Abstract
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.
Highlights
In real life, most decision-making problems involve multiple schemes and multiple attributes, which are called multi-attribute decision-making (MADM) problems
Using the overall dominance and overall disadvantage to calculate the inflow and outflow, we can increase the credibility of the alternative ranking
The single-valued neutrosophic sets (SVNSs) are useful tools to depict the uncertainty of the MADM
Summary
Most decision-making problems involve multiple schemes and multiple attributes, which are called multi-attribute decision-making (MADM) problems. Liu [44] proposed a PROMETHEE multi-attribute decision-making method based on attribute association for decision-making problems with known attribute fuzzy measures and interval hesitant fuzzy sets. Liu and Guan [47] adopted the information entropy to determine the objective weight corresponding to each indicator, and used the PROMETHEE-II method to select suppliers It can be seen from the above that the PROMETHEE and TODIM methods are very common in MADM problems. In the PROMETHEE method, the calculation of the inflows and outflow of the alternatives lack persuasiveness and readability Both of these methods have some shortcomings, and in order to solve these problems, a new method is proposed based on them.
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