International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/2955 2020 2020 College of Natural and Health Sciences, Zayed University, Abu Dhabi, UAE Rachid Rachid College of Natural and Health Sciences, Zayed University, Abu Dhabi, UAE Farid El Ktaibi Department of Mathematics, LMNO, Universite de caen-Normandie, Campus 2, Science 3, 14032 Caen, France Christophe Chesneau Variables that have revived new interest through computational developments and extensive data analysis. This article contributes to the subject by generalizing the bivariate copula introduced recently in8 and based on the concept of the counter-monotonic shock method. The proposed copula has the feature of covering the full range of negative dependence induced by two dependence parameters, which is not so common in the specialized literature. We examine the main characteristics of this copula. In particular, the absolutely continuous and singular copula components are derived. Analytical expressions of important concordance measures, such as Spearman’s rho and Kendall’s tau, are established, along with expressions of the product moments. A real neutrosophic data set, based on the daily quality of air in the New York Metropolitan Area, is used to illustrate the applicability of the proposed copula, with quite convincing results.   2025 2025 258 278 10.54216/IJNS.250124 https://www.americaspg.com/articleinfo/21/show/2955