aspg-21-1204-1791468730 20261008141210 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2022 18 4 Sarannya Kumari R Research Scholar, Catholicate College, Pattanamthitta, Kerala, India. ORCID ID-0000-0002-0050-6218 Sunny Kalayathankal Principal (Professor & Dean of Research), Jyothi College of Engineering, Thrissur, Kerala,India. ORCID ID-0000-0002-0680-1031 Mathews George Department of Mathematics, Providence College of Engineering, Alappuzha, Kerala, India Florentin Smarandache Department of Mathematics, University of New Mexico 705 Gurley Ave. Gallup, NM 87301, USA. ORCID ID-0000-0002-5560-5926 In this paper, we introduce a new type of fuzzy Neutrosophic set called n-Cylindrical fuzzy Neutrosophic set (n-CyFNS), with I as independent neutrosophic component. The n-CyFNS can be claimed as the largest extension of fuzzy sets. In n-CyFNS, the degree of positive, neutral and negative membership functions are satisfying the condition, 0≤ βA(x) ≤1 and 0≤ αA n(x) + γAn(x) ≤ 1, n>1, is an integer. Also the distance between two n- CyFNS and its properties are also defined. Along with basic operations on n- CyFNSs, we put forward two concepts-Neutrosophic affinity degree & Neutrosophic similarity index which is used to compare and correlate n-CyFNSs respectively. A comparison is made in the n-CyFNS environment using the existing correlation measures to check its reliability. 2022 355 374 1204 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.180430 https://www.americaspg.com/journal/21/article/1204 https://www.americaspg.com/storage/407.pdf