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International Journal of Neutrosophic Science
Volume 11 , Issue 1, PP: 30-38 , 2020 | Cite this article as | XML | Html |PDF

Title

Plithogenic Cubic Sets

Authors Names :   S.P. Priyadharshini   1     F. Nirmala Irudayam   2     F. Smarandache   3  

1  Affiliation :  Dept of Mathematics, Nirmala College for Women, India

    Email :  priyadharshini125@gmail.com


2  Affiliation :  Dept of Mathematics, Nirmala College for Women, India

    Email :  nirmalairudayam@ymail.com


3  Affiliation :  Dept. Math and Sciences, University of New Mexico, Gallup, NM, USA

    Email :  smarand@unm.edu



Doi   :   https://doi.org/10.54216/IJNS.0110103

Received: May 11, 2020 Accepted: August 28, 2020

Abstract :

 In this article, using the concepts of cubic set and plithogenic set, the ideas of  plithogenic fuzzy cubic set, plithogenic intuitionistic fuzzy cubic set, Plithogenic neutrosophic cubic set are introduced and its corresponding internal and external cubic sets are discussed with examples. Primary properties of the Plithogenic neutrosophic cubic sets were also discussed.This concept is extremely suitable for addressing problems involving multiple attribute decision making as this plithogenic neutrosophic set are described by four or more value of attributes and the accuracy of the result is also so precise.

 

Keywords :

 

Fuzzy set , Intuitionistic fuzzy set , Neutrosophic set , Cubic set , Plithogenic set , Plithogenic fuzzy cubic set , Plithogenic Intuitionistic fuzzy cubic set , Plithogenic neutrosophic cubic set.

 

References :

[1] R.Anita Cruz and F.Nirmala Irudayam, “Neutrosophic Soft Cubic set”, International Journal of Mathematics trends and Technology 46 (2), pp.88-94, 2017.

[2] K.T. Atanassov, “Intuitionistic fuzzy sets”, Fuzzy sets and Systems 20, pp.87- 96,1986.

[3] Y.B.Jun, C.S.Kim and K.O.Yang, “Cubic sets”, Annals of Fuzzy Mathematics and Informatics 4(3),pp.83-98, 2012.

[4] Y.B. Jun, F.Smarandache and C.S. Kim, “Neutrosophic Cubic set”, New Mathematics and Natural Computation, 13 (1), pp.41-54, 2017.

[5] Majid Khan , Ismat Beg and Muhammad Gulistan, “Exponential Laws and Aggregation Operators on Neutrosophic Cubic Sets”, International Journal of Neutrosophic Science (IJNS), Vol. 4, No. 1,pp. 47-71, 2020

[6] Nivetha Martin and Florentin Smarandache, “Plithogenic Cognitive Maps in Decision Making”, International Journal of Neutrosophic Science (IJNS) ,Vol. 9, No. 1,pp. 09-21, 2020

[7] Prem Kumar Singh, “Plithogenic set for multi-variable data analysis”, International Journal of Neutrosophic Science (IJNS), Vol. 1, No. 2, pp. 81-89, 2020

[8] F.Smarandache, “A Unifying Field in Logics. Neutrosophy: Neutrosophic Probability, Set and Logic”, Rehoboth: American Research Press, 1999.

[9] F.Smarandache, “Neutrosophic set, a generalisation of the intuitionistic fuzzy sets”, Inteer J. PuBre Appl. Math. 24, pp.287-297,2005.

[10]F.Smarandache, “Neutrosophy and Neutrosophic Logic, First International Conference on Neutrosophy,NeutrosophyLogic, Set, Probability and Statistics” University of New Mexico,Gallup,NM 87301,USA, 2002.

[11] F.Smarandache “Neutrosophy, A new Branch of Philosophy”,= Multiple Valued Logic /An International Journal, USA, ISSN 1023-6627, Vol;. 8, No.3, pp.297-384, 2002.

[12] F.Smarandache, “Plithogeny, PlithogenicSet, Logic,Probability, and Statistics”, 141 pages, Pons Editions,Brussels,Belgium,2017, arXiv.org (Cornell University), Computer Science-Artificial Intelligence, 03Bxx:abstract:https://arxiv.org/abs/1808.03948,book:https://arxiv.org/ftp/arxiv/papers/1808/1808.03948.pdf,HarvardSAO/NASAADS: http://adsabs.harvard.edu/cgi-bin/bib_query?arXiv:1808.03948.

[13] Turksen, “Interval valued fuzzy sets based on normal forms”, Fuzzy sets and Systems, 20, pp.191-210,1968.

[14] B. Turksen,“ Interval-valued fuzzy sets and compensatory”  Fuzzy Sets and Systems, 51, pp.295–307,1992.

[15] I. B. Turksen, “Interval-valued strict preference with Zadeh triples”, Fuzzy Sets and Systems 78, pp.183–195,1996.

[16] Victor Christianto, Robert N. Boyd  and Florentin Smarandache “Three Possible Applications of Neutrosophic Logic in Fundamental and Applied Sciences”, International Journal of Neutrosophic Science (IJNS)Vol. 1, No. 2, pp. 90-95, 2020

[17] Wang, H.; Smarandache, F.; Zhang, Y. Q.; Sunderraman, R. “Interval Neutrosophic Sets and logic: Theory and Applications in Computing”; Hexis, Phoenix, Ariz, USA, 2005. 

[18] L.A Zadeh, “Fuzzy sets”, Inform and Control 8, pp.338-353,1965.

 


Cite this Article as :
S.P. Priyadharshini , F. Nirmala Irudayam , F. Smarandache, Plithogenic Cubic Sets, International Journal of Neutrosophic Science, Vol. 11 , No. 1 , (2020) : 30-38 (Doi   :  https://doi.org/10.54216/IJNS.0110103)