N-Cylindrical Fuzzy Neutrosophic Sets
1Research Scholar, Catholicate College, Pattanamthitta, Kerala, India.
ORCID ID-0000-0002-0050-6218
2Principal (Professor & Dean of Research), Jyothi College of Engineering, Thrissur, Kerala,India.
ORCID ID-0000-0002-0680-1031
3Department of Mathematics, Providence College of Engineering, Alappuzha, Kerala, India.
4 Department of Mathematics, University of New Mexico 705 Gurley Ave. Gallup, NM 87301, USA.
ORCID ID-0000-0002-5560-5926
Emails: saranya6685@gmail.com; sunnyjoseph2014@yahoo.com,;mathews.g@providence.edu.in;
smarand@unm.edu
* Correspondence: saranya6685@gmail.com
Abstract
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.
Keyword: n- Cylindrical fuzzy neutrosophic sets (n-CyFNSs), height of n-CyFNS; peak of n-CyFNS, right cylindrical fuzzy Neutrosophic set (n-RCyFNS); neutosophic affinity degree; neutrosophic similarity index.