International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/1204 2020 2020 Research Scholar, Catholicate College, Pattanamthitta, Kerala, India. ORCID ID-0000-0002-0050-6218 Sarannya Kumari R Principal (Professor & Dean of Research), Jyothi College of Engineering, Thrissur, Kerala,India. ORCID ID-0000-0002-0680-1031 Sunny Kalayathankal Department of Mathematics, Providence College of Engineering, Alappuzha, Kerala, India Mathews George Department of Mathematics, University of New Mexico 705 Gurley Ave. Gallup, NM 87301, USA. ORCID ID-0000-0002-5560-5926 Florentin Smarandache 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 2022 355 374 10.54216/IJNS.180430 https://www.americaspg.com/articleinfo/21/show/1204