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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

Abstract:A neutrosophic cubic set is the hybridization of the concept of a neutrosophic set and an interval neutrosophic set. A neutrosophic cubic set has the capacity to express the hybrid information of both the interval neutrosophic set and the single valued neutrosophic set simultaneously. As newly defined, little research on the operations and applications of neutrosophic cubic sets has been reported in the current literature. In the present paper, we propose the score and accuracy functions for neutrosophic cubic sets and prove their basic properties. We also develop a strategy for ranking of neutrosophic cubic numbers based on the score and accuracy functions. We firstly develop a TODIM (Tomada de decisao interativa e multicritévio) in the neutrosophic cubic set (NC) environment, which we call the NC-TODIM. We establish a new NC-TODIM strategy for solving multi attribute group decision making (MAGDM) in neutrosophic cubic set environment. We illustrate the proposed NC-TODIM strategy for solving a multi attribute group decision making problem to show the applicability and effectiveness of the developed strategy. We also conduct sensitivity analysis to show the impact of ranking order of the alternatives for different values of the attenuation factor of losses for multi-attribute group decision making strategies.

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 order to deal with these disadvantages, we propose a new cross entropy measure under a single-valued neutrosophic set (SVNS) environment, namely NS-cross entropy, and prove its basic properties. Also we define weighted NS-cross entropy measure and investigate its basic properties. We develop a novel multi-attribute group decision-making (MAGDM) strategy that is free from the drawback of asymmetrical behavior and undefined phenomena. It is capable of dealing with an unknown weight of attributes and an unknown weight of decision-makers. Finally, a numerical example of multi-attribute group decision-making problem of investment potential is solved to show the feasibility, validity and efficiency of the proposed decision-making strategy.

The objective of the paper is to introduce a new cross entropy measure in a neutrosophic cubic set (NCS) environment, which we call NC-cross entropy measure. We prove its basic properties. We also propose weighted NC-cross entropy and investigate its basic properties. We develop a novel multi attribute decision-making (MADM) strategy based on a weighted NC-cross entropy measure. To show the feasibility and applicability of the proposed multi attribute decision-making strategy, we solve an illustrative example of the multi attribute decision-making problem.