Recently, the TODIM has been used to solve multiple attribute decision making (MADM) problems. The single-valued neutrosophic sets (SVNSs) are useful tools to depict the uncertainty of the MADM. In this paper, we will extend the TODIM method to the MADM with the single-valued neutrosophic numbers (SVNNs). Firstly, the definition, comparison, and distance of SVNNs are briefly presented, and the steps of the classical TODIM method for MADM problems are introduced. Then, the extended classical TODIM method is proposed to deal with MADM problems with the SVNNs, and its significant characteristic is that it can fully consider the decision makers’ bounded rationality which is a real action in decision making. Furthermore, we extend the proposed model to interval neutrosophic sets (INSs). Finally, a numerical example is proposed.

The single-valued complex neutrosophic set is a useful tool for handling the data with uncertainty and periodicity. In this paper, a single-valued complex neutrosophic EDAS (evaluation based on distance from average slution) model has been established and applied in green supplier selection. Firstly, the definition of single-valued complex neutrosophic set and corresponding operational laws are briefly introduced. Next, to fuse overall single-valued complex neutrosophic information, the SVCNEWA and SVCNEWG operators based on single-valued complex neutrosophic set, Einstein product and sum are proposed. Furthermore, the single-valued complex neutrosophic EDAS model has been established and all computing steps have been depicted in detail. Finally, a numerical example of green supplier selection and a comparison analysis have been given to illustrate the practicality and effectiveness of this new model.

Fuzzy information in venture capital can be well expressed by neutrosophic numbers, and TODIM method is an effective tool for multi-attribute decision-making. The distance measure is an essential step in TODIM method. The keystone of this paper is to define several new distance measures, in particular the improved interval neutrosophic Euclidean distance, and these measures are applied in the TODIM method for multi-attribute decision-making. Firstly, the normalized generalized interval neutrosophic Hausdorff distance is defined and proved to be valid in this paper. Secondly, we define a weighted parameter interval neutrosophic distance and discuss whether different weight parameters affect the decision result based on TODIM method. Thirdly, considering the preference perspective of decision-makers in behavioral economics, we define the improved interval neutrosophic Euclidean distance with the known parameter of risk preference. Finally, an application example is given to compare the effects of different parameters on the result and discuss the feasibility of these two distance measures in TODIM method.

Single-valued neutrosophic sets (SVNSs) can effectively describe the multi-attribute decision-making (MADM) problems which are characterized by incompleteness and uncertainty. Aiming at the MADM problem of SVNSs, a series of methods are proposed to solve the problem, such as the TODIM and PROMETHEE methods. The main idea of the TODIM method is to establish a relative superiority function of scheme relative to other schemes based on the value function of prospect theory, and the ranking of alternatives is determined according to the obtained superiority. In the PROMETHEE method, the decision maker selects the preference function for each attribute according to their preference, and then calculates the priority index, inflow, outflow and net flow according to the difference of the attribute values of scheme, so as to determine the ranking of alternatives. In this paper, a new method based on PROMETHEE and TODIM is proposed to solve the MADM problem under the single-valued neutrosophic environment. Based on the calculation formula of inflow and outflow in PROMETHEE method, and the calculation formula of overall dominance in the TODIM method, a new integrated formula is obtained.

In this paper, the TODIM method is used to solve the multi-attribute decision-making problem with unknown attribute weight in venture capital, and the decision information is given in the form of single-valued neutrosophic numbers. In order to consider the objectivity and subjectivity of decision-making problems reasonably, the optimal weight is obtained by combining subjective weights and objective weights. Subjective weights are given directly by decision makers. Objective weights are obtained by establishing a weight optimization model with known decision information, then this method will compare with entropy weight method. These simulation results also validate the effectiveness and reasonableness of this proposed method.

A Novel TOPSIS-MABAC Method for Multi-attribute Decision Making with Interval Neutrosophic Set