International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/1287 2020 2020 Fuzzy Algebras and Decision-Making Problems Research Unit, Department of Mathematics, School of Science, University of Phayao, Mae Ka, Mueang, Phayao 56000, Thailand Aiyared Iampan Department of Mathematics, Bharathiyar University, Coimbatore-641046, Tamilnadu, India P. Jayaraman Department of Mathematics, Bharathiyar University, Coimbatore-641046, Tamilnadu, India S. D. Sudha Laboratory of Information Processing, Faculty of Science Ben M’Sik, Universit´s Hassan II, BP 7955 Casablanca, Morocco Said Broumi Department of Mathematics, Rajah Serfoji Government College, Thanjavur-613005, Tamilnadu, India N. Rajesh Interval-valued neutrosophic sets (IVNSs) are a notion that was initially developed by Wang et al.19 The idea of IVNSs to deductive systems (DSs) in Hilbert algebras is presented in this study. It is shown how intervalvalued neutrosophic deductive systems (IVNDSs) relate to their level cuts. In addition, certain related features are examined as well as the homomorphic inverse image of IVNDSs in Hilbert algebras. 2022 2022 363 374 10.54216/IJNS.190133 https://www.americaspg.com/articleinfo/21/show/1287