A novel interval-valued neutrosophic AHP with cosine similarity measure

Neutrosophic Logic (Smarandache in Neutrosophy neutrosophic probability: set, and logic, American Research Press, Rehoboth, 1998) has been applied to many multicriteria decision-making methods such as Technique for Order Preference by Similarity to an Ideal Solution, Višekriterijumsko kompromisno rangiranje Resenje, and Evaluation based on Distance from Average Solution. Interval-valued neutrosophic sets are subclass of neutrosophic sets. Interval numbers can be used for their truth-membership, indeterminacy-membership, and falsity-membership degrees. The angle between the vector representations of two neutrosophic sets is defined cosine similarity measure. In this paper, we introduce a new Analytic Hierarchy Process (AHP) method with interval-valued neutrosophic sets. We also propose an interval-valued neutrosophic AHP (IVN-AHP) based on cosine similarity measures. The proposed method with cosine similarity provides an objective scoring procedure for pairwise comparison matrices under neutrosophic uncertainty. Finally, an application is given in energy alternative selection to illustrate the developed approaches.