An extended multiple attribute group decision-making TODIM method based on the neutrosophic numbers

Abstract

Neutrosophic numbers (NNs), which contain determinate part and indeterminate part, are considered as a useful tool to express the indeterminate evaluation information which is common in real situation. The TODIM which is the short of Interactive and Multicriteria Decision Making in Portuguese can take the bounded rationality of decision makers into consideration based on the prospect theory. However, the classical TODIM method can only process the multiple attribute decision making (MADM) problems in which the attribute values are crisp numbers. The purpose of the paper is to give a new method to handle multiple attribute group decision making problems with neutrosophic numbers, which means we combine the TODIM with neutrosophic numbers to deal with MADM problems. In this paper, we firstly introduce the definition, the properties and the operational laws of the neutrosophic numbers, and then the possibility degree function is introduced concisely. Secondly, we represent the idea and steps of TODIM, and then we extend the TODIM method to the multiple attribute group decision making (MAGDM) with neutrosophic numbers. Finally, we use an illustrative example to demonstrate the practicality and effectiveness of the proposed method.