTN-ordered weighted arithmetic operator and SVTN-hybrid arithmetic operator. We then examine the properties of these SVTN-information aggregation operators. By using the SVTN-weighted geometric operator and SVTN-hybrid geometric operator, we also define a multi attribute group decision making method, called SVTN-group decision making method. We finally give an illustrative example and comparative analysis to verify the developed method and to demonstrate its practicality and effectiveness.

This book is a printed edition of the Special Issue "Neutrosophic Multi-Criteria Decision Making" that was published in Axioms

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One of the most efcient tools for modeling uncertainty in decision-making problems is the neutrosophic set (NS) and its extensions, such as complex NS (CNS), interval NS (INS), and interval complex NS (ICNS). Linguistic variables have been long recognized as a useful tool in decision-making problems for solving the problem of crisp neutrosophic membership degree. In this paper, we aim to introduce new concepts: single-valued linguistic complex neutrosophic set (SVLCNS-2) and interval linguistic complex neutrosophic set (ILCNS-2) that are more applicable and adjustable to real-world implementation than those of their previous counterparts. Some set-theoretic operations and the operational rules of SVLCNS-2 and ILCNS-2 are designed. Then, gather classications of the candidate versus criteria, gather the signicance weights, gather the weighted rankings of candidates versus criteria and a score function to arrange the candidates are determined. New TOPSIS decision-making procedures in SVLCNS-2 and ICNS-2 are presented and applied to lecturer selection in the case study of the University of Economics and Business, Vietnam National University. The applications demonstrate the usefulness and efciency of the proposal.

This book offers a comprehensive guide to the use of neutrosophic sets in multiple criteria decision making problems. It shows how neutrosophic sets, which have been developed as an extension of fuzzy and paraconsistent logic, can help in dealing with certain types of uncertainty that classical methods could not cope with. The chapters, written by well-known researchers, report on cutting-edge methodologies they have been developing and testing on a variety of engineering problems. The book is unique in its kind as it reports for the first time and in a comprehensive manner on the joint use of neutrosophic sets together with existing decision making methods to solve multi-criteria decision-making problems, as well as other engineering problems that are complex, hard to model and/or include incomplete and vague data. By providing new ideas, suggestions and directions for the solution of complex problems in engineering and decision making, it represents an excellent guide for researchers, lecturers and postgraduate students pursuing research on neutrosophic decision making, and more in general in the area of industrial and management engineering.

This book addresses new concepts, methods, algorithms, modeling, and applications of green supply chain, inventory control problems, assignment problems, transportation problem, linear problems and new information related to optimization for the topic from the theoretical and applied viewpoints of neutrosophic sets and logic. The book is an innovatory of new tools and procedures, such as: Neutrosophic Statistical Tests and Dependent State Samplings, Neutrosophic Probabilistic Expert Systems, Neutrosophic HyperSoft Set, Quadripartitioned Neutrosophic Cross-Entropy, Octagonal and Spherical and Cubic Neutrosophic Numbers used in machine learning. It highlights the process of neutrosofication {which means to split the universe into three parts, two opposite ones (Truth and Falsehood), and an Indeterminate or neutral one (I) in between them}. It explains Three-Ways Decision, how the universe set is split into three different distinct areas, in regard to the decision process, representing: Acceptance, Noncommitment, and Rejection, respectively. The Three-Way Decision is used in the Neutrosophic Linguistic Rough Set, which has never been done before.

Single-valued trapezoidal neutrosophic numbers (SVTNNs) have a strong capacity to depict uncertain, inconsistent, and incomplete information about decisionmaking problems.