aspg-24-1009-1791482377 20261008175937 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group Journal of Neutrosophic and Fuzzy Systems JNFS 2771-6430 2771-6449 2022 2 2 Mikail Bal Gaziantep University, Turkey Prem Kumar Singh Department of Computer science and Engineering, Gandhi institute of Technology and Management-Visakhapatnam 530045, India Katy D. Ahmad Islamic university Of Gaza, Palestine Recently, Turiyam set is introduced for dealing the fourth dimensional data sets. These types of data sets exists when an expert unable to categorize them in Euclidean, Non-Euclidean, Hybrid or NeutroGeometry. To deal with these types of data set Turiyam matrix and its algebra is required. Hence the current paper introduce the concept of Symbolic Turiyam R-module as a generalization of the corresponding neutrosophic one by using the algebra of symbolic Turiyam set. The paper also presents concept pf finite Turiyam modulo integer and illustrate many examples to show and clarify the validity of this work. 2022 8 19 1009 https://creativecommons.org/licenses/by/4.0/ 10.54216/JNFS.020201 https://www.americaspg.com/journal/24/article/1009 https://www.americaspg.com/storage/9577.pdf