A New Method Based on PROMETHEE and TODIM for Multi-Attribute Decision-Making with Single-Valued Neutrosophic Sets

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.

CPT-Todim Method for Interval-Valued Bipolar Fuzzy Multiple Attribute Group Decision Making and Application to Industrial Control Security Service Provider Selection

“…Guo et al (2020) found out mixed TODIM method which is capable of settling the site choice of Carbon storage. According to the characteristics of TODIM method and PROMETHEE method, Xu et al (2020) combined them skillfully and successfully applied them to the single-valued neutrosophic environment. This pattern of combining the TODIM method with another approach seems to have been a recent trend among researchers.…”

A New Picture Fuzzy Entropy and Its Application Based on Combined Picture Fuzzy Methodology with Partial Weight Information

“…Recently, Arya and Kumar [ 34 , 54 ] combined TODIM and VIKOR methods skillfully and implemented them to the picture fuzzy environment. Xu et al [ 55 ] implemented the integration of TODIM and PROMETHEE method under single-valued neutrosophic environment. This pattern of integrating the TODIM method with another technique realizes to have been a recent trend among researchers.…”

A New Single-Valued Neutrosophic Rough Sets and Related Topology

“…In Svns, three independent membership functions (truth, indeterminacy, and falsity) are considered; hence, it can be regarded as extensions of fuzzy set [3] and intuitionistic fuzzy set [4]. ere are many works on the theory and application of Svns (see Abdel-Basset [5], Ye [6,7], Samant [8], Yang [9,10], Zhang [11][12][13], Zavadskas [14], and Xu [15] as well as Peng's review paper [16]). e fusion of neutrosophic sets with rough sets theory [17] is an important research direction.…”