More on R-Union and R-Intersection of Neutrosophic Soft Cubic Set
Abstract:
R-unions and R-intersections, R-OR, R-AND of Neutrosophic soft cubic sets are introduced and related properties are investigated. We show that the R-union (R-intersection) of internal neutrosophic soft cubic set is also an internal neutrosophic soft cubic set. We show that the R-union and the R-intersection T-external (I-external, F-external) neutrosophic soft cubic sets are also T-external ( I-external, F-external) neutrosophic soft cubic sets. The conditions for the R-intersection of two cubic soft sets to be both an external neutrosophic soft cubic set and an internal neutrosophic soft cubic set. Further we provide a condition for the R- intersection and R union of two T-internal (I-internal, F-internal) neutrosophic soft cubic sets are T-external (I-external, F-external) neutrosophic soft cubic sets.
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References:
R. Anitha Cruz and F. Nirmala Irudayam, Neutrosophic Soft Cubic Set, International Journal of Mathematics Trends andTechnology, 46(2),88–94(2017).
R. Anitha Cruz and F. Nirmala Irudayam, More on P-union and P- intersection of Neutrosophic Soft Cubic Set, Neutrosophic Sets and Systems (communicated).
Atanassov, K. (1986). “Intuitionistic fuzzy sets”. Fuzzy Sets and Systems 20,87–96.
D. Molodtsov, Soft Set Theory–First Results, Computers and Mathematics with Application, 37, 19–31 (1999).
Pabita Kumar Majii, “Neutrosophic soft set” Annals of Fuzzy Mathematics and Informatics 5, 157–168 (2013).
P.K. Majii, R. Biswas and A.R. Roy, “Fuzzy soft sets”, Journal of Fuzzy Mathematics, Vol 9, no. 3, 589–602, (2001).
P.K. Majii, R. Biswas and A.R .Roy, “Intuitionistic Fuzzy soft sets”, The Journal of Fuzzy Mathematics, Vol 9, (3) 677–692 (2001).
L. J. Kohout, W. Bandler, (1996) Fuzzy interval inference utilizing the checklist paradigm and BK relational products, in: R.B. Kearfort et al. (Eds.), Applications of Interval Computations, (pp. 291–335), Kluwer, Dordrecht.
F. Smarandache. (1999) A Unifying Field in Logics. Neutrosophy: Neutrosophic Probability, Set and Logic, Rehoboth: American Research Press.
F. Smarandache, Neutrosophic set, a generalization of the Intuitionistic fuzzy sets, Inter. J. Pu Bre Appl. Math. 24, 287–297(2005).
F. Smarandache, Neutrosophy and Neutrosophic Logic, (2002) First International Conference on Neutrosophy, Neutrosophy Logic, Set, Probability and Statistics University of New Mexico, Gallup, NM 87301, USA
I. B. Turksen, Interval-valued fuzzy sets and compensatory AND, Fuzzy Sets and Systems 51, 295–307(1992).
Turksen, “Interval valued fuzzy sets based on normal forms”. Fuzzy Sets and Systems, 20, 191–210, (1968).
I. B. Turksen, Interval-valued strict preference with Zadeh triples, Fuzzy Sets and Systems 78, 183–195 (1996).
H. Wang, F. Smarandache, Y.Q. Zhang and R. Sunderraman, (2005) Interval Neutrosophic Sets and logic: Theory and Applications in Computing, Hexis; Neutrosophic book series, No.5.
Y.B. Jun, C.S. Kim and K.O. Yang, Cubic sets, Annals of Fuzzy Mathematics and Informatics 4(3), 83–98 (2012),.
Young Bae Jun, Florentin Smarandache, and Chang Su Kim, R-intersections and R-unions of neutrosophic cubic sets, IEEE International Conference on Fuzzy Systems, 2441–2443 (2016).
Jun YB, Smarandache F, Kim CS (2017) Neutrosophic cubic sets. New Mathematics and Natural Computation 13, 41–54
L.A. Zadeh, Fuzzy sets, Inform Control 8, 338–353 (1965).