International Journal of Mathematics Trends and Technology
Volume 46 | Number 2 | Year 2017 | Article Id. IJMTT-V46P515 | DOI : https://doi.org/10.14445/22315373/IJMTT-V46P515
This paper acts as a base for the amalgamation of the already existing cubic set, Neutrosophic cubic set and the theory of soft sets and named as Neutrosophic soft cubic set (NSCS). Here we define internal neutrosophic soft cubic set (INSCS) and external neutrosophic soft cubic set (ENSCS) and also propose the new idea of 3 /1 INSCS (or 3/2 ENSCS), 3/2 INSCS (or 3/1 ENSCS). Further P-order, P-union, P-intersection as well as R-order, R-union, R-intersection are introduced for Neutrosophic soft cubic sets which acts as a tool to study some of their properties of newly introduced sets.
[1] Y.B. Jun, C.S. Kim and K.O. Yang, Cubic sets, Annals of Fuzzy Mathematics and Informatics 4(3) (2012), 83–98.
[2] Turksen,“Interval valued fuzzy sets based on normal forms”. Fuzzy Sets and Systems, 20,(1968),pp.191–210.
[3] F. Smarandache, A Unifying Field in Logics. Neutrosophy: Neutrosophic Probability, Set and Logic, Rehoboth: American Research Press, 1999.
[4] L.A.Zadeh,Fuzzysets, Inform Control 8(1965),338–353
[5] I. B. Turksen, Interval-valued strict preference with Zadeh triples, Fuzzy Sets and Systems 78 (1996) 183–195..
[6] H.Wang,F.Smarandache, Y.Q.ZhangandR.Sunderraman, Interval Neutrosophic Sets and logic: Theory and ApplictionsinComputing,Hexis;Neutrosophicbookseries,No.5, 2005.
[7] D. Molodtsov , Soft Set Theory–First Results, Computers and Mathematics with Application, 37 (1999) 19–31.
[8] Pabitra Kumar Maji, “Neutrosophic soft set” Annals of Fuzzy Mathematics and Informatics 5 (2013), 157–168.
[9] F. Smarandache, Neutrosophic set, a generalisation of the intuitionistic fuzzy sets, Inter. J. Pu Bre Appl. Math. 24 (2005) 287–297.
[10] F. Smarandache, Nuetrosophy and Neutrosophic Logic, First International Conference on Neutrosophy, Nuetrosophy Logic, Set, Probability and Statistics University of New Mexico, Gallup, NM 87301, USA (2002)
[11] L. J. Kohout, W. Bandler, Fuzzy interval inference utilizing the checklist paradigm and BKrelational products, in: R.B. Kearfort et al. (Eds.), Applications of Interval Computations, Kluwer, Dordrecht, 1996, pp. 291–335.
[12] R. Sambuc, Functions Φ-Flous, Application `a l’aide au Diagnostic en Pathologie Thyroidienne, Th`ese de Doctorat en M´edecine, Marseille, 1975.
[13] I. B. Turksen, Interval-valued fuzzy sets and compensatory AND, Fuzzy Sets and Systems 51 (1992) 295–307.
[14] L. A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning-I, Inform. Sci. 8 (1975) 199–249.
[15] P.K.Maji , R. Biswas ans A.R.Roy, “Fuzzy soft sets”, Journal of Fuzzy Mathematics, Vol 9, no.3, 2001 pp – 589-602,
[16] P.K.Maji, R. Biswas ans A.R.Roy, “Intuitionistic Fuzzy soft sets”, The journal of fuzzy Mathematics, Vol 9, (3)(2001), 677 – 692.
[17] Pabitra Kumar Maji, Neutrosophic soft set, Annals of Fuzzy Mathematics and Informatics, Volume 5, No.1,(2013).,157-168.
R. Anitha Cruz, F. Nirmala Irudayam, "Neutrosophic Soft Cubic Set," International Journal of Mathematics Trends and Technology (IJMTT), vol. 46, no. 2, pp. 88-94, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V46P515
PDF 
Abstract 
Keywords 
References 
Citation