aspg-21-1287-1791475951 20261008161231 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2022 19 1 Aiyared Iampan Fuzzy Algebras and Decision-Making Problems Research Unit, Department of Mathematics, School of Science, University of Phayao, Mae Ka, Mueang, Phayao 56000, Thailand P. Jayaraman Department of Mathematics, Bharathiyar University, Coimbatore-641046, Tamilnadu, India S. D. Sudha Department of Mathematics, Bharathiyar University, Coimbatore-641046, Tamilnadu, India Said Broumi Laboratory of Information Processing, Faculty of Science Ben M’Sik, Universit´s Hassan II, BP 7955 Casablanca, Morocco N. Rajesh Department of Mathematics, Rajah Serfoji Government College, Thanjavur-613005, Tamilnadu, India 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 363 374 1287 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.190133 https://www.americaspg.com/journal/21/article/1287 https://www.americaspg.com/storage/2673.pdf