A single-valued neutrosophic set is a special case of neutrosophic set. It has been proposed as a generalization of crisp sets, fuzzy sets, and intuitionistic fuzzy sets in order to deal with incomplete information. In this paper, a new approach for multi-attribute group decisionmaking problems is proposed by extending the technique for order preference by similarity to ideal solution to single-valued neutrosophic environment. Ratings of alternative with respect to each attribute are considered as singlevalued neutrosophic set that reflect the decision makers' opinion based on the provided information. Neutrosophic set characterized by three independent degrees namely truth-membership degree (T), indeterminacy-membership degree (I), and falsity-membership degree (F) is more capable to catch up incomplete information. Single-valued neutrosophic set-based weighted averaging operator is used to aggregate all the individual decision maker's opinion into one common opinion for rating the importance of criteria and alternatives. Finally, an illustrative example is provided in order to demonstrate its applicability and effectiveness of the proposed approach.

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In this paper, we propose new vector similarity measures of single valued and interval neutrosophic sets by hybridizing the concepts of Dice and cosine similarity measures. We present their applications in multi attribute decision making under neutrosophic environment. We use these similarity measures to find out the best alternative by determining the similarity measure values between the ideal alternative and each alternative. The results of the proposed similarity measures have been validated by comparing with other existing similarity measures reported in the literature for multi attribute decision making. The main thrust of the proposed similarity measures will be in the field of practical decision making, medical diagnosis, pattern recognition, data mining, clustering analysis, etc.

Neutrosophic cubic set is the hybridization of the concept of neutrosophic set and interval 9 neutrosophic set. Neutrosophic cubic set has the capacity to express the hybrid information of both 10 the interval neutrosophic set and the single valued neutrosophic set simultaneously. As newly 11 defined, little research on the operations and applications of neutrosophic cubic sets appear in the 12 current literature. In the present paper we propose the score, accuracy functions for neutrosophic 13 cubic sets and prove their basic properties. We firstly develop TODIM method in neutrosophic cubic 14 set environment, which we call NC-TODIM. We establish a new NC-TODIM method in 15 neutrosophic cubic set environment for solving MAGDM in neutrosophic cubic set environment 16 problems. We illustrate the proposed NC-TODIM method for solving a MAGDM problem to show 17 applicability and effectiveness of the developed method. We also conduct sensitivity analysis to 18show the impact of ranking order of the alternatives for different values of attenuation factor of 19 losses for multi-attribute group decision making problem. 20Keywords: neutrosophic cubic set; single valued neutrosophic set; interval neutrosophic set; multi 21 attribute group decision making; TODIM method; NC-TODIM 22

Many multi-attribute group decision-making (MAGDM) strategies have been introduced in the literature to deal with decisionmaking problems in uncertain environment. Many of them are based on fuzzy numbers and they are not able to cope with indeterminacy and inconsistency involving in decision making. In recent years, some neutrosophic multi-attribute group decision-making strategies have been successfully developed to deal with uncertainty, indeterminacy, and inconsistency in decision making. Among them, TODIM (an acronym in Portuguese of interactive and multiple attribute decision making) strategy based on prospect theory has received more attention due to its great performance in considering the bounded rationality of decision makers. In this paper, we develop a TODIM strategy to deal with multi-attribute group decisionmaking problem in trapezoidal neutrosophic numbers environment. To establish the TODIM strategy, we employ score function, accuracy function, and Hamming distance function for trapezoidal neutrosophic numbers. Lastly, we solve an illustrative numerical example to show the applicability and usefulness of the proposed strategy. A comparison analysis is also provided.