The interval neutrosophic uncertain linguistic variables can easily express the indeterminate and inconsistent information in real world, and TOPSIS is a very effective decision making method more and more extensive applications.

Decision-making activities are prevalent in human life. Many methods have been developed to address real-world decision problems. In some practical situations, decision-makers prefer to provide their evaluations over a set of criteria and weights.

Smarandache was the first who introduced the idea of neutrosophic sets (NSs), which is further extension of the concepts of intuitionistic fuzzy sets (IFSs), interval valued intuitionistic fuzzy sets (IVIFSs) from philosophical perspective.

The paper investigates a technique for order preference by similarity to ideal solution (TOPSIS) method to solve multi-attribute decision making problems with bipolar neutrosophic information.

In order to take into account quantitative and qualitative information in real complex decision making issue, a multiple-valued neutrosophic uncertain linguistic set (MVNULS) is initially proposed, which includes the uncertain linguistic part and the multiple-valued neutrosophic set (MVNS). Consequently, it has the advantages of them in expressing evaluation information.

There are many practical decision-making problems in people’s lives, but the information given by decision makers (DMs) is often unclear and how to describe this information is of critical importance.

This paper presents TOPSIS approach for multi attribute decision making in refined neutrosophic environment. The weights of each decision makers are considered as a single valued neutrosophic numbers.