Bipolar neutrosophic sets are the extension of neutrosophic sets and are based on the idea of positive and negative preferences of information. Projection measure is a useful apparatus for modelling real life decision making problems. In the paper, we define projection, bidirectional projection and hybrid projection measures between bipolar neutrosophic sets. Three new methods based on the proposed projection measures are developed for solving multi-attribute decision making problems.

Bipolar neutrosophic sets are the extension of neutrosophic sets and are based on the idea of positive and negative preferences of information. Projection measure is a useful apparatus for modeling real life decision making problems.

In this study, we give a new outranking approach for multi-attribute decision-making problems in bipolar neutrosophic environment.

In this paper, the idea bipolar single-valued neutrosophic (BSVN) set was introduced. We also introduce bipolar single-valued neutrosophic topological space and some of its properties were characterized. Comparing Bipolar single-valued neutrosophic sets with score function, certainty function and accuracy function .Bipolar single-valued neutrosophic weighted average operator (Aω) and bipolar single-valued neutrosophic weighted geometric operator (Gω) were developed and based on Bipolar single-valued neutrosophic set, a multiple decision making problem were evaluated through an example to select the desirable one.

In this paper, we define projection and bidirectional projection measures between rough neutrosophic sets. Then two new multi criteria decision making methods are proposed based on neutrosophic projection and bidirectional projection measures respectively. Then the proposed methods are applied for solving multiple criteria group decision making problems. Finally, two numerical examples are provided to demonstrate the applicability and effectiveness of the proposed methods.

Bipolar neutrosophic set(BNS) is a generalization of bipolar fuzzy set and neutrosophic set that can describe the uncertain information from both positive and negative perspectives. In this contribution, we study the multi-attribute decision making methods based on the distance measure under the uncertain information which the attribute weights are incompletely known or completely unknown.

“Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc.