International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/2833 2020 2020 Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai, Tamil Nadu 602105, India Aiyared Aiyared Department of Mathematics, Bharath Institute of Higher Education and Research, Chennai-600073, India K. Arulmozhi Department of Mathematics, School of Science, University of Phayao, Mae Ka, Mueang, Phayao 56000, Thailand. Aiyared Iampan We introduce the concept of cosine trigonometric q-rung Diophantine neutrosophic interval-valued set (CosTq-rung DioNSIVS). The fact that CosTq-rung DioNSIVS combines q-rung neutrosophic interval-valued set, q-rung neutrosophic set and neutrosophic interval-valued set is one of its distinguishing characteristics. A new idea of CosTq-rung DioNSIVWA, CosTq-rung DioNSIVWG, GCosTq-rung DioNSIVWA and GCosTq-rung DioNSIVWG is proposed in this study. We also look at the idempotency, boundedness, commutativity, and monotonicity of the CosTq-rung DioNSIVS based on algebraic operations. We considered new kinds of two distances in the proposed models, besides Euclidean and Hamming distances. The CosTq-rung DioNSIVS method was used to analyze the cosine trigonometric aggregation procedures. The study's concluding results include several fascinating and captivating discoveries. 2024 2024 240 257 10.54216/IJNS.240321 https://www.americaspg.com/articleinfo/21/show/2833