Volume 18 • Issue 4 • PP: 355-374 • 2022
N-Cylindrical Fuzzy Neutrosophic Sets
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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.
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References
[1]. Ashraf S, Abdullah S, Spherical aggregation operators and their application in multi attribute group decisionmaking,
Int J Intell Syst 34(3):493–523 (2019)
[2]. C. Antony Crispin Sweety and R.Jhansi, Fermatean Neutrosophic sets, International Journal of Advanced
Research in Computer and Communication Engineering, Vol. 10, Issue 6 (2021)
DOI 10.17148/IJARCCE.2021.10605
[3]D.Ajay, P.Chellamani, Pythagorean Neutrosophic Fuzzy Graphs, International journal of neutrosophic
science, Vol. 11, No. 2, PP. 108-114, 2020
[4]. I.Arokiarani, J.Martina Jency, More on fuzzy Neutrosophic sets and fuzzy Neutrosophic topological spaces,
International Journal of innovative research & studies, 3(5),642-652, 2014.
[5] .I. Arokiarani, I.R Sumati, J.Martina Jency,Fuzzy Neutrosophic soft topological spaces, International Journal
of Mathematical Archives, 4(10), 225-238, 2013.
[6]. Atanassov,K. Intuitionistic fuzzy sets, Fuzzy Sets and Systems, Vol.20, 87-96, (1986).
[7]. A. Kharal, A Neutrosophic Multicriteria Decision Making Method, New Mathematics and Natural
Computation, Creighton University, USA, 2013.
[8]. F.Smarandache, A Unifying Field in Logics: Neutrosophic Logic, Neutrosophy, Neutrosophic Set,
Neutrosophic Probability; American Research Press: Rehoboth, DE, USA, 1999.
[9]. F.Smarandache, Degree of Dependence and Independence of Neutrosophic Logic Components Applied in
Physics, 2016 Annual Spring Meeting of the American Physical Society (APS) Ohio-Region Section, Dayton,
Ohio, USA, 08-09 April 08 2016.
[10]. F. Smarandache ,Degree of Dependence and Independence of the (Sub)Components of Fuzzy Set and
Neutrosophic Set, Neutrosophic Sets and Systems, Vol. 11,95-97,2016.
[11]. I. M. Hanafy, A. A. Salama and K. Mahfouz, Correlation Coefficients of Neutrosophic Sets by Centroid
Method, International Journal of Probability and Statistics, 2(1), 9–12, 2013.
[12]. J. Ye, Vector Similarity Measures of Simplified Neutrosophic Sets and Their Application in Multi criteria
Decision Making International Journal of Fuzzy Systems, Vol. 16, No. 2, 204–215, 2014.
[13]. J. Ye, Multicriteria decision-making method using the correlation coefficient under single-valued
neutrosophic environment, International Journal of General Systems, 42(4), 386–394, 2013.
[14] Mohamed Bisher Zeina , Omar Zeitouny , Fatina Masri , Fatima Kadoura , Said Broumi, Operations on
Single-Valued Trapezoidal Neutrosophic Numbers using (α,β,γ)-Cuts “Maple Package”, International Journal of
Neutrosophic Science, Vol. 15 , No. 2 , (2021) : 113-122 (Doi : https://doi.org/10.54216/IJNS.150205)
[15] M. Mullai , Said Broumi, Dominating Energy in Neutrosophic graphs, International Journal of Neutrosophic
Science, Vol. 5 , No. 1 , (2020) : 38-58 (Doi : https://doi.org/10.54216/IJNS.050104)
[16]. M. Rafiq et al. / The cosine similarity measures of spherical fuzzy sets and their applications, Journal of
Intelligent & Fuzzy Systems, DOI:10.3233/JIFS-181922
[17] Ngan Thi Roan , Florentin Smarandache, H-Max Single-Valued Neutrosophic Distance Measure in Medical
Diagnosis, International Journal of Neutrosophic Science, Vol.15, No. 2 , (2021) :62-
76 (Doi : https://doi.org/10.54216/IJNS.150201)
[18]. R.Jansi, K.Mohana and F. Smarandache, Correlation Measure for Pythagorean Neutrosophic Fuzzy Sets
with T and F as Dependent Neutrosophic Components, Neutrosophic sets and systems, 30,202-212, 2019
[19]. S. Broumi, F. Smarandache, Correlation Coefficient of Interval Neutrosophic set, Proceedings of the
International Conference ICMERA, Bucharest, October 2013.
[20] S. Broumi, F. Smarandache, Several Similarity Measures of Neutrosophic Sets, Neutrosophic Sets and
Systems, 1, 54–62, 2013.
[21]. Tahir Muhammed, An approach toward decision-making and medical diagnosis problems using the concept
of spherical fuzzy sets, Neural Computing andApplications,(2018)https://doi.org/10.1007/s00521-018-3521-
2(012,-volV)(0123
[22]. Yager, R. R, Pythagorean membership grades in multi criteria decision making, IEEE Trans Fuzzy Syst
22(4), 958–965, (2014).
[23]. Yager, R. R, Generalized Ortho pair fuzzy sets, IEEE Trans Fuzzy Systems,(2016)
[24]. Zadeh, L.A, Fuzzy Sets, Information and Control, Vol.8, 338-353,( 1965)
[25]. ZhangX, XuZ ,Extension of TOPSIS to multiple criteria decision making with pythagorean fuzzy sets,
International Journal of Intelligent Systems , 29(12),1061–1078. (2014)
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